The current price of Natasha corporation stock is $$6.$ In each of the next two

years, this stock price can either go up by $$2\mathrm{.}50$ or go down by $$2\mathrm{.}00.$ The

stock pays no dividends. The one$-$year risk free rate is $3\%$ and will remain

constant. Using the binomial model, calculate the price of a two$-$year call

option on Natasha stock with a strike price of $$7.$

b$)$ Rebecca is interested in purchasing a European call on a hot new stock, UP$,$

Inc. the call has a strike price of $$100$ and expires in $90$ days. The current

price of UP stock is $$120$ and the stock has a standard deviation of $40\%$ per

year. The risk free interest rate is $6\mathrm{.}18\%$ per year.

d$1=$ln$[$S$/$PV$($K$)]/\backslash$sigma T$1/2+\backslash$sigma T$1/2/2$ and d$2=$ d$1-\backslash$sigma T$1/2$

Using the Black$-$Scholes formula to compute the price of the call.

c$)$ Use put$-$call parity to compute the price of the put with the same strike and

expiration date.