Show details

Consider a two-period binomial model. Assume that the maturity is T = 1 and each period is At = i. The stock has an initial price os $100 and can go up 15% (log return) or down 10% (log return) per annum with equal probabilities. Assume that the annual continuous compounding interest rate is r = 0.02. Consider an put-like option with intrinsic value (K St)+ if exercised at time t 6 {0,1,2}. This option, however, can only be exercised at even times. That is, it can only be exercised in periods 16 E {0, 2}, and it cannot be exercised in periods t = 1. Such as option is called a Bermudan option. Assume that the strike price is K = 95. (a) Draw a binomial tree for this model. Mark the nodes of the tree in which the option can be exercised. (b) Use backwards induction to show that the price of the Bermudan option is 1.29. Consider how the Snell envelop has to be adjusted for periods in which the option cannot be exercised. (c) What is the optimal exercise rule