16. When there are no dividends, the early exercise of an American put depends on a trade-off 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 a two-period binomial model with u = 1.10 and d = 0.90. Suppose the initial stock price is 100, and we are looking to price a two-period American put option with a strike of K = 95.
(a) First, consider a "low" interest rate of R = 1.02. Show that early exercise of the American put is never optimal in this case.
(b) Now consider a "high" interest rate of R = 1.05. Show that it now becomes optimal to exercise the put early in some circumstances. What is the early exercise premium in this case?
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