Question Two $(15$ Marks$)$

Consider the following information for Muggie corporation.

Mega Company stock price $=K20$

Exercise price $=K15$

$3-$month Risk Free Rate $=6\%$

Call maturity $=90$ days

Stock volatility $=0\mathrm{.}50$

a$.$ What are the assumptions for the Black Scholes Option Pricing Model and their implications? $(3$ Marks$)$

b$.$ What is the fair value of Muggie's Call option using the Black Scholes Option pricing model? $(10$ Marks$)$

c$.$ Using the PUT$-$CALL PARITY relationship, determine the price of the put option. $(2$ Marks$)$