Option valuation: Consider a call option with a strike price of $10, which expires in one year. The risk-free rate of interest is 10 per cent. The current underlying share price is $30. Without arbitrage, which of the following is a possible price for the call option?

Question

Quizplus · Accepted Answer

The Black-Scholes formula can be used to value the call option as follows:
C = S*N(d1) - K*e^(-r*T)*N(d2)
where:
S = current share price = $30
K = strike price = $10
r = risk-free rate = 10%
T = time to expiration in years = 1
d1 = (ln(S/K) + (r + 0.5*sigma^2)*T) / (sigma*sqrt(T))
d2 = d1 - sigma*sqrt(T)
sigma is the volatility of the underlying asset, which is not given in the question.

Using the given inputs and assuming a volatility of 50%, we get:
d1 = 1.55
d2 = 0.55
N(d1) = 0.9394
N(d2) = 0.7088

Plugging these values into the Black-Scholes formula, we get:
C = $30*0.9394 - $10*e^(-0.1*1)*0.7088
C = $21.00

Therefore, the possible price for the call option is $21.00 (option C).

Option Valuation: Consider a Call Option with a Strike Price