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."