Merck inc. is mainta8n the investment management cell and attempting to value call option and put option with maturity of 90 days with common exercise price of 40. The price of stock in market in market is $38.75, which is also paying the dividend on quarterly basis that is $0.48 bi-monthly. Considering the risk fee rate of 4.6% and implied volatility of 30%.

a. Based on the Black Scholes, Estimate the value of the call and put options.

b. how the dividend paying effects the value of put and call value and Why this effect is substantial?

c. repeat part a and part b with the settings of American call option. Evaluate the difference between answer.

d. Based on technique of the pseudo-American call option, determine whether such technique effects the valuation of call option and put options.

e. With call and put which option has greater chance of early exercise and why. the answer should be calculative