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HO3 - Math 238 Financial Mathematics Problem set 3 February...

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Math 238, Financial Mathematics Problem set 3 February 5, 2009 These problems are due on Friday February 13. You can give them to me in class, drop them in my office, or put them in my mailbox outside the mathematics department. Problem 1 Consider a company with N outstanding shares and M outstanding European warrants. War- rants are contracts that entitle the holder to purchase γ shares from the company at time T at a price K per share. Find an implicit equation for the determination of the price W of the warrant. Show that this price at time t T is equal to the price of Nγ/ ( N + ) European call option with the stock price S replaced by S + ( M/N ) W , which gives an implicit equation for W . Interpret this formula in financial terms. (Hull Ch 12.10.) Problem 2 Derive the price of an ‘average price’ European call option in which the payoff is h = parenleftbigg S ( T ) - I ( T ) T parenrightbigg + with I ( t ) = integraldisplay t 0 S ( s ) ds Here S ( T ) is the standard geometric Brownian motion process with constant mean return μ and
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