The stock of GS Co. pays dividends at an annual continuously compounded yield of 0.12. The annual continuously compounded risk-free interest rate is 0.34. Certain call options on the stock of GS Co. have time to expiration of 99 days. The option currently trades for $56.

(a) Suppose = 0.03(per day). Find the price of the call option 65 days from expiration, all other things equal. [answer: $54.98]

(b) Suppose = 0.11. Find the price of the call option if the interest rate suddenly increases to 0.66, all other things equal. [answer: $59.52]

(c) Suppose = 0.04. Find the price of the call option if the stocks dividend yield suddenly decreases to 0.02, all other things equal. [answer:$56.40 ]

Where

d₁ =[ln(St/K) + (r + 0.5²)(T t)]/ [(T t)]

d₂= d₁ (T t)