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Submitted By: Ankit Kochar PGDBM 2010 - 12 NLDIMSR Analysis Of Option Strategies, Greeks And India VIX

Analysis of Option Strategies, Greeks-Ankit Kochar

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  • Page | 1

    Submitted By:

    Ankit Kochar

    PGDBM 2010 - 12

    NLDIMSR

    Analysis Of Option Strategies, Greeks And India VIX

  • Page | 2

    Submitted by

    Ankit Kochar

    N.L.Dalmia Institute of Management Studies and Research

    Mira Road (E), Mumbai-401104

    Report on

    Analysis of

    Option Strategies, Greeks

    and

    India VIX

  • Page | 3

    Acknowledgement

    Working on the Project with Religare Securities Limited has been a wonderful

    experience over a period of the last two months. It was a great privilege working

    with the Firm and getting a firsthand knowledge of some of the functions performed

    by them.

    I sincerely wish to express my gratitude to Prof. P.L.Arya, Director, N.L. Dalmia

    Institute of Management Studies and Research for his encouragement and support

    towards completion of this project.

    I forward my sincere thanks to Mr. Sanjay Trivedi Head Options Trading -

    Religare Securities Limited without whom this project would not have been

    possible. I also express my gratitude towards him for encouraging me to take

    initiative while doing my project and giving me full co-operation in completing my

    project.

    I am thankful to all the officials of Religare Securities Limited, who were

    forthcoming and enthusiastic to answer all my queries. I would like to take this

    opportunity to thank them for their kind cooperation and patience.

    At the end I would like to thank all those who have indirectly helped me complete

    my project & I may not have mentioned in this acknowledgement.

    Ankit Kochar

    PGDBM - FINANCE

    N. L. Dalimia Institute of Management Studies and Research

  • Page | 4

    Certificate

    This is to certify that Mr. Ankit Kochar student of N. L. Dalmia Institute of

    Management Studies and Research has successfully completed his summer training

    under my guidance at Religare Securities Limited, Mumbai.

    The duration of the summer project entitled Analysis of Option Strategies, Greeks

    and India VIX was Nine weeks, from 2nd May 2011 to 30th June 2011.

    I have gone through the report and certify that it has been prepared to my

    satisfaction and all the facts mentioned have been verified to the best of my

    knowledge.

    Project Guide

    _______________

    Mr. Sanjay Trivedi

    Head Option Trading

    Religare Securities Limited

  • Page | 5

    TABLE OF CONTENTS

    Sr .No Topic Pg

    1 Executive Summary 6

    2 Introduction to Options 8

    3 Open Interest 12

    4 Put Call Ratio 14

    5 Implied Volatility 17

    6 Option Greeks 25

    7 Volatility Spreads 33

    8 Volatility Arbitrage 47

    9 Dynamic Delta Hedging 48

    10 India VIX 49

    11 Computation of India VIX 51

    12 Using VIX with Option Strategies 57

    13 Conclusion 58

    14 Bibliography 60

  • Page | 6

    EXECUTIVE SUMMARY

    In this volatile market it is becoming extremely difficult for day traders and

    investors to predict the future market movement. Trading in this choppy market is

    becoming complex day by day and we need to be equipped with new tools and

    market indicators with which we can predict the market behavior and invest

    accordingly. Option market have grown by leaps and bound in current market

    phase.

    While the very core of derivative products is to manage risk, it is important to

    appreciate that all derivatives are highly geared, or leveraged, transactions.

    Traders/investors are able to assume large positions - with similar sized risks - with

    very little up-front outlay and the risk to the investor is high. A thorough grasp of

    product technicalities is only one aspect of the knowledge and skills that traders

    require. Every trader has a view of the market and their end objective is, of course,

    profit from that view. And the most effective route to achieving this is to form a

    view that proves to be correct, having positioned one's self to obtain the maximum

    profit from it.

    By their very nature financial markets are volatile. Through the use of derivative

    products, it is possible to manage volatility and risks of faced by the financial agents.

    Given the different risk bearing capacity of them, with some of the agents being risk-

    averse and some risk-lover, derivatives emerged essentially to satisfy both of them.

    Volatility plays a great role in derivatives, especially in options. Volatility is both the

    boon and bane of all traders you cant live with it and you cant really trade

    without it. If a trader estimation of volatility is right, than through different volatility

    strategy he could make a lot of profit. Now many companies gives more emphasis

    on volatility related activities, because one can make money if one have the

    knowledge about it, whether market moves up or down.

  • Page | 7

    Project Learnings :

    Understanding volatility and its importance in derivatives, Types of volatility,

    how to calculate different types of volatility i.e. historical volatility, Implied

    volatility. Studied the impact of four major indicators

    Put-call ratio (PCR)

    open interest (OI)

    implied volatility (IV)

    Studied the Volatility Strategies to handle the market volatility effectively

    and encash on it.

    Relationship between Spot price and PCR.

    Dynamic delta hedging.

    Working on ODIN- software used for options trading.

    Studied the Options Greeks used in derivatives market such as Delta,

    Gamma, Theta, Vega and Rho. And also studied how hedging can be done

    using the derivatives Greeks.

    Studied the importance of Greeks on volatility spread

    Understanding India VIX,

    Developed a Real time VIX Calculator

    Trading VIX options(whenever introduced)

  • Page | 8

    Introduction To Options

    Options are of two types - calls and puts. Calls give the buyer the right but not the

    obligation to buy a given quantity of the underlying asset, at a given price on or

    before a given future date. Puts give the buyer the right, but not the obligation to sell

    a given quantity of the underlying asset at a given price on or before a given date.

    Options are fundamentally different from forward and futures contracts. An option

    gives the holder of the option the right to do something. The holder does not have to

    exercise this right. In contrast, in a forward or futures contract, the two parties have

    committed themselves to doing something. Whereas it costs nothing (except margin

    requirements) to enter into a futures contract, the purchase of an option requires an

    up-front payment.

    Intrinsic Value:

    The difference between the strike price and current value of the underlying asset is

    called the intrinsic value of the option premium. In a call option, if the value of the

    underlying asset is higher than the strike price, the option premium has an intrinsic

    value and is an in-the-money option. If the value of the underlying asset is lower

    than the strike price, the option has no intrinsic value and is an out-of- the-money

    option. If the value of the underlying asset is equivalent to the strike price, the call

    option is at-the-money

  • Page | 9

    In a put option, if the value of the underlying asset is lower than the strike price, the

    option has an intrinsic value and is an in-the-money option. If the value of the

    underlying asset is higher than the strike price, the option has no intrinsic value and

    is an out-of-the-money option. If the value of the underlying asset is equivalent to

    the strike price, the put option is at-the money The intrinsic value component of

    the option premium cannot be negative, only if the option is in-the-money, will it

    have an intrinsic value, other wise the intrinsic value will be zero. On expiration day,

    intrinsic value is zero.

    Time Value:

    Time value is the amount an investor is willing to pay for an option, in the hope that

    at some time prior to expiration its value will increase because of a favourable

    change in the price of the underlying asset. Time value reduces as the expiration

    draws near and on expiration day, the time value of the option is zero. For an in-

    the-money option, the difference between premium and the intrinsic value will

    denote time value of the option. For out-of-the money option and an at-the-

    money option the premium will denote only time value.

    Thus, if the BSE June call of 4000 is quoting at a premium of Rs. 40, when the

    underlying BSE index is quoting at 4035, the intrinsic value of the option premium is

    Rs. 35, as the call option buyer can buy the index at 4000, when it is quoting at 4035.

