PLEASE SHOW CALCULATIONS IN DETAIL:

a. Calculate the price of a four-month European put option on a non- dividend-paying stock with a strike price of $60 when the current stock price is $55, the continuously compounded risk-free interest rate is 10% per annum, and the volatility is 31% per annum.

b. Calculate the price of the put option if a dividend of $2.50 is expected in three months.

Answer: d₁ = -.21 d₂ = -.39 N(d₁) = .4168 N(d₂) = .3483 p = $5.74 S0 = $52.56 d1 = -.46 d2 = -.64 N(d1) = .3228 N(d2) = .2611 p = $7.29