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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)
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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.
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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.
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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.
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Volatility:
As volatility falls, Vega decreases for in-the-money and out-of-the-money options.
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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.
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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.
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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
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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.
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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
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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
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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
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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
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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
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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.
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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
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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
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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.
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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.
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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.
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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.
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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.
Page | 53
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:
Page | 54
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
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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.
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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/