HS [4]

The current price of a stock in the "Hello Sailor" entertainment company (HS) is

$100. Each period the stock price either moves up by a factor u = 1.5 or down by a factor d = 1/u. (HS is in a highly variable industry.) The per period interest rate is 5%.

Consider the following "compound option" written on HS: You buy the option at time 0. The compound option gives you the right to at time 1 choose to receive one of the following two options:

• A call option on HS with exercise price 100 and expiring in period 2.

• A put option on HS with exercise price 100 and expiring in period 2.

Calculate the price of this "compound option."