    While the time value of the option premium is Rs. 5, the difference between the

    option premium and the intrinsic value.

    Factors affecting premium

    The theoretical premium or the price of an option is determined by the following

    factors

    1. The price of the underlying asset: (S)

    Changes in the underlying asset price can increase or decrease the premium of an

    option. These price changes have opposite effects on calls and puts. For instance, as

    the price of the underlying asset rises, the premium of a call will increase and the

  • Page | 10

    premium of a put will decrease. A decrease in the price of the underlying assets

    value will generally have the opposite effect.

    2. The strike price: (K)

    The strike price determines whether or not an option has any intrinsic value. An

    options premium generally increases as the option becomes further in the money,

    and decreases as the option becomes more deeply out of the money.

    3. Time until Expiration: (T)

    As expiration approaches, the levels of an options time value, for both puts and

    calls, decreases or decays.

    4. Volatility: (o)

    Volatility is simply a measure of risk (uncertainty), or variability of the price of an

    options underlying. Higher volatility estimates reflect greater expected fluctuations

    (in either direction) in underlying price levels. This expectation generally results in

    higher option premiums for puts and calls alike, and is most noticeable with at-the-

    money options.

    5. Interest Rate: (Rfr)

    This effect reflects the cost of carry the interest that might be paid for margin, in

    case of an option seller or received from alternative investments in the case of an

    option buyer for the premium paid. Higher the interest rate, higher is the premium

    of the option as the cost of carry increases.

  • Page | 11

    Types of Options:

    There are two common types of Options:

    The American Option:

    This option can be exercised any time on or before the expiration date. Otherwise,

    the option will expire worthless and cease to exist as a financial instrument. The

    writer of an American-style option can be assigned at any time, either when or

    before the option expires, although early assignment is not always predictable.

    European Option:

    This option can be exercised only on the expiration date. This period may vary with

    different classes of options. Likewise, the writer of a European style option can be

    assigned only on the expiration day. However, both the American and European

    type option can be squared-off any-time during the time-period of the option. An

    Option is a very flexible risk management tool and over the years, options have been

    designed for a number of underlying as well as on futures contracts of various

    underlying. Options have been traded for spot and futures contracts of stock indices,

    spot and futures contracts of individual stocks, futures contracts of commodities,

    metals, energy products and many more.

  • Page | 12

    Open Interest

    Open Interest is the total number of outstanding contracts that are held by market

    participants at the end of the day. It can also be defined as the total number of

    futures contracts or option contracts that have not yet been exercised (squared off),

    expired, or fulfilled by delivery.

    Open interest applies primarily to the futures market. Open interest, or the total

    number of open contracts on a security, is often used to confirm trends and trend

    reversals for futures and options contracts.

    Open interest measures the flow of money into the futures market. For each seller of

    a futures contract there must be a buyer of that contract. Thus a seller and a buyer

    combine to create only one contract.

    Therefore, to determine the total open interest for any given market we need only to

    know the totals from one side or the other, buyers or sellers, not the sum of both.

    The open interest position that is reported each day represents the increase or

    decrease in the number of contracts for that day, and it is shown as a positive or

    negative number.

    Observations while monitoring open interest

    Increasing open interest means that new money is flowing into the marketplace. The

    result will be that the present trend (up, down or sideways) will continue.

    Declining open interest means that the market is liquidating and implies that the

    prevailing price trend is coming to an end.

    A leveling off of open interest following a sustained price advance is an early

    warning of the end to an uptrend or bull market.

  • Page | 13

    An increase in open interest along with an increase in price is said to confirm an

    upward trend. Similarly, an increase in open interest along with a decrease in price

    confirms a downward trend.

    An increase or decrease in prices while open interest remains flat or declining may

    indicate a possible trend reversal.

    Open Interest - A confirming indicator

    An increase in open interest along with an increase in price is said to confirm an

    upward trend. Similarly, an increase in open interest along with a decrease in price

    confirms a downward trend. An increase or decrease in prices while open interest

    remains flat or declining may indicate a possible trend reversal.

    The relationship between the prevailing price trend and open interest can be

    summarized by the following table:

    Price Open Interest Interpretation

    Rising Rising Market is Strong

    Rising Falling Market is Weakening

    Falling Rising Market is Weak

    Falling Falling Market is Strengthening

  • Page | 14

    Put Call Ratio

    Put Call Ratio is an important indicator that can help one in gauging the future

    direction of the market.

    If the Put call ratio rises then there is hope of higher prices in the near future.

    If the Put call ratio falls it is a sign of weakness in the market.

    The Put/Call Open Interest Ratio is simply the number of Put options Open Interest

    in a given day divided by the number of Call options Open Interest in same day.

    It can be measured in short or long term expectations. It gives an investor an idea of

    what the rest of the market is thinking. If more people are putting in orders for puts

    on a near term option than calls on the same near term option it is an indicator that

    short term the investors in that stock are thinking bearish. The opposite is true if the

    call orders significantly outweigh the put orders.

    If Put Call ratio is high, there are more Put options trading in the market, it means

    that more people are buying a right to sell i.e. more people want to sell in the future-

    an indicator of bearishness.

    If the put call ratio is lower than it indicates bullishness, as more people want to buy

    in the future.

    But,

    There is also a contrarian sentiment measure, which says:

    PCR>1 = Bullishness (oversold)

    PCR

  • Page | 15

    Relation between PCR OI and Spot price:

    Date

    PCR

    June

    Spot

    Price(June)

    PCR

    July

    Spot

    Price(July)

    India

    VIX Volume

    5/26/2011 1.359812 5395.95 1.361217 5407

    5/27/2011 1.319498 5472 1.127084 5481.35

    5/30/2011 1.284234 5467 1.10548 5477.75

    5/31/2011 1.374839 5554.8 1.297201 5566.1 16.82

    6/1/2011 1.41606 5592.5 1.271027 5605.85 16.73

    6/2/2011 1.456007 5563 1.292263 5575 17.98 83452.85

    6/3/2011 1.359184 5533.8 1.280253 5546.4 17.61 116783.3

    6/6/2011 1.36395 5536.5 1.265886 5550.5 18.21 91609.65

    6/7/2011 1.368682 5563 1.301424 5577 18.03 81820.4

    6/8/2011 1.323823 5533 1.328426 5547.5 18.58 81645.65

    6/9/2011 1.333737 5522 1.345429 5536 18.58 88267.35

    6/10/2011 1.184702 5466.7 1.330407 5480 18.54 92235.85

    6/13/2011 1.289768 5501.9 1.314462 5516 18.91 105076.8

    6/14/2011 1.2920 5516.1 1.2912 5531.65 18.51 86435.35

    6/15/2011 1.1572 5452.8 1.3009 5469.9 19.14 103047.2

    6/16/2011 1.086584 5409 1.312023 5426 19.66 157936.7

    6/17/2011 1.031033 5372.7 1.263015 5388.6 20.27 128335.4

    6/20/2011 0.907709 5265 1.16609 5278 22.18 221753.6

    6/21/2011 0.901582 5276.1 1.165635 5286.55 21.31 142086.4

    6/22/2011 0.916585 5283 1.250078 5292.65 20.89 123561.8

    6/23/2011 0.997049 5319 1.222976 5330 19.5 144326.6

    6/24/2011 1.283494 5484 1.268465 5497 19.32 241442.1

    6/27/2011 1.509599 5536.6 1.2858 5550.9 19.99 188432.5

    6/28/2011 1.560638 5546 1.350334 5565 19.49 169163.6

    6/29/2011 1.582332 5608 1.368156 5629.95 19.46 176382.7

    6/30/2011 2.112093 5647.8 1.237012 5652.55 18.41 176706.9

  • Page | 16

    Interpretations:

    There is direct correlation between PCR OI and Nifty. Whenever PCR OI

    moves upwards Nifty rallies and vice versa.

