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

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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

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

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

Mathematical expression of intrinsic value of a call option max(S-X, 0) When S>X, S-X>0  take S-X When S { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/13/3962442/slides/slide_6.jpg", "name": "Mathematical expression of intrinsic value of a call option max(S-X, 0) When S>X, S-X>0  take S-X When SX, S-X>0  take S-X When S

value Intrinsic value XS Intrinsic value of a call option

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 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/13/3962442/slides/slide_10.jpg", "name": "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 XS, X-S>0  take X-S When X

Intrinsic value of a put option value Intrinsic value XS

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 S0

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 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

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.

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

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

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

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

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?

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.

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

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

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

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