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Consider a call option having the strike price K and exercise time t. Suppose further that the nominal interest rate is r, compounded continuously,

 

Consider a call option having the strike price K and exercise time t. Suppose further that the nominal interest rate is r, compounded continuously, and also that the price of the security follows a geometric Brownian motion with variance parameter o2. Derive the formula that is used to price the unique cost of the option that does not give rise to an arbitrage. [5]

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