Question

There is an American put option on a stock that expires in two months. The stock price is $100 and the standard deviation of the stock returns is 72 percent. The option has a strike price of $112 and the risk-free interest rate is an annual percentage rate of 5.6 percent.

What is the price of the option? Use a two-state model with one-month steps

Answer 1

Discounted value at point 0 ie P0 = (0.4595 * 6.456 + 0.5405*30.77) / 1.004711

= (2.967 + 16.63) / 1.004711

= 19.597 / 1.004711

= 19.51

Intrinsic value = 112 -100 = 12

price of put option = Higher of IV or discounted value at C0 = Higher of ( 19.51 , 12 ) = 19.51

Please not this is an American option that means it can be exercised before the maturity. Hence at any point in time it value cannot be less than the intrinsic value. Hence we have cosnidered the intrisic values at various nodes.