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Unformatted text preview: 1 NBA 6730: Derivative Securities Lecture 11: Option Pricing II 09/30/2010 George Gao NBA6730Derivative Securities I 2 Agenda We will see how to extend the Binomial pricing model beyond plainvanilla European calls and puts, and how the Binomial model is related to the wellknown BSM model. More on Binomial model Build the Binomial tree BlackScholesMerton option pricing model 2 NBA6730Derivative Securities I 3 (1) TwoPeriod Binomial Model The stock price tree: The price tree for a European call: max , 0 max , 0 max , 0 NBA6730Derivative Securities I 4 (1) TwoPeriod Binomial Model How do we get the call price today : Dynamic programming (i.e., start at the end, work backwards) From the oneperiod Binomial model: Recall is the riskneutral probability of price moving up: Once we know and , we have a oneperiod model and calculate the call price: 3 NBA6730Derivative Securities I 5 (2) IBM Example: Non Dividend IBM is currently traded at $100 and the simple quarterly interest rate is 3.33%. Every quarter, the price of IBM either rises by 30% or falls by 10%. Whats the value of a European call with strike price K=$110 and 6 months to maturity? The price tree for a European call looks like: 100 130 90 169 117 81 169 110 59 117 110 7 81 110 0 NBA6730Derivative Securities I 6 (2) IBM Example: Non Dividend Riskneutral pricing on the stock implies .. .. So we get the value of call at the end of first quarter: .. . 23.55 , .. . 2.56 The call tree now looks like: Finally, the call price today is: .... . 9.05 Question: how to price a call if IBM distributes a 5% dividend at the end of first quarter? 23.55 2.56 59 7 4 NBA6730Derivative Securities I 7 (3) IBM Example: Dividend The new stock price tree looks like: The price tree for a European call looks like 100 130 123.5 90 85.5 160.55 111.15 76.95 160.55 110 50.55 111.15 110 1.15 76.95 110 0 NBA6730Derivative Securities I 8 (3) IBM Example: Dividend Riskneutral probability is unchanged: ......
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This note was uploaded on 10/26/2010 for the course JOHNSON 6730 taught by Professor Georgegao during the Fall '10 term at Cornell University (Engineering School).
 Fall '10
 GeorgeGao

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