risk_neutral_callpricing

risk_neutral_callpricing - Economics 141A Fall, 2010 Risk...

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Unformatted text preview: Economics 141A Fall, 2010 Risk Neutral Call Pricing last update: 11/15/10 We compute the price of a European call option by means of risk-neutral expectation. This is an illustrative example of the actual computation; more importantly, this is the central example. Notation. We continue the same general notation that we have used so far. Q is the risk-neutral probability measure and W Q is its associated Brownian motion. A European call option with underlying stock price process S ( t ), strike price K , and maturity T has a payoff given by ( S ( T )- K ) + . Risk-Neutral Calculation for a Call Option. We remind ourselves of the two conditioning results from the both sets of previous notes. Consider a derivative contract on an underlying stock with payoff V ( T ) at maturity. Then the value of the contract at time t is V ( t,S ( t )) = E Q [ e- r ( T- t ) V ( T ) |F ( t )] (1) If the derivative contract has a simple payoff ( S ( T )), i.e. a payoff at maturity which is function of the stock price alone, then the expectation does not depend on the...
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This note was uploaded on 04/09/2012 for the course ECON 142 taught by Professor Mess during the Fall '11 term at UCLA.

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risk_neutral_callpricing - Economics 141A Fall, 2010 Risk...

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