Create Presentation
Download Presentation

Download Presentation
## Introduction to Financial Derivatives

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**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