Consider pricing a call option on the S&P $500$ Index with the expiration date in $4$ months and a strike price of $$100.$ The S&P $500$ can move up

by $35\%$ or down by $20\%$ every $2$ months, and is currently trading for $$100.$ The annual risk$-$free rate is $5\%.$

A$.(*)$ What is the bi$-$monthly risk$-$free rate $($i$.$e$.,$ the risk free rate used to discount$/$compound money for $2$ months$)?$

$\%$

$($Use at least four decimals for intermediate calculations, and write your final answers in percentage with three decimals$)$

B$.(*)$ What is the risk$-$neutral probability that the stock will go up over the next $2$ months?

$\%$

$($Use at least four decimals for intermediate calculations, and write your final answers in percentage with two decimals$)$

C$.(**)$ What would you estimate the value of the Call option to be today? What would you estimate the value of the Call option to be in two

months if the S&P $500$ goes up in value? What if it goes down? Complete the following binomial trees reporting the dynamics of the price of

the underlying asset and of the Call option.

$($Use at least four decimals for intermediate calculations, and write your final answers in percentage with two decimals$).$

Call Option Price Dynamics