Problem $2.$

Consider a European call option on a non$-$dividend$-$paying stock where the stock price is $$100,$ the

strike price is $$120,$ the $($annualized$)$ risk$-$free rate is $2\%,u=e^{\sqrt[\phantom{2}]{t}},d=\frac{1}{u},$ the $($annualized$)$

volatility is $20\%$ per year, and the time to expiration is six months.

Use a $15$ timestep tree to determine the current market value of this six$-$month European call

option. Do this manually by applying the Cox$-$Ross$-$Rubinstein framework, and be sure to show

your work.

What is the current market value of an otherwise identical $($i$.$e$.,$ same underlying asset, same

strike price, interest rate, same volatility, same number of timesteps, and time to expiration$)$

European put option?