    It can be interpreted that at high PCR, lot of put writing is done which is

    helping market to rally and at low PCR, lot of call writing is done which is

    perhaps dragging market down.

    Conclusion:

    In the end we can conclude that Put/Call ratio is yet another tool and gives us a

    clear picture many times that when to exit or when to enter the market but then also

    one cannot rely only on Put/call ratio to survive in the market and earn money. This

    fact also cannot be ignored that it is a very powerful tool, which helps the speculator

    a great extent to predict the market movement and invest accordingly. Put Call ratio

    will be read along with volatility.

  • Page | 17

    Implied Volatility

    Implied Volatility can be defined as the volatility of an instrument as implied by the

    prices of an option on that instrument, calculated using an options pricing model.

    An options value consists of several components

    The strike price

    Expiration date,

    The current stock price,

    Dividends paid by the stock (if any),

    The implied volatility of the stock and

    Interest rates.

    Instead of substituting a volatility parameter into an option model (e.g. Black-

    Scholes) to determine an option's fair value, the calculation can be turned round,

    where the actual current option price is input and the volatility is output. Therefore

    implied volatility is that level of volatility that will calculate a fair value actually

    equal to the current trading option price. This calculation can be very useful when

    comparing different options on the same underlying & different strike prices. The

    implied volatility can be regarded as a measure of an option's "expensiveness" in the

    market, and issued by traders setting up combination strategies, where they have to

    identify relatively cheap and expensive option contracts. Rising implied volatility

    causes option prices to rise while falling implied volatility results in lower option

    premiums.

    As there are many options on a stock, with different strike prices and expiration

    dates, each option can, and typically will, have a different implied volatility. Even

    within the same expiration, options with different strike prices will have different

    implied volatilities.

    Implied volatility represents the markets expectation of a stocks future price moves.

    High-implied volatility means the market expects the stock to continue to be volatile

  • Page | 18

    i.e., make large moves, either in the same direction or up and down. Conversely,

    low implied volatility means the market believes the stocks price moves will be

    rather conservative. Because implied volatility is a surrogate for option value, a

    change in implied volatility means there is a change in the option value. Many times,

    there will be significant changes in the implied volatility of the calls vs. the puts in a

    stock. This signals that there may be a shift in the bias of the market.

    It is seen that the volatilities of both the calls & puts increase with the falling index

    levels & top out at a point when index is bottoming out & vice versa. So, it can be

    inferred quite conclusively that Call & Put IVs have an inverse correlation with the

    movement in the broader market. Although, the inference drawn is from the

    historical data and therefore doesnt guarantee to repeat itself in future, it, still, can

    be used in conjunction with other technical indicators to improve the decisiveness of

    the market direction predicted using those indicators.

    Implied volatility is that level of volatility which is calculated from the current

    trading option price. This can help to gauge whether options are cheap or expensive.

    However the prices of deep ITM and deep OTM options are relatively insensitive to

    volatility

    As there are many options on a stock, with different strike prices and expiration

    dates, each option can, and typically will, have a different implied volatility. Even

    within the same expiration, options with different strike prices will have different

    implied volatilities.

    For example, suppose a certain futures contract is trading at 98.50 with interest rate

    at 8%. Suppose also that a 105 call with three months to expiration is available on

    this contract, and that our best guess about the volatility over the next three months

    is 16%. If we want to know the theoretical value of the 105 call we might feed all

    these inputs into a theoretical pricing model. Using the Black-Scholes model, we find

    that option has a theoretical value of .96. Having done this we might compare the

    options theoretical value to its price in the marketplace. To our surprise, we find

    that the option is trading for 1.34. The discrepancy between our value of .96 and the

  • Page | 19

    marketplaces value of 1.34 must be due to difference of opinion concerning one or

    more of the inputs into the model. Since all other inputs are expect volatility. So, the

    marketplace must be using volatility other than 16% to evaluate the 105 call.

    To know the actual volatility in the marketplace, we can ask the following question;

    if we hold all other inputs except volatility what volatility must we feed into our

    theoretical pricing model to yield a theoretical value identical to the price of the

    option in the marketplace? In our example, clearly the volatility has to be higher

    than 16%. So, we start to raise the volatility and fitting it into black-Scholes model

    we find that at a volatility of 18.55, the 105 call has a theoretical value of 1.34. This

    volatility is known as implied volatility. When we solve for the implied volatility of

    an option we are assuming that the theoretical value (the options price) is known,

    but that the volatility is unknown. In effect, we are running the theoretical pricing

    model backwards to solve for this unknown.

    The implied volatility in the marketplace is constantly changing because option

    prices, as well as other market conditions, are constantly changing. It is as if the

    marketplace were continuously polling all the participants to come up with

    consensus volatility for the underlying contract. This is not a poll in the true sense,

    since all traders do not huddle together and eventually vote on the correct volatility.

    However, as bids and offers are made, the trade price of an option will represent the

    equilibrium between supply and demand. This equilibrium can be translated into an

    implied volatility.

    Assuming a trader had a reliable theoretical pricing model, if he determines the

    future volatility of an underlying contract he would be able to accurately evaluate

    options on that contract. He might then look at the difference between each options

    theoretical value and its price in the marketplace, selling any options which were

    overpriced relative to the theoretical value, and buying any options which were

    underpriced. If given choice between selling one of two overprice options, he might

    simply sell the one which was most overpriced. However, a trader who has access to

    implied volatilities might use a different yardstick for comparison. He might

  • Page | 20

    compare the implied volatility of an option to either a volatility forecast, or to the

    implied volatility of other options on the same underlying contract. Going back to

    our example, with a theoretical value of .96 and a price of 1.34, the 105 call is .38

    overpriced. But in volatility terms it is 2.5% overpriced since its theoretical value is

    based on a volatility of 16% while its price is based on a volatility of 18.5% (the

    implied volatility). Due to the unusual characteristics of an options, it is often more

    useful for the serious trader to consider an options price in terms of implied

    volatility rather in terms of its total price.

    If a contract has a high value and a low price, then a trader will want to be a buyer. If

    a contract has a low value and a high price, then a trader will want to be seller. For

    an option trader this usually means comparing the future volatility with the implied

    volatility. If implied volatility is low with respect to the expected future volatility, a

    trader will prefer to buy the option; if implied volatility is high, a trader will prefer

    to sell options. Of course, future volatility is an unknown, so we tend to look at the

    historical and forecast volatilities to help us make an intelligent guess about the

    future. But in the final analysis, it is the future volatility which determines an

    options value.

    Generally, the implied volatilities of calls and puts show a distinct pattern, called the

    skew of implied volatility. Implied volatility tends to be higher for out-of-the-

    money (OTM) options compared to at-the-money (ATM) options. This is because

    OTM options present more risk on very large moves to compensate for this risk, they

    tend to be priced higher. But equally OTM calls and puts do not necessarily have the

    same implied volatility, and this difference represents the bias or skew of the market.

    The skew can be caused by a strong directional bias in the stock or the market, or by

    very large demand for either calls or puts, which pushes implied volatility higher.

