OPTIONS - Introduction to Option Valuation

8/13/2019 OPTIONS - Introduction to Option Valuation

1/21

Introduction

1.

Welcome to the Knowledge Check.

If you have prior knowledge of Options

Introduction to Option Valuation, try the

Knowledge Check. A perfect score is no

guarantee that you know everything covered

in the tutorial, but a less than perfect score

will help you identify any knowledge gaps.

If the subject of this tutorial is new to you,the Knowledge Check will indicate the level of

the information that you're about to

encounter. You may think you don't know

much about this area, but you might surprise

yourself!

2.


2/21

Question 1 of 5

A call option on widgets expires tomorrow. Ithas a strike price of EUR 100. The current

market price of widgets is EUR 90.

Assume that interest rates are zero, widgets

are non-income producing, and there is no

holding cost.

Which of the following statements is true?

The option is in the money.

The option is at the money.

The option is out of the

money.

3.

Question 2 of 5

An agent owns a USD 110 call option on

widget futures. The price of the widget

futures contract is USD 100. The option costs

USD 3.

What is the time value of this option?

Zero

USD 10

-USD

10

USD 3

4.

Question 3 of 5

All other things remaining equal, which of

the following would increase the value of a

put option on a futures contract?

5.


3/21

A decrease in the maturity of the option

An increase in the underlying price of the futures

contract

An increase in the volatility of the futures contract

Question 4 of 5

An American-style call option has a strike

price of EUR 50, and three months to expiry.

Interest rates for the period are 10%, and

volatility is 5%. The current price of the

underlying asset is EUR 75.

Should the option be exercised early?

Yes

No

6.

Question 5 of 5

Which of the following is the correct put-call

parity equation?

7.

OBJECTIVES

On completion of this tutorial, you will be

able to:

explain when an option is 'in' or 'out'of the money

8.


4/21

show how an option price is brokeninto two components: intrinsic value

and time value

describe the major influences onoption values

outline the upper and lowerboundaries of option prices

and explain the factors affecting the

exercise decision

describe the 'put-call' parityrelationship

Prerequisite Knowledge

Prior to studying this tutorial, you should

have simple familiarity with the discounting

of future values, and a good understanding of

the concepts outlined in the following

tutorial:

OptionsAn Introduction

9.


5/21

10.


6/21

11.


7/21

Forward Prices

How do forward prices affect 'moneyness'?

Consider a one-year European call option

struck on widgets at USD 105. The underlying

price is currently USD 100, while the forward

price is USD 110. The 'moneyness' of theoption can be expressed relative to the spot

and the forward price.

Relative to the spot

price

Relative to the

forward price

This option is 'out of

the money' (OTM),

because it would not

make sense to

exercise at USD 105when the market

price was only USD

100. However, this

option is not

exercisable now; it is

exercisable in one

years time.

This option is 'in the

money' (ITM)it

would make sense to

buy widgets at USD

105 if the price wasactually USD 110.

Different markets have different conventions;equity markets tend to relate option strike

prices to spot prices, while interest rate

markets tend to focus on forward prices. In

the foreign exchange market, American-style

options usually relate the strike to the spot FX

rate, while European-style options usually

relate the strike to the forward FX rate.

Rather than attempting to use different

practices in different markets, it is best to be

precise; rather than referring to an at-the-

money option, it would be better to use the

terms 'at-the-money forward' or 'at-the-

money spot'.

Note that for options on futures, the debate

is irrelevant; futures prices are already

forward prices so 'moneyness is a simple

12.
http://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page007.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page007.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page007.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page007.html


8/21

comparison between strike price and market

price. We will sometimes take advantage of

this by using imaginary futures contracts in

our example.


9/21

Option Moneyness

Option moneyness is summarized in the

following table:

13.

Moneyness Example 1

A call option is written on a futures contract.

It has a three-month maturity and a strike

price of EUR 100. Three-month interest rates

are 4%. The current futures price is EUR 100.

What is the option moneyness?

In the money

At the money

Out of the

money

14.

Moneyness Example 2

A put option is written on an underlying

asset. It has a one-year maturity and a strike

price of EUR 100. The asset generates no

income, and has no ownership or storagecosts. One-year interest rates are 5%. The

current asset price is EUR 100.

Which of the following statements is true?

The option is in the money

15.


10/21

forward.

The option is at the money

forward.

The option is out of the money

forward.

Components of Option Value 16.


11/21

17.

18.


12/21

Intrinsic Value

A 3-month American call option on a

hypothetical futures contract has a strike

price of EUR 100. The current price of a

futures contract is EUR 90. The option costs

EUR 5.

Assuming that interest rates are zero, what is

the intrinsic value of this option?

EUR 5

-EUR

10

Zero

-EUR 5

19.

20.


13/21

Factors Affecting Option Value An

Overview

It is comparatively easy to calculate the

intrinsic value of an option, but much harder

to estimate the option's time value. This is

because time value includes the value of'optionality' (considered either as the

additional premium required by an option

seller to compensate for the risk, or the

amount a buyer is willing to pay for the

possibility of future payoffs).

So how are fair prices for options obtained?

