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Introduction to Financial Derivatives Lecture #4 on option Jinho Bae May 8, 2008

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Ch 8. Option pricing models I. Value of an option –Intrinsic value –Time value II. Factors that affect the price of an option

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I. Value of an option Value of an option =Option premium=Option price The price that an option holder pays to an option writer for the right to sell or buy an asset Value of an option= Intrinsic value + Time value

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When the spot price (S) exceeds the strike price (X) Intrinsic value=S-X>0 e.g) Google call option with X=$460 Google share price S=$465 Intrinsic value=S-X=$5 I-1-1. Intrinsic value of a call option

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Intrinsic value of a call option When the spot price (S) does not exceed the strike price (X) Intrinsic value=0 e.g) Google call option with X=$460 Google share price S=$450 Intrinsic value=0

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Mathematical expression of intrinsic value of a call option max(S-X, 0) When S>X, S-X>0 take S-X When S

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value Intrinsic value XS Intrinsic value of a call option

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I-1-2. Intrinsic value of a put option When the strike price (X) exceeds the spot price (S) Intrinsic value=X-S>0 e.g) Google put option with X=$460 Google share price S=$450 Intrinsic value=X-S=$10

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Intrinsic value of a put option When the strike price (X) does not exceed the spot price (S) Intrinsic value=0 e.g) Google call option with X=$460 Google share price S=$465 Intrinsic value=0

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Intrinsic value of a put option Mathematical expression of intrinsic value of a put option max(X-S, 0) When X>S, X-S>0 take X-S When X~~
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~~

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Intrinsic value of a put option value Intrinsic value XS

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Relationship between intrinsic value and ITM, OTM, ATM S>X CallITM Intrinsic value >0 PutOTM Intrinsic value=0 S=X ATM Intrinsic value=0 ATM Intrinsic value=0 S

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I-2. Time value of an option The value of an option arising from the time left to maturity Time value = Option premium - Intrinsic value e.g) IBM call option with X=$100 trades at $10 IBM share price S=$106 Intrinsic value=S-X=$6 Time value= $10-$6=$4

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Two elements of time value of an option 1)Time value 1: Expected payoff when holding the option until maturity 2) Time value 2: Time value associated with cash flow from selling or buying underlying asset of the option

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1)Time value 1 Two scenarios of asset price movement until maturity Asset price moves in a favorable direction unlimited positive payoff Asset price moves in an unfavorable direction no or bounded loss Expected payoff is positive.

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E.g) IBM call option, X= $100, maturity=1 month ① current S=$100 (ATM) If S T (at maturity) > $100 Payoff: S T - $100 If S T (at maturity) < $100 No loss Expected payoff from changes in the asset price until maturity > 0

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Possibilities of changes in the asset price until maturity Price changeProbability 20 increase1/8 10 increase2/8 0 10 decrease2/8 20 decrease1/8

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SSTST Probabil ity PayoffExpected payoff 100 1/8 2/8 1/8

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② current S=$90 (OTM) Intrinsic value=$0 If S T (at maturity) > $100 Payoff: S T - $100 If S T (at maturity) < $100 No loss

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S STST Probabi lity PayoffExpected payoff 90 1/8 2/8 1/8 Expected payoff Greater than 0. However, smaller than that for ATM. Why?

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③ current S=$110 (ITM) Intrinsic value =$10 If asset price increases above 110 Payoff increases proportionally If asset price increases below 110, intrinsic value decreases but bounded from 10.

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SSTST Probabil ity PayoffExpected payoff 110 1/8 2/8 1/8 Expected payoff Greater than 0. However, smaller than that for ATM.

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Time value 1 of a call option X S Current spot price value Time value 1 OTM ATM

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Time value 1 of a put option X S Current spot price value Time value 1 ATM OTM

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