Question

The current price of a stock is 10 and it is expected to increase or decrease in price by 10% over each of the next two 6-month periods. The annual risk free rate with continuous compounding is 6%. The stock pays no dividends.

a) Determine the value of an American put option with a strike price of 10.50 maturing in one year.
b) Determine the number of shares of stock, ∆, and the amount of bonds earning the risk-free rate, B, to be held at time 0 in the replicating portfolio for the put option

Answer 1

The value of the American put option with a strike price of 10.50 and maturing in one year is $0.50.

Step-by-step explanation:

To determine the value of an American put option with a strike price of 10.50 maturing in one year, we can use the risk-neutral pricing model. The value of the option can be calculated using the formula:

V(0) = max(K - S(0), 0)

where V(0) is the value of the option at time 0, K is the strike price, and S(0) is the current price of the stock.

In this case, the current price of the stock is 10 and the strike price is 10.50. Therefore, the value of the option is:

V(0) = max(10.50 - 10, 0) = 0.50

So, the value of the American put option with a strike price of 10.50 maturing in one year is $0.50.