
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