Question

Suppose that the assumptions of the BSM model hold.  Supposing that the expected return of a stock is higher than the risk-free rate, the expected return of call option with K=100 will be higher than the expected return on a call option with K=110.

T OR F

Answer 1

Answer-

The statement is True.

We know the Put call parity relation is

C + K / ( 1 + r )T = S + P

C = S + P - K / ( 1 + r )T ------------------- (1)

C = Call option
P = Put option
S = Stock price
K = Strike price
r = risk free rate

Given Strike price K = 100 & K = 110

Substituting the K values in the equation 1 we get

C = S + P - 100 / ( 1 + r )T ------------- (2)

C = S + P - 110 / ( 1 + r )T ------------- (3)

Considering all the other value we can conclude from the above equations that expected return on Call option for strike price of 100 will be higher than the expected return on Call option for strike price of 110.

Call value of Equation (2) will be higher than the Call value of Equation (3) as we are subtracting a higher number in equation (3)