HO1 - Math 238, Financial Mathematics Problem set 1 January...

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Unformatted text preview: Math 238, Financial Mathematics Problem set 1 January 13, 2009 These problems are due on Tusday January 20 . 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 Let S t be the current stock price, K the strike price of the option, T the expiration time of the option, t the current time, S T the stock price at time T , r the risk-free interest rate, c the price of a European call option and p the price of a European put option. Explain why the two portfolios (a) one European call option plus cash equal to Ke- r ( T- t ) , and (b) one European put option plus one share, have the same payoff at time T : max( S T ,K ). Deduce that the value of the portfolios today must be the same, so that c + Ke- r ( T- t ) = p + S . Explain this put-call parity relation with figures . (Ch. 8, Hull; Ch. 9, Bjork) Problem 2 Carry out a two-step binomial tree risk-neutral pricing analysis for an option whose payoff is f uu ,f ud ,f...
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