An American put option with a time to maturity of 1.5 years and an exercise price of $38 is written on a stock whose current price is $35. The stock will distribute a 1.5% dividend seven months from now, 2.0% dividend 13 months from now, and a 2.05% dividend 19 months from now. The risk-free interest rate is 2.5% p.a. (compounded continuously) and the stock’s volatility is 38% p.a..
a. Please use a three-step binomial tree to estimate the option value. Also estimate the option’s delta using the next two nodes as shown in class (you only have to estimate the current delta, not for the future nodes).
b. Now, recalculate the put value and delta assuming an exercise price of $30. Compare the new price and delta with those obtained in part a. Which can you conclude?