Question

The current price of the stock of Mont Tremblant Air is C$100. During each six-month period it will either rise by 11.1% or fall by 10% (equivalent to an annual standard deviation of 14.9%). The interest rate is 5% per six-month period.

a. Calculate the value of a one-year European call option on Mont Tremblant’s stock with an exercise price of C$102.

b. Recalculate the value of the Mont Tremblant call option, assuming that it is an American option.

Answer 1

Value of call = S N (d1) - K e rt N(d2) where In d2 d1-o Vt

Annual standard deviation = 14.9%

Hence, semi annual standard deviation = 14.9% / 2^0.5 = 10.54%

B C 8 S 100.00 2.00 1 year 2 six months period 10.54% 102 Strike price of call option 5.00% Formula Used 9 t 10 o 11 K 12 r Values 13 Output 0.612737401 (LN(C8/C11)+(C12+C10^2/2)*C9)/(C10*SQRT(C9) 0.463737401 C14-C10*SQRT(C9) 14 d1 15 d2 16 N(d1) 0.729975006 NORMSDIST(C14) 0.678582051 NORMSDIST(C15) 17 N(d2)= 10.3688C8*C16-C11*EXP(-C12 C9)*C17 18 Value of the call option, C

Part (a)

the value of a one-year European call option on Mont Tremblant’s stock with an exercise price of C$102 = $ 10.3688

Part (b)

An american call option has the same value as an european call option because it is never optimal to exercise an american option before maturity.

Hence, the value of the Mont Tremblant call option, assuming that it is an American option = $ 10.3688