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

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Presentation on theme: "Introduction to Financial Derivatives Lecture #4 on option Jinho Bae May 8, 2008."— Presentation transcript:

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

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

3 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

4 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

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

6 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

7 value Intrinsic value XS Intrinsic value of a call option

8 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

9 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

10 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

11 Intrinsic value of a put option value Intrinsic value XS

12 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

13 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

14 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

15 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.

16 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

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

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

19 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

20 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?

21 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.

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

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

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


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