Question One $(15$ Marks$)$

A stock price is currently K$100.$ Over each of the next two six$-$month periods it is expected to go up by $10\%$ or down by $10\%.$ The risk$-$free interest rate is $8\%$ per annum with continuous compounding.

a$.$ What are some of the assumptions considered under Binomial Option Price Calculations $(2$ marks$)$

b$.$ What is the value of a one$-$year European call option with a strike price of K$100(6$ marks$)$

c$.$ How is time Value affected under a European style and American style option $(2$ marks$)$