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

Need help w/ financial derivatives exercises

November 25th, 2013, 8:31 am

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).
User avatar
Posts: 221
Joined: September 16th, 2005, 7:44 am

Need help w/ financial derivatives exercises

November 25th, 2013, 10:06 am

what is your question(s)?
User avatar
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

Need help w/ financial derivatives exercises

November 25th, 2013, 10:50 am

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
knowledge comes, wisdom lingers

PW by JB has been "Serving the Quantitative Finance Community" since 2001. Continued...

Twitter LinkedIn Instagram



Looking for a quant job, risk, algo trading,...? Browse jobs here...