Over the coming year, Stock X price will decrease to $80 from its current level of $100 or it will rise to $125. The one-year interest rate is 2.5%. Consider a one-year put option on stock X with a strike price of $118.

(a) To replicate this put, find the number of shares to be purchased or sold and the units of ZCB with face value of $1 to be purchased or sold.

(b) Use the replicating-portfolio method to value this put.

(c) In a risk-neutral world, what is the probability that stock X will rise in price?

(d) Use the risk-neutral method to check your valuation of the put. 5

Stock X price is $100 and could go up by 17% or down by 15% in each six-month period. A one-year put option on stock X has an exercise price of $98. The interest rate is 2.5% a year.

(a) Find a equivalent standard deviation of returns of stock X.

(b) What is the value of the put?