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
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?