Consider the stock of Examples 14.3 and 14.4, which has \(\sigma=.20\) and an initial price of \(\$ 62\). The interest rate is \(10 \%\), compounded monthly. Consider a 5-month option with a strike price of \(\$ 60\). This option can be declared, after exactly 3 months, by the purchaser to be either a European call or a European put. Find the value of this "as you like it" option.

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Example 14.3 (A 5-month call) Consider a stock with a volatility of its logarithm of = .20. The current price of the stock is $62. The stock pays no dividends. A certain call option on this stock has an expiration date 5 months from now and a strike price of $60. The current rate of interest is 10%, compounded monthly. We wish to determine the theoretical price of this call using the binomial option approach. First we must determine the parameters for the binomial model of the stock price fluctuations. We shall take the period length to be I month, which means At = 1/12. The parameters are found from equations (13.1) to be u = e = 1.05943 d=e=94390 R=1+1/12 1.00833. Then the risk-neutral probability is q (R-d)/(u-d) = .55770. We now form the binomial lattice corresponding to the stock price at the begin- ning of each of six successive months (including the current month). This lattice is