Pay-later options are options for which the buyer is not required to pay the premium up front (i.e., at the time that the contract is entered into). At expiration, the holder of a pay-later option must exercise the option if it in in the money, in which case he pays the premium at that time. Otherwise the option is left unexercised and no premium is paid.

The stock of the CCC Corporation is currently valued at \(\$ 12\) and is assumed to possess all the properties of geometric Brownian motion. It has an expected annual return of \(15 \%\), an annual volatility of \(20 \%\), and the annual risk-free rate is \(10 \%\).

(a) Using a binomial lattice, determine the price of a call option on CCC stock maturing in 10 months' time with a strike price of \(\$ 14\). (Let the distance between nodes on your tree be 1 month in length.)

(b) Using a similar methodology, determine the premium for a pay-later call with all the same parameters as the call in part \((a)\).

(c) Compare your answers to parts \((a)\) and (b). Do the answers differ; if so why, if not why not? Under what conditions would you prefer to hold which option?