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redgum
Topic Author
Posts: 4
Joined: November 21st, 2013, 2:38 pm

### Need help w/ financial derivatives exercises

Thank you in advance for your help! I'm really lost with these exercisesThe underlying asset price equals 1000, the risk-freerate is r = 5%, and a call option maturity is T = 1, its strikeis k = 945, and its premium is c0 = 200.a) Compute the premium p0 of the homologous putoption.b) Solve a) if there is a dividend d = 20 with matu-rity in four months. Suppose that p0 = 100 and implementan arbitrage strategy.c) Solve a) for future options, under the assumptionthat 1000 equals the underlying future quotation. Supposethat p0 = 100 and implement an arbitrage strategy.d) Consider the assumptions of a) and constructa fund with price 1100 and guaranteeing 945 in one year.Give a figure representing the fund return as a function ofthe underlying asset return.4) a) Consider a binomial model with T = 3t,d = 0.5, u = 2 and er(4t) = 1.25. Suppose that S0 = 200 andprice an American put whose strike is k = 100. Compute alsothe optimal stopping time, as a random variable. Withoutcomputations, can in this case the usual put − call parityhold if one deals with American options?b) Consider a binomial model with T = 3t, d =0.5, u = 2 and er(4t) = 1. A risky share with price S0 = 200will pay the dividend D = 20 a few moments after 2t.Give the stochastic evolution of an American call optionprice with strike k = 200. Give the optimal stopping timeas a random variable.????????????????5) Consider Exercises 4a) and 4b) and provide the com-plete evolution of the hedging strategy for the Americanoptions buyer (pay attention to the dividend effect).

cemil
Posts: 221
Joined: September 16th, 2005, 7:44 am

### Need help w/ financial derivatives exercises

daveangel
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

### Need help w/ financial derivatives exercises

your first set of questions can pretty much be answered by using put call parity (you have omitted to say that the options are European but I am assuming that they are.a) p0 = 200 - (1000 - 945/1.05) = 200 - 100 = 100b) p0 = 200 - ((1000-20/(1+0.05*4/12))-945/1.05) = 119.67. therefor buy the put at 100 and buy the stock at 1000 and sell the call at 200.c) etc
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