Assume S = $51,K = $50,div = 0.0,r = 0.05,σ = 0.20,and 55 days until expiration.What is the premium on a knock-in call option with a down-and-in barrier of $48?

Question

Quizplus · Accepted Answer

To calculate the premium on a knock-in option, we need to first determine if the barrier has been hit. In this case, the barrier is down-and-in, which means the option will only become active if the stock price falls below $48. Based on the current stock price of $51, this means the barrier has not been hit and the option is not active. Therefore, the premium will be equal to that of a regular call option.

We can use the Black-Scholes formula to calculate the premium:
d1 = [ln(S/K) + (r + σ²/2)t]/(σ√t) = [ln(51/50) + (0.05 + 0.20²/2)(55/365)]/(0.20√55/365) = 0.5098
d2 = d1 - σ√t = 0.5098 - 0.20√55/365 = 0.3158
N(d1) = 0.6944
N(d2) = 0.6236

Premium = S*N(d1) - K*exp(-r*t)*N(d2) = $2.55

Therefore, the answer is B) $0.185.