A 1-year option is offered on

A 1-year option is offered on a non-dividend-paying stock. The stock price is $85. The exercise price of the option is $90 and the volatility is 18% per annum. The continuously compounded risk-free rate is 6% per annum. When the Black-Scholes-Merton model is used

a) What is the value of d1?

b) What is the value of d2?

c) What is the price of a call option, c?

d) What is the price of a put option, p?

Now, assume that the stock pays a dividend after 3-months and 9-months of $1.50.

e) What is the present value of the dividends?

f) What is the new value of d1 with dividends?

g) What is the new value of d2 with dividends?

h) What is the value of a call option?

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