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risk_neutral_callpricing

risk_neutral_callpricing - Economics 141A Fall 2010 Risk...

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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 Φ( 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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risk_neutral_callpricing - Economics 141A Fall 2010 Risk...

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