Question 1: European and American Puts (4/10)

You wish to price an European

put on a stock which currently trades for $100. The put expires in nine months, and has a

strike of $100. The nine-month interest rate (annualized continuously compounded) is 5%.

The estimated volatility of the stock is 25%. The stock pays no dividends.

(i) What is the Black-Scholes-Merton price of the European put?

(ii) What is the price of the European put according to a standard 3-step binomial tree?

(iii) Suppose the standard 3-step binomial tree is the true description of stock price

movements in the real world. If the European put is trading for $6, is there an

arbitrage? If not, explain why not. If so, explain in detail what your strategy is.

(iv) What is the price of the American put according to a 3-step binomial tree?

(v) Under what circumstances, if any, do you exercise the put before maturity?

hint: This question is asking specically about at what point in this tree you want to

exercise early - this is not about general \conceptual" question. You can simply answer

(for example) \In period 2, when the stock price goes up twice, I would exercise early".