Question

Wildcat’s stock is volatile, you expect its stock price either increases or decreases by 30% over
a year of time. suppose the current stock price is $100 and you have an American put option
with exercise price of $102. The option has two years to expiration. If the risk-free interest rate
is 10%.
a. What is the risk-neutral probability ππ for the up state?
b. Draw the binomial trees (two years) and mark the stock prices for each of the nodes.
c. For each of the nodes, work backwards and find the value of the option i) if it is kept, ii) if
it is exercised, and iii) the optimal choice.
d. Find the value of the American put option.
e. Is there any state in year one that the option holder would choose to exercise the option
early?

Answer 1

A put option gives the option buyer the right to sell the Stock at a strike price.

The payoff of put option = Max(X-S,0) where S is stock price and X is exercise price.

In American put option, the option can be exercised before the maturity,

therefore payoff of the option at each period is compared to holding it for one more period.