Precise calculations may involve the use of a

sophisticated pricing model. There are many

such models, all of which will have to take

into account the following:

Interest rates

Relationship between the strike price & the

asset price

Maturity

Volatility of the underlying asset

21.
http://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page014.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page014.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page015.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page015.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page015.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page016.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page016.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page017.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page017.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page017.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page016.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page015.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page015.htmlhttp://www.fsiconnect.org/lms/content/Custom/fsi-intuition-com/Content/imported_1542972/lo_0101/lo_0101page014.html


14/21

22.


15/21

Relationship Between theStrike Price & the

Asset Price

23.

Maturity

An increase in the maturity of an option will affect the forward prices of the underlying; these will

generally rise as a function of interest rates and other cash flows associated with the assets. Thiswill have the effect on prices noted previously. However, a greater effect will generally be the

fact that a longer maturity allows prices to move more. Consequently, the possible future payoffs

from an option will increase and the option value will rise. The graph below shows the effect of

time to maturity on put and call prices (both are at the money with a strike price of USD 5 and

volatility of 10%).

24.


16/21

The value of both options will increase as prices have 'more time' to move and hence generate a

return to the option holder. However, because forward prices will increase over time, the value

of the put rises less steeply than that of the call.

Volatility of the Underlying Asset

The amount of fluctuation of an asset price is known as its volatility the higher the volatility, the

more a vanilla option is worth.

To see this, assume two underlying assets, A and B, have an underlying price of USD 100.However, the price of B changes by more, on average, than that of A. Would you rather own a

USD 100 call option on asset A, or one on asset B? The potential losses on both options are the

samethe price might fall below USD 100, and the option would be worthless. However, the

potential payoffs are greater for asset B than for asset A. Therefore, the call option on asset B will

be higher.

25.


17/21

Effect of a Rise in Volatility

Returning to our simple example (3-month call optionstrike price USD 5) we can show theeffect of an increase of volatility, using our particular model, in this graph:

A rise in volatility leads to an increase in the value of our sample call option. Note that a change

in volatility has no effect on intrinsic value; it only influences the potential 'optionality'. Just as

time value is at its maximum for an option that is at the money, so too any price increases due to

higher volatility are at their maximum for ATM options.

If volatility is zero, then we simply have a payoff diagram; there is no 'optionality' because the

price does not change.

It is also worth noting that the increase in volatility would give additional value to this option

even when the underlying market is some way from the strike price. For instance, if the

underlying market is trading at USD 4.60, then a USD 5 call is almost worthless if priced using 10%

volatility; however, at 30% volatility, this option is worth around USD 0.13.

26.

Intrinsic Value


18/21

A 3-month call option on a fictional futures

contract is struck at GBP 50. The contract is

trading at a price of GBP 60. The price of the

option is GBP 11. Interest rates are zero.

What is the intrinsic value?

GBP 11

GBP 10

Zero

GBP 1

28.

Option Price Limits & Exercise Decisions

Upper Boundary for the Price of a Call Option

We can quickly establish simple maximum and

income-bearing assets. For a call option, whet

never be worth more than the current asset p

If the price of the call option was greater than

option, buy the stock, and invest the differenc

deliver the stock and be left with the invested

they would be left with the invested cash, plu

riskless profit would be obtained.

29.


19/21

30.

Lower Boundary for the Price of a Call Option

(American)

An American-style call option can never sell for less than

its intrinsic value, otherwise an option could simply be

bought, exercised immediately, and the asset that had

been bought through the option would then be sold into

the market.

For example, if a USD 100 call option cost USD 7 when

the underlying asset had a market price of USD 110, then

by purchasing the call, exercising it immediately, and

then selling the asset, a riskless profit could be obtained:

Risk-less profit = (USD 110 - USD 100) - USD 7

= USD 3

The option price will naturally disallow such

'easy' money.

Furthermore, we know that no option can have a

negative value; at worst an option holder can simply walk

away. The relationship is thus:

31.

Lower Boundary for the Price of a Call Option (European)

For a European-style call option the relationship needs to be adjusted since the

forward price is not equal to the spot price. To illustrate the difference, imagine

two portfolios:

32.


20/21

At expiry time T, the share is trading at a price AT. Consider portfolio 1:

If K < AT, then the option will be exercised at the price K, using the money whichhad been previously invested. The share you have purchased is worth AT.

If K > AT, then the option expires worthless, and the portfolio is simply worth themoney invested, which will generate the amount K. So at time T Portfolio 1

is worth the greater of ATand K.

Portfolio 2 will always be worth the future share price, AT; the value of Portfolio 1

is always higher than or equal to the value of Portfolio 2.

Using the terminology above, we get:

Options cannot have a negative value; consequently the lower bound must be:

Lower Boundary for the Price of a Put Option

American options are straightforward, as once again the value can never be less than intrinsic

value.

To illustrate the lower bound for a European option we will once again examine a pair of

imaginary portfolios.

33.


21/21

If, at time T, AT < K, then the option would be exercised. The underlying share would be

delivered and an amount K would be received. The portfolio would be worth K.

If, at time T, AT > K, then the option would expire worthless and the portfolio would be worth the

value of the stock, that is, AT.

At expiry, Portfolio 1 is worth the greater of ATand K. Portfolio 2 is only ever worth K. The value

of Portfolio 1 is always higher than or equal to the value of Portfolio 2;

Options cannot have a negative value; consequently the lower bound must be:

34.35.36.37.38.39.40.

Documents

OPTIONS - Introduction to Option Valuation