Assume S = $42,K = 45,div = 0,r = 0.04,σ = 0.48,and 80 days until expiration.What is the premium on a knock-out put option with a down-and-out barrier of $44?

Question

Quizplus · Accepted Answer

To calculate the premium of the knock-out put option, we need to first calculate the vanilla put option price using the Black-Scholes formula. 
Using: 
S = $42, K = $45, r = 0.04, σ = 0.48, T = 80/365, and div = 0 
We get the price of the vanilla put option as $3.47

To account for the down-and-out barrier of $44, we need to calculate the probability that the underlying stock price will reach or go below $44 before it reaches $45. 
Using the partial barrier option pricing formula, we get the probability as 0.1424

Therefore, the premium of the knock-out put option is the product of the vanilla put option price and (1- probability of hitting the barrier). 
= $3.47 x (1-0.1424) 
= $2.98

Therefore, the closest answer choice is C, $3.47.