Consider the valuation of a European call on Microsoft with strike price of $100\mathrm{.}00$ and

$3-$months$’$ time to maturity. The current price is $100\mathrm{.}00$ and the volatility is $40\%$ over

the option$’$s lifetime. The risk$-$free rate is $2\%.$

a$)$ Calculate the arbitrage free value of the call

b$)$ If the stock pays a dividend of $4$ USD next month will this affect your previous

calculations?

c$)$ Estimate the probability that an investor holding the call will exercise the

option at maturity.

d$)$ An analyst predicts that the expected stock return is $20\%$ calculate the

physical probability that the option will be exercised.