    Implied volatility acts as a proxy for option value. It is the only parameter in option

    pricing that is not directly observable from the market, and cannot be hedged or

    offset with some other trading instrument. Because all other factors can be locked

    in, the price of the option becomes entirely dependent on the implied volatility.

  • Page | 21

    This is an important fact to consider when looking for relative value in options.

    Volatility Skew is U shaped, the bottom of the U being the at-the-money strike.

    From there, the skew rises on both sides. This formation is sometimes referred to as

    the smile curve. The farther an options strike is from the market price of the

    underlying instrument, the higher the options volatility. Volatility skews are present

    when two or more options on the underlying have a significant difference in implied

    volatility levels. The volatility skew gauges and accounts for the limitation that exists

    in most option pricing models and is used to give an edge in estimating an option's

    worth.

    Basically, there are two types of Volatility historic volatility and implied volatility.

    Historic volatility is based on historic prices of the futures and implied volatility is

    based on the volatility calculated from options i.e. volatility implied by premiums in

    options.

    Generally as the IV of Call option increases, its option price should decrease & vice-

    versa. Therefore, Call IV and its option price are inversely related.

  • Page | 22

    As the IV of Put option increases, its option price increases & vice-versa. Therefore, Put

    IV and its option price are directly related.

    When spot price falls, call price also falls because it goes out of the money and thus

    demands lesser price.

    When spot price falls, put price also falls because it goes in the money and thus

    demand higher price.

    spot price falls--->call price falls--->IV increases

    Spot price falls--->put price rises--->IV increases

    If the market is falling, suppose call delta is 0.3(otm) and put delta is -0.7(itm) , I will go

    for long straddle because the decrease in call price (0.3x) will be lesser and increase in

    put price (0.7x) will be higher, thus there will be net positive payoff

    High-implied volatility means the market expects the stock to continue to be volatile

    i.e., make large moves, either in the same direction or up and down. Conversely, low

    implied volatility means the market believes the Index/stocks price moves will be

    rather conservative. Because implied volatility is a surrogate for option value, a change

    in implied volatility means there is a change in the option value. Many times, there

    will be significant changes in the implied volatility of the calls vs. the puts in a stock.

    This signals that there may be a shift in the bias of the market.

    It is seen that the volatilities of both the calls & puts increase with the falling index

    levels & top out at a point when index is bottoming out & vice versa. So, it can be

    inferred quite conclusively that Call & Put IVs have an inverse correlation with the

    movement in the broader market. Although, the inference drawn is from the historical

    data and therefore doesnt guarantee to repeat itself in future, it, still, can be used in

    conjunction with other technical indicators to improve the decisiveness of the market

    direction predicted using those indicators.

    Implied volatility is that level of volatility which is calculated from the current trading

    option price. This can help to gauge whether options are cheap or expensive. However

  • Page | 23

    the prices of deep ITM and deep OTM options are relatively insensitive to volatility

    If volatility rises and PCR falls, it has bearish implications.

    If volatility falls and PCR rises, it has bullish implications.

    when VIX goes down and OIO PCR goes up its bullish

    when VIX goes down but OI PCR also goes down then (no comments)

    when volatility increases spot price decreases, so when Volatility increases ,call

    price should decrease since it is getting out of the money (spot price decreases) and

    put price should increase since it is getting in the money (spot price decreases).

    Inference

    However relationship between the IV of the options we trade and the actual

    volatility that the underlying Index/stock displays is important. Over time, IV tends

    to move up and down with actual volatility. If the Index/stock becomes more

    volatile over time, the market expects that it will continue to be more volatile in the

    future, and IVs of the options tend to go up.

    In other words, it can also be said that the implied volatility of an option refers to the

    volatility that is connoted by the option market price depending on the pricing

    model of an option. The volatility of an option actually gives the theoretical option

    value that is same as the current market price.

    The implied volatility very often gives the measure of the relative value of the

    option. But it does not give the price of the option and this is because the option

    price depends directly on the underlying instrument price. For the options that are

    included in the delta neutral portfolio, implied volatility plays as the most important

    factor in order to determine the option value. Because of the huge importance of the

  • Page | 24

    implied volatility, rather than the price, the options are generally cited in terms of

    volatility.

    The options that are based on the same underlying security but having different

    expiration time and strike value, will generally give dissimilar implied volatility.

    This happens because the volatility of the underlying security is variable and is

    dependent on various factors like underlying security's price level, recent variance of

    the underlying security and the time passage.

  • Page | 25

    Options Greeks:

    The Greeks have given us feta cheese, philosophy, mathematics, and the oedipal

    complex. They also tell us how much risk our option positions have.

    There are ways of estimating the risks associated with options, such as the risk of the

    stock price moving up or down, implied volatility moving up or down, or how

    much money is made or lost as time passes. They are numbers generated by

    mathematical formulas. Collectively, they are known as the "greeks", because most

    use Greek letters as names. Each greek estimates the risk for one variable: delta

    measures the change in the option price due to a change in the stock price, gamma

    measures the change in the option delta due to a change in the stock price, theta

    measures the change in the option price due to time passing, vega measures the

    change in the option price due to volatility changing, and rho measures the change

    in the option price due to a change in interest rates.

    Delta

    Delta is the change in the price of an option for a one point move in the underlying.

    Positive delta means that the option position will rise in value if the stock price rises,

    and drop in value if the stock price falls. Negative delta means that the option

    position will theoretically rise in value if the stock price falls, and theoretically drop

    in value if the stock price rises.

    Call options: 0 < Delta < 1

    Put options: -1 < Delta < 0

    In-the-money options: Delta approaches 1 (call: +1, put: -1)

    At-the-money options: Delta is about 0.5 (call: +0.5, put: -0.5)

  • Page | 26

    Out-of-the-money options: Delta approaches 0

    Long calls have positive delta; short calls have negative delta. Long puts have

    negative delta; short puts have positive delta. Long stock has positive delta; short

    stock has negative delta. The closer an option's delta is to 1 or 1, the more the price

    of the option responds like actual long or short stock when the stock price moves.

    Call deltas can be interpreted as the probability that the option will finish in the

    money. An at-the-money option, which has a delta of approximately 0.5, has roughly

    a 50/50 chance of ending up in-the-money.

    Time to expiration:

    As time passes, the delta of in-the-money options increases and the delta of out-of-

    the-money options decreases.

    Gamma

    Gamma is the change in an options delta for a one-point change in the price of the

    underlying.

    Gamma tells us how "stable" the delta is. A big gamma means that delta can start

    changing dramatically for even a small move in the stock price.

    The gamma of a long option position (both calls and puts) is always positive. This

    means that the delta increases as the underlying price increases and that delta falls as

    the underlying price falls.

    Stock has zero gamma as its delta is always 1 it never changes. Positive gamma

    means that the delta of long calls will become more positive and move toward +1

    when the stock prices rises, and less positive and move toward 0 when the stock

    price falls. It means that the delta of long puts will become more negative and move

    toward 1 when the stock price falls, and less negative and move toward 0 when the

    stock price rises. The reverse is true for short gamma.

  • Page | 27

    At-the-money options have the largest gamma. The further an option goes in-the-

    money or, out-of-the-money the smaller is gamma.

    Time to expiration:

    As time passes, the gamma of at-the-money options increases, the gamma of deep in-

    the-money and out-of-the-money options decreases.

    Volatility:

    As volatility falls, the gamma of at-the-money options increases, the gamma of deep

    in-the-money and out-of-the-money options decreases.

