Reference no: EM132785441

Comparative statics of option prices: For this question, consider a two{period binomial model. The current level of the underlying is S = 100, and the size of up{ and down{moves are u = 1:10 and d = 0:90 per period, respectively. The risk-free interest rate will be specied in each of the sub{questions. The rates are given as continuously compounded and per period in the tree (i.e., you can think of each period as 1 year).

1. When there are no dividends, the early exercise of an American put depends on a trade{o between insurance value (which comes from volatility) and time value (a function of interest rates). Thus, for example, for a given level of volatility, early exercise of the put becomes more likely if interest rates are higher. This question provides a numerical illustration.

Consider an American put option expiring after two periods with a strike price of 95.

(a) First, consider a "low"interest rate of r = 1:98%. Show that early exercise of the American put is never optimal in this case. What is the price of the put today?

(b) Next, consider a "high" interest rate of r = 4:879%. Show that it now becomes optimal to exercise the put early in some circumstances. What is the early exercise premium in this case (the dierence between the prices of an American and European put today)?