Lecture11_PricingOptionII - 1 NBA 6730: Derivative...

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Unformatted text preview: 1 NBA 6730: Derivative Securities Lecture 11: Option Pricing II 09/30/2010 George Gao NBA6730-Derivative Securities I 2 Agenda We will see how to extend the Binomial pricing model beyond plain-vanilla European calls and puts, and how the Binomial model is related to the well-known BSM model. More on Binomial model Build the Binomial tree Black-Scholes-Merton option pricing model 2 NBA6730-Derivative Securities I 3 (1) Two-Period Binomial Model The stock price tree: The price tree for a European call: max , 0 max , 0 max , 0 NBA6730-Derivative Securities I 4 (1) Two-Period Binomial Model How do we get the call price today : Dynamic programming (i.e., start at the end, work backwards) From the one-period Binomial model: Recall is the risk-neutral probability of price moving up: Once we know and , we have a one-period model and calculate the call price: 3 NBA6730-Derivative 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 NBA6730-Derivative Securities I 6 (2) IBM Example: Non Dividend Risk-neutral 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 NBA6730-Derivative 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 NBA6730-Derivative Securities I 8 (3) IBM Example: Dividend Risk-neutral 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).

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Lecture11_PricingOptionII - 1 NBA 6730: Derivative...

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