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Introduction to Financial Derivatives. Lecture #4 on option Jinho Bae May 8, 2008. Ch 8. Option pricing models. I. Value of an option Intrinsic value Time value II. Factors that affect the price of an option. I. Value of an option. Value of an option =Option premium=Option price

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## Introduction to Financial Derivatives

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**Introduction to Financial Derivatives**Lecture #4 on option Jinho Bae May 8, 2008**Ch 8. Option pricing models**I. Value of an option • Intrinsic value • Time value II. Factors that affect the price of an option**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**I-1-1. Intrinsic value of a call option**• 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**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**Intrinsic value of a call option**• Mathematical expression of intrinsic value of a call option max(S-X, 0) • When S>X, S-X>0 take S-X • When S<X, S-X<0 take 0**Intrinsic value of a call option**value Intrinsic value X S**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**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**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<S, X-S<0 take 0**Intrinsic value of a put option**value Intrinsic value X S**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**Two elements of time value of an option**• 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**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.**E.g) IBM call option, X= $100, maturity=1 month**① current S=$100 (ATM) • If ST (at maturity) > $100 Payoff: ST - $100 • If ST (at maturity) < $100 No loss • Expected payoff from changes in the asset price until maturity > 0**② current S=$90 (OTM)**• Intrinsic value=$0 • If ST (at maturity) > $100 Payoff: ST - $100 • If ST (at maturity) < $100 No loss**Expected payoff**• Greater than 0. • However, smaller than that for ATM. Why?**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.**Expected payoff**• Greater than 0. • However, smaller than that for ATM.**Time value 1 of a call option**X S value Time value 1 Current spot price OTM ATM**Time value 1 of a put option**X S value Time value 1 Current spot price ATM OTM

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