A$.$ Consider the information the information below and answer the questions that follow

i$.$ Calculate The Option value for a two period Binomial European Call option with the following terms and the time values $(6$ MLRKS$)$

$>$ Current Price of underlying asset $k100$

$>$ Serike price of underlying asset $,80$

$>$ One period risk free rate of return $10\%$

$>$ Stock price caa cilher go up or down by $15\%$

ii$.$ compare the rerults if the stock price can go up or down by $30\%6(4$ MARKS$)$

B$.$ According to Emanuel Derman, writing in the Journal of Derivatives, Winter, $2000,$ p$.64$ he says "Good theories, like Black$-$Scholes$-$Merton, provide a theoretical laboratory in which you can explore the likely offect of possible causes. They give you a common language with which to quantify and communicate your feelings about value:"

Riding on that background and given the following information

$>$ Current Price of underlying asset

$k100$

$>$ Strike price of underlying asset

$k80$

$$ Omepuriod risk free rate of retum

$>$ Stock price can cither go up of down by $20\%\%$

$>$ Time pcriod $6$ months

i$.$ Determine the call value $(6$ MARKS$)$

$18.$ What is the dieme value for holding on to the option $(2$ MARKS$)$

iii. What is the Pat Option Price using the PUT.CALI. Parity relationahip $(?)$ MARKS$)$