    The gamma of ATM options is higher when either volatility is lower or there are

    fewer days to expiration.

    Theta

    Theta is an estimate of how much the theoretical value of an option decreases when

    1 day passes and there is no move in either the stock price or volatility the theta for a

    call and put at the same strike price and the same expiration month are not equal.

    Long calls and long puts always have negative theta. Short calls and short puts

    always have positive theta. Stock has zero theta its value is not eroded by time.

    But theta doesn't reduce an option's value in an even rate. Theta has much more

    impact on an option with fewer days to expiration than an option with more days to

    expiration.

    Theta is highest for ATM options, and is progressively lower as options are ITM and

    OTM. This makes sense because ATM options have the highest extrinsic value, so

    they have more extrinsic value to lose over time than an ITM or OTM option.

  • Page | 28

    Time to expiration:

    As time passes, the theta of at-the-money options increases, the theta of deep in-the-

    money and out-of-the-money options decreases.

    Volatility:

    (Subject to certain conditions)(i.e. we either gain in gamma at the cost of theta or vice

    versa).

    Vega

    An estimate of how much the theoretical value of an option changes when volatility

    changes by 1%. Higher volatility means higher option prices. The reason for this is

    that higher volatility means a greater price swings in the stock price, which

    translates into a greater likelihood for an option to make money by expiration.

    Long calls and long puts both always have positive Vega. Short calls and short puts

    both always have negative Vega. Stock has zero Vega its value is not affected by

    volatility. Positive Vega means that the value of an option position increases when

    volatility increases and decreases when volatility decreases. Negative Vega means

    that the value of an option position decreases when volatility increases, and

    increases when volatility decreases.

    Vega is highest for ATM options, and is progressively lower as options are ITM and

    OTM. This means that the value of ATM options changes the most when the

    volatility changes. The Vega of ATM options is higher when either volatility is

    higher or there are more days to expiration.

    Time to expiration:

    As time passes, Vega decreases. Time amplifies the effect of volatility changes. As a

    result, Vega is greater for long-dated options than for short dated options.

  • Page | 29

    Volatility:

    As volatility falls, Vega decreases for in-the-money and out-of-the-money options.

  • Page | 30

    In a nutshell,

    If you are

    Delta

    (hedge ratio)

    Gamma

    (curvature)

    Theta (time

    decay)

    Vega

    (volatility)

    Long the underlying positive 0 0 0

    short the underlying negative 0 0 0

    Long Calls positive positive negative positive

    Short Calls negative negative positive negative

    Long Puts negative positive negative positive

    Short Puts positive negative positive negative

    SENSTIVITY OF GAMMA:

    The magnitude of gamma is consistent with the uncertainty whether the

    option will expire in or out of money.

    Highest around the at-the-money level (uncertainty is maximum),

    particularly when the option is approaching expiry

    The gamma for ITM and OTM options increase with the increase in volatility

    and the time to maturity (Uncertainty increases)

    Gamma for ATM option falls with the increase in volatility and increase in

    time to maturity

    Normally towards end of the month, traders stop playing with gamma

    because it becomes difficult to handle.

    SENSTIVITY OF THETA:

    A Gamma and Theta position will be opposite in sign and size will also

    correlate.

    The owner of a Gamma (who is net long options) is subject to time decay of

    spot doesnt move much, but benefits from price movements.

  • Page | 31

    As expiration approaches Gamma of an ATM option becomes increasingly

    large and the same is also true about Theta.

    The Theta of an ATM option increases as expiration approaches. This implies

    that a short term option will decay more quickly than a long term option.

  • Page | 32

    MOST IMPORTANT THINGS TO UNDERSTAND:

    We have already learnt from B & S that gamma and Theta are of the same

    magnitude (opposite in sign)

    Though Theta and Gamma are equal and opposite, Theta is more or less fixed

    in terms of loss per day whereas gamma is directly proportional to change in

    the price of the underlying.

    When there is a big move in the price of the underlying gamma change is

    more than Theta and therefore for a delta hedged portfolio with long potion

    and short underlying (positive gamma) position it returns in a positive cash

    flow.

    The positive or negative effect of changing market conditions is summarized

    below:

    If your delta position is you want the underlying contract to

    Positive rise in price

    Negative fall in price

    If your gamma position is you want the underlying contract to

    Positive move very swiftly, regardless of direction

    Negative move slowly, regardless of direction

    If your theta position is you want the underlying contract to

    Positive increase the value of your position

    Negative decrease the value of your position

    If your vega position is you want the underlying contract to

    Positive rise

    Negative fall

  • Page | 33

    Volatility Spreads

    Volatility is subject to the forces of supply and demand. Implied volatility will tend

    to rise during periods when demand from options buyers is strongest and will fall

    when demand is weakest. The key for all options trader is to buy volatility when it is

    perceived to be low and to sell volatility when it is perceived to be high.

    If a rise in volatility is expected If a fall in volatility is expected

    Long straddle Short straddle

    Long strangle Short strangle

    Short butterfly Long butterfly

    Buying both the call option and put option at the same at the money strike price is a

    popular delta neutral option trading strategy, called a Long Straddle, profiting when

    the underlying stock moves up or down significantly.

    Learnings: When you select ATM for Long Straddle, we try to check the delta of the

    ATM (Strike price).

    Select the one which gives answer closest to 0.

    Finding these target options is a two-step process:

    1. Look for the Unusual - Look for call or put options with current volume that is in

    excess of the average daily trading volume, particularly in near-term months.

    2. Compare Open Interest - Make sure that the current volume exceeds the prior

    day's open interest, which indicates that today's activity represents new positions.

  • Page | 34

    Straddle

    Long straddle Short straddle

    Anticipations

    and

    characteristics

    Market directional neutral

    (delta=0) and implied volatility

    increase (Vega>0).

    Limited loss - Unlimited profit -

    Important cost - Needs a large

    market move in either direction.

    Market directional neutral

    (delta=0) and implied volatility

    decrease (Vega0)

    Limited loss - Unlimited profit -

    Important cost - Needs a large

    market move in either direction.

    Market directional neutral

    (delta=0) and implied volatility

    down (vega

  • Page | 35

    Long straddle

    LONG STRADDLE - Bullish & Bearish trade, forecasting explosive movement in

    price either way

    COMBINATIONS: Combinations represents strategies which involve taking

    positions in both calls and puts on the same stock.

    It involves buying a call and a put option with same exercise price and date of

    expiration.

    Involves initial cost of investment.

    While most straddle are executed with one-to-one ratio (one call for each put),

    this is not the requirement. A straddle can also be rationed, so that it consists

    of unequal numbers of calls and puts. Any spread where the number of long

    market contracts (long calls or short puts) and short market contracts (short

    calls or long puts) are unequal is considered a ratio spread

    Example:

    Buy Call Buy Put

    Strike Price: Rs. 70.0 Strike Price: Rs. 70.0

    Premium : Rs. 5.0 Premium : Rs. 4.0

    Initial Investment: Rs. 9.0

  • Page | 36

    When stock price is Rs. 70 - Maximum Loss of Rs. 9. Hence loss is limited up

    to the initial investment.

    Investor can earn profit if the stock price moves in either direction

    significantly. Hence, suitable if volatility is expected. But our view should be

    different from general view.

    Risk: Limited, but should not really be viewed as a low risk strategy because you are

    paying out for two options which are both wasting assets

    Reward: Unlimited

    When to use: You believe that the stock/index is about to make a large move in

    either direction. A good time to utilize straddles is where there has been a prolonged

    period of extreme quietness (in prices) and implied volatility is around multiyear

    lows. If this is the case look to do longer dated months rather than the shorter ones

    Volatility expectation: Very bullish. Volatility increases improve the position

    substantially. Volatility should therefore be monitored closely.

