European and American puts Consider a two-step binomial tree, where a stock that pays no dividends has current price 100, and at each time step can increase by 20% or decrease by 10%. The possible values at time T = 2 are thus 144, 108 and 81. The annually compounded interest rate is 10%.
(a) Calculate the price of a two-year 106-strike European put using (i) a replication argument and (ii) risk-neutral expectation.
(b) Calculate the price of a two-year 106-strike American put using replication, and hence verify that the American put has price strictly greater than the European.
(c) Calculate the prices of a two-year 86-strike European put and American put. What is different to (b)?
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