Answer the following two questions on this paper. Work in groups of $2$ or $3$ people. Each person who wishes to get credil for this paper must personally sign above. Please do not sign on behalf of a person who is not here. As on exams, you must show your work or show what you enter in your financial calculator.

Both questions are based on the following:

A stock today has a price of $$S$ per share. The stock currently and for the foreseeable future pays no dividends. Each year the stock's value will equal one of the following:

ux previous year's value; or

$dx$ previous year's value.

The riskless yearly interest rate is given by $i,$ where $u>(1+i)>d.$

A call option on a share of XYZ stock, with a strike price of $$K,$ can be exercised at the expiry date of the option. The payoff of the option will be either

$C_u=$max$\{(Su-K),0\}$ if the stock price is $Su$; or

$C_d=$max$\{(Sd-K),0\}$ if the stock price is $Sd.$

A put option, with a strike price of $$K,$ can also be exercised at the expiry date of the option. The payoff of the option will be either

$P_u=$max$\{(K-Su),0\}$ if the stock price is $Su$; or

$P_d=$max$\{(K-Sd),0\}$ if the stock price is $Sd.$

Recall that $p^{**}$ denotes $\frac{1+i-d}{u-d}.$