    Profit: Unlimited for an increase or decrease in the underlying

  • Page | 37

    Loss: Limited to the premium paid in establishing the position. Loss will be greatest

    if the underlying is at the initiated strike at expiry.

    Breakeven: Reached if the underlying rises or falls from option strikes by the same

    amount as the premium cost of establishing the position.

    Time decay: Hurts a lot, remember you have double time erosion because of the two

    options bought. Decay depends a lot on volatility if volatility increases time decay

    will decrease etc.

    LONG STRADDLE IDEAS

    Work best on stocks/indexes that are likely to experience explosive moves.

    Always best to use some sort of time stop because of the time decay

    If youre expecting a very large breakout then better to trade strangles

    Very hard trade to make money on if you buy the options when volatility is

    high

    The new option trader often finds long straddle attractive because strategies with

    limited risk and unlimited profit potential offer great appeal, especially when the

    profit is unlimited in both directions. However, if the hoped for movement fails to

    materialize, he soon find that losing money little by little hurt a lot at the end,

    because you have paid for two option. So, one have to very careful while choosing

    this strategy.

    http://www.learnmoney.co.uk/options/option_strategies_long_strangle.html

  • Page | 38

    SHORT STRADDLE

    Forecasting little movement or a good contraction in movement

    For traders who are generally neutral about a stocks potential. The stock may rise or

    fall but is generally in a range bound pattern. The trade works because both the

    option premiums fall.

    Generates initial positive cash flow for the investor as he is taking short

    position in both call and put options.

    Also known as top straddle or straddle writes.

    Example:

    Sell Call Sell Put

    Strike Price: Rs. 70.0 Strike Price: Rs. 70.0

    Premium : Rs. 5.0 Premium : Rs. 4.0

    Initial Inflow: Rs. 9.0

  • Page | 39

    When stock price is Rs. 70 - Maximum profit of Rs. 9. Hence profit is limited

    up to the initial investment.

    Loss can be unlimited if the stock price moves in either direction

    significantly. Hence, suitable if volatility is not expected

    Risk: Unlimited

    Reward: Limited

    When to use: For aggressive investors who don't expect much short-term volatility,

    the short straddle can be a risky, but profitable strategy. If you only expect a

    moderately sideways market consider selling strangles instead

    Volatility expectation: Bearish, volatility increases wreck the position. Straddles are

    not as susceptible to volatility increases as strangles. Keep an eye on volatility

    throughout the position

    Profit: Limited to the premium received, highest profit when the market settles at

    the sold strike

    Loss: Unlimited for either an increase or decrease in the underlying.

    Breakeven: Reached if the underlying rises or falls from sold strike by the same

    amount as the premium received from establishing the position.

    Time decay: Helps, especially when the trade is initiated in periods of high volatility

  • Page | 40

    LONG STRANGLE

    Bullish & Bearish trade, forecasting explosive movement either way, even more so

    than with a Long Straddle

    Also known as bottom vertical combination.

    Created by buying a call and a put option of same stock and expiration

    period but of different strike prices.

    Initial investment is needed.

    Example:

    Buy a Call Buy a Put

    Strike Price: Rs. 70.0 Strike Price: Rs. 65.0

    Premium : Rs. 5.0 Premium: Rs. 4.0

    Initial Investment: Rs. 9.0

  • Page | 41

    When stock price is in the range of both strike prices i.e. Rs.70 Rs. 65

    Maximum Loss of Rs. 9.0. Hence loss is limited to the initial investment.

    Investor can earn profit if the stock price moves in either direction

    significantly. Hence, suitable if volatility is expected.

    Risk: Limited

    Reward: Unlimited

    The Trade: Buying out-of-the-money calls and puts

    When to use: You believe the stock/index will have an explosive move either up or

    down. This strategy is similar to the buy straddle but the premium paid is less but

    then a larger move is needed to show a profit.

    Volatility expectation: Very bullish, increases in volatility work marvels for the

    position

    Profit: The profit potential is unlimited although a substantial directional movement

    is necessary to yield a profit for both a rise and fall in the underlying.

    Loss: Occurs if the market is static; limited to the premium paid in establishing the

    position

    Breakeven: Occurs if the market rises above the higher strike price at B by an

    amount equal to the cost of establishing the position, or if the market falls below the

    lower strike price at A by the amount equal to the cost of establishing the position.

    Time decay: This position is a big wasting asset. As time passes, value of position

    erodes toward expiration value. If volatility increases, erosion slows, if volatility

    decreases, erosion speeds up.

  • Page | 42

    LONG STRANGLE IDEAS

    Can mix the strikes up depending on whether you lean towards the bull or bear tract

    but are still overall neutral - Perhaps you feel the odds slightly favor a bull move. If

    stock is at 5.00 instead of buying the 4.50P and 5.50C you could buy the 4.50P and

    6.00 call

    Use some sort of time stop because time erosion is your enemy

    If you expect a mega move than better strategy than straddles because strangles are

    cheaper to buy therefore can buy more with the same amount of capital

  • Page | 43

    Short Strangle

    Strangle can also be created selling call and put options.

    This is known as short strangle or top vertical combination.

    Created by selling a call and a put option of same stock and expiration

    period but of different strike prices.

    Strike price of put option is less than strike price of call option.

    Generates positive inflow for the investor.

    Example:

    Sell a Call Sell a Put

    Strike Price: Rs. 70.0 Strike Price: Rs. 65.0

    Premium : Rs. 5.0 Premium : Rs. 4.0

    Initial Inflow: Rs. 9.0

  • Page | 44

    When stock price is in between the strike prices, investor can earn a limited

    profit.

    If the stock price moves significantly, than the investor can make loss which

    can be limited. Hence, suitable if volatility is not expected.

  • Page | 45

    Butterfly

    Short butterfly Long butterfly

    Anticipations

    and

    characteristics

    Market direction neutral

    (delta=0) and implied volatility

    up (Vega>0)

    Limited loss - Limited profit -

    Low cost - Needs a large market

    move in either direction.

    Preferably always done at ATM

    Market direction neutral

    (delta=0) and implied volatility

    down (Vega

  • Page | 46

    Spreads

    short call

    spread or bull

    spread or

    volatility

    spread

    (here we

    neutralize delta

    with futures or

    ratio spreads

    and only trade

    volatility)

    Implied volatility direction

    depends on the strikes:

    If a rise in implied volatility is

    expected: 1*buy ATM call / sell

    1*ITM call

    If a fall in implied volatility is

    expected: buy 1*OTM call / sell

    1*ATM call

    Unlimited profit - Unlimited

    loss - Limited protection - Low

    cost - Risk profile at expiration

    Long put

    spread or bear

    spread

    Implied volatility direction

    depends on the strikes:

    If a rise in implied volatility is

    expected: buy 1*ATM put / sell

    1*OTM put

    If a fall in implied volatility is

    expected: buy 1*ITM put / sell

    1* ATM put

    Unlimited profit - Unlimited

    loss - Limited protection - Low

    cost

  • Page | 47

    Volatility Arbitrage

    The traders involved in the volatility arbitrage can be of two types - long volatility

    and short volatility. Traders are said to be long volatility when they buy options and

    they are known as short volatility when they sell options.

    The traders who wish to be engaged in volatility arbitrage should be able to forecast

    the future realized volatility of the underlying. The traders can do that by

    determining the daily returns for the particular underlying asset depending on the

    sample data of the last 252 days. The traders should also consider other factors like

    whether there will be any unexpected events in the near future or whether the

    period will be unexpectedly volatile or not. If the trader can predict the market price

    of an option depending on the implied volatility, we can say that the trader is

    capable of carrying out the volatility arbitrage trade.

    A volatility arbitrage strategy is generally implemented through a delta neutral

    portfolio consisting of an option and its underlying asset. A long position in an

    option combined with a short position in the underlying asset is equivalent to a long

    volatility position. This strategy will be profitable if the realized volatility on the

    underlying asset eventually proves to be higher than the implied volatility on the

    option when the trade was initiated. Conversely, a short position in an option

    combined with a long position in the underlying asset is equivalent to a short

    volatility position, which will be profitable if the realized volatility on the

    underlying asset is ultimately lower than the option's implied volatility.

  • Page | 48

    Delta hedging

    It is a kind of option strategy that offsets the long and short positions in order to

    diminish the risk that is associated with the movements of the prices of underlying

    assets. The delta hedging strategy is grounded on the price change of option, which

    is caused by the price change of the underlying security.

    In other words, it can also be said that delta hedging is a plan that is adopted by the

    derivative dealers in order to reduce the exposure of the portfolio to certain

    underlying instruments. The derivative dealer first determines the delta of the

    portfolio with respect to the underlying security and then turns the delta of the

    portfolio to zero by adding an offsetting position in the underlying security

    The derivative delta is used to hedge or eliminate a derivative holding with

    underlying security position or vice-versa. The number of underlying security units

    that is required to hedge a derivative is same as the delta of derivative. The concept

    of delta hedging is implemented in order to cover the positions of trading and also to

    arbitrage the difference between the costs required for the purchasing of adequate

    amount of underlying and the cost of derivative. Since the value of delta changes

    according to the underlying price, the delta hedge also must be adjusted

    continuously.

    ISSUES IN DELTA HEDGING

    The log-normal assumption may not be valid.

    The volatility estimate may not be correct.

    The hedge may not be done frequently enough to prevent losses due to hedge

    slippage or Gamma Risk.

  • Page | 49

    INDIA VIX

    ABSTRACT

    In the recent weeks of market turmoil, financial news services have begun routinely

    reporting the level of the India VIX. While this new practice is healthy in the sense

    that investors are asking for more information in helping to assess the state of the

    current economic environment and to guide through turbulent waters, it is

    important to understand exactly what the index means in order to fully

    misconception.

    India VIX is Indias volatility Index which is a key measure of market expectations

    of near-term volatility conveyed by NIFTY stock index option prices. This volatility

    index is computed by NSE based on the order book of NIFTY Options. For this, the

    best bid-ask quotes of near and next-month NIFTY options contracts which are

    traded on the F&O segment of NSE are used. India VIX indicates the investors

    perception of the markets volatility in the near term i.e. it depicts the expected

    market volatility over the next 30 calendar days. Higher the India VIX values, higher

    the expected volatility and vice-versa. NSE will also start derivatives based on India

    VIX. Most probably NSE will come out with India VIX Futures first followed by

    India VIX options as had been done by the CBOE in the past.

    In attempting to understand VIX, it is important to emphasize that it is forward-

    looking, measuring volatility that the investors expect to see. It is not backward-

    looking, measuring volatility that has been recently realized. Conceptually, VIX is

    like a bonds yield to maturity. Yield to maturity is the discount rate that equates a

    bonds price to the present value of its promised payments. As such, a bonds yield

    is implied by its current price and represents the expected future return of the bond

    over its remaining life.

    It is important to understand that Volatility Index is different from a price index

    such as NIFTY or Sensex. The price index measure the direction of the market and is

  • Page | 50

    computed using the price movement of the underlying stocks whereas Volatility

    Index measures the dispersion or variance or change and is computed using the

    order book of the underlying index options and is denoted as an annualized

    percentage. VIX can enable us to provide an index upon which futures and options

    contracts on volatility could be written. The social benefits of trading volatility have

    long been recognized.

    Now if we consider all the option writers present in the market. There would be

    millions of such people and if we try to calculate the average volatility from the

    options they have written, we can get a value which can describe the overall

    sentiments of the market about volatility. This is what Volatility Index really tells us.

    It uses the prices of the options to guess the future volatility, of course, after doing

    several other operations as well but in a nutshell, it is the reverse process of option

    pricing taken all the options being traded into account and thus calculating the

    sentiment of the entire market. You can read the exact method of calculating India

    VIX here.

    Now what does a particular value of the India VIX indicates? Suppose the value of

    India VIX is 19.63 which means people are thinking that over the next 30 days

    markets can move up or down by 5.67% [19.63 divided by square root of 12] and

    demanding premium as per this value. Low value of VIX indicates stability in the

    market while higher value indicated stress, fear and anxiety.

  • Page | 51

    India VIX Calculations

    Before we understand how India VIX (India Volatility index) is calculated, lets

    understand what volatility is and what volatility index is.

    Volatility refers to the amount of uncertainty or risk about the size of changes in a

    security or index value. A higher volatility means that a securitys value can

    potentially vary over a larger range of values. This means that the price of the

    security can change dramatically. A lower volatility means that a securitys value

    does not fluctuate dramatically, but changes in value at a steady pace over a period

    of time.

    The Volatility Index indicates the volatility in the market at present or in the near

    future. India VIX indicates the markets perception of the expected near term

    volatility. All securities portfolios as well as stock market indices are subjected to

    volatility and thus the studying them can be helpful because options prices are

    chiefly governed by the volatility in the market.

    Calculations for India VIX: India VIX is a volatility index based on the index option

    prices of NSEs benchmark index NIFTY. India VIX uses the computation

    methodology of CBOE, with suitable amendments to adapt to the NIFTY options

    order book. India VIX is computed using the best bid and ask quotes of the out-of-

    the-money near and mid-month NIFTY option contracts, which are traded on the

    F&O segment of NSE. There are several factors which are used to calculate the index.

    Some important ones are these

    1) Time to Expiry: Time to expiry of the options contracts of Nifty that are selected

    to calculate the index. The time to expiry is computed in minutes instead of days in

    order to arrive at a level of precision expected by professional traders.

    2) Interest Rate: The NSE Mibor rate of relevant tenure (i.e 30 days or 90 days) is

    being considered as risk-free interest rate for the respective expiry months of the

    NIFTY option contracts.

  • Page | 52

    3) The Forward Index Level: A methodology called the forward index level is being

    used to select the contracts which will be used to calculate the index. India VIX is

    computed using out-of-the-money option contracts. Out-of-the-money option

    contracts are identified using forward index level. The forward index level helps in

    determining the at-the-money (ATM) strike which in turn helps in selecting the

    option contracts which shall be used for computing India VIX. The forward index

    level is taken as the latest available price of NIFTY future contract for the respective

    expiry month.

    4) Bid-Ask Quotes: The strike price of NIFTY option contract available just below

    the forward index level is taken as the ATM strike. NIFTY option Call contracts with

    strike price above the ATM strike and NIFTY option Put contracts with strike price

    below the ATM strike are identified as out-of-the-money options and best bid and

    ask quotes of such option contracts are used for computation of India VIX. In respect

    of strikes for which appropriate quotes are not available, values are arrived through

    interpolation using a statistical method namely Natural Cubic Spline. After

    identification of the quotes, the variance (volatility squared) is computed separately

    for near and mid-month expiry.

    5) Weightage: The variance is computed by providing weightages to each of the

    NIFTY option contracts identified for the computation, as per the CBOE method. The

    weightage of a single options contract is directly proportional to the average of best

    bid-ask spread of that option contract and inversely proportional to the option

    contracts strike price. Finally, the variance for the near and mid-month expiry

    computed separately is interpolated to get a single variance value with a constant

    maturity of 30 days to expiration. The square root of the computed variance value is

    multiplied by 100 to arrive at the India VIX value. In a nutshell, from usage point of

    view, higher the VIX index value, higher the volatility.

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    India VIX:: Computation methodology

    India VIX uses the computation methodology of CBOE, with suitable amendments

    to adapt to the NIFTY options order book.

    The formula used in the India VIX calculation is:

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    Time to expiration (T)

    India VIX calculation measures the time to expiration in years, using minutes till

    expiration.

    The time to expiration is given by the following expression:

    T = {MCurrent day + MSettlement day + MOther days}/ Minutes in a year

    Where,

    MCurrent day = Number of minutes remaining until midnight of the current day

    (from computation time 3.30 pm up to 12.00 am)

    MSettlement day = Number of minutes from midnight until closing hours of trading

    (i.e. 3:30 p.m.) on expiry day

    MOther days = Total number of minutes in the days between current day and expiry

    day excluding both the days

    In the hypothetical example provided, the near month option has 9 days and next

    month option has 37 days to expiration. Accordingly, the time to expiration

    (T1) for the near month and (T2) for the next month works out to:

    T1 = {510 + 930 + 11520) / 525,600 = 0.02466

    T2 = {510+ 930 + 51840) / 525,600 = 0.10137

    India VIX uses put and call options in the near and next month expiration, in order

    to bracket a 30-day calendar period. It may be noted that CBOE VIX rolls to the next

    and far month with less than a week to expiration. However, with 3 trading days left

    to expiry, India VIX rolls to the next and far month.

    Risk free Interest Rate (R)

    The relevant tenure of NSE MIBOR rate (i.e. 30 days or 90 days) is being considered

    as risk free interest rate for the respective expiry months of the NIFTY option

    contracts.

    Determination of forward index level, F

    Volatility index is computed using mainly the quotes of the out of the money (OTM)

    options. The strip of OTM option contracts for computing India VIX could be

  • Page | 55

    identified if the at-the money (ATM) strike is identified. In case of CBOE, the

    forward index level is arrived at by using the strike price at which the absolute

    difference between the call and put prices is minimum. NSE has an actively traded,

    large and liquid NIFTY futures market. Therefore the latest available traded price of

    the NIFTY futures of the respective expiry month is considered as the forward index

    level. This helps in determining the ATM strikes and thus the OTM strikes for the

    purpose of computation of India VIX.

    Computation of K0

    K0 is the strike price just below the forward index level. This is considered as the at-

    the money strike (K0).

    Selection of option contracts to be used in the calculation

    As stated earlier, India VIX is computed using mainly the quotes of the OTM

    options. All call options contracts with strike prices greater than K0 and all put

    option contracts having strike prices less than K0 are therefore considered for this

    purpose.

    Computation of Mid-price Q(Ki)

    As seen above, for computation of India VIX, Q(Ki), the midpoint of the bid ask

    quote for each option contract with strike Ki , is required. In respect of the ATM

    strike, the average of the mid prices of both call and put options are considered

  • Page | 56

    Computation of Volatility

    The volatility for both near month and next month options are then calculated by

    applying the formula for calculating the India VIX with time to expiration of T1 and

    T2, respectively

    The contribution of a single option to India VIX value is proportional to the quote of

    that option and inversely proportional to the option contracts strike price.

    Computation of India VIX from the Volatilities

  • Page | 57

    Using VIX Options with Options Strategies

    Many volatile options strategies such as the Long Straddle and the Long Strangle

    depends on rising volatility in order to ensure profitability. If implied volatility in

    the market drops, these volatile options strategies may not profit even if the

    underlying asset moves strongly. With VIX options, VIX put options may be bought

    in conjunction with these volatile options strategies so that losses occurring from a

    reduction in implied volatility would be offset by the gains in the VIX put options as

    the VIX falls. This forms a hedge against volatility for options strategies sensitive to

    volatility. Similarly, options strategies sensitive to rising volatility, such as the Short

    Straddle, could similarly be hedged by buying VIX call options.

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    Conclusion

    NSE is soon going to start India VIX Futures trading which is going to be the first

    instrument based on the volatility index for India. Securities and Exchange Board of

    India (SEBI), Indias market regulator, has given permission to the stock exchanges

    for starting derivatives based on volatility index. NSE will be submitting the

    application to SEBI to start the F&O contracts based on India VIX soon.

    Its a very good product and very relevant for the current stock market conditions

    and also very necessary for the Indian markets to have a product based on the

    market volatility if we want to make India, a developed and matured market.

    NSE has also started real time dissemination of India VIX which is one step towards

    introduction of India VIX derivatives. India VIX futures and India VIX options can

    be used to hedge the risk of market volatility.

    The contract specifications like contract lot size, tick values, margin requirements are

    not yet out but the real question is whether it is going to attract enough liquidity or

    not? Right now, there are only two exchanges which have successfully launched

    instruments on the volatility index in the world, VIX by CBOE and VSTOXX by

    Eurex. Other exchanges tried but failed to make it popular among the traders.

    Looking at the history of volatility index products in the world arena, there are more

    failures then successes when it comes to instruments on volatility index and hence

    there is a huge question mark on whether India VIX is going to be successful or not.

    In India, high market volatility and absence of other developed products to hedge

    volatility risks may make India VIX a success.

    The India VIX will be a useful tool for option writers attempting to manage their

    risk, as their P&L is driven by the difference between realized volatility and implied

  • Page | 59

    volatility over the life of options written. Products based on the India VIX family of

    indices will allow Indian traders to hedge against sudden price movements (i.e.

    reducing Gamma exposure) and to take directional bets on the realized volatility of

    the Nifty.

    Because the VIX formula isolates expected volatility from other factors that could

    affect option prices such as dividends, interest rates, changes in underlying price and

    time to expiration, the VIX options offer a way for investors to buy and sell option

    volatility without having to deal with factors that have an impact on the value of an

    option position.

    All of this means that option traders now have a new instrument to add to their

    trading arsenal - one that isolates volatility, trades in a range, has high volatility of

    its own and cannot go to zero. By buying VIX calls or puts (or spreads), traders can

    now have access to volatility trades.

  • Page | 60

    Bibliography

    Hull, John C. Option, Futures, and Other Derivatives. Pearson Education, Inc.

    Sheldon Natenberg. Option volatility And Pricing

    NCFM Derivatives Core Module

    NCFM Option trading Strategies Module

    NCFM White paper India VIX

    Web Bibliography

    www.nseindia.com

    www.bseindia.com

    www.ivolatility.com

    www.investopedioa.com

    www.calloptioputoption.com

    www.Cboe.com

    www.indiaderivatives.com

    www.theoptionsguide.com

    www.optionistics.com

    www.optiontradingpedia.com

    optionwala.com

    optiongreeks.org

    www.thinkorswim.com

    Appendix

    Excel Sheets (3)

    http://www.nseindia.com/http://www.bseindia.com/http://www.ivolatility.com/http://www.investopedioa.com/http://www.riskglossary.com/http://www.indiaderivatives.com/