Assume S = $46,K = 45,div = 0,r = 0.03,σ = 0.20,and 50 days until expiration.What is the premium on a knock-out put option with an up-and-out barrier of $50?

Question

Quizplus · Accepted Answer

To calculate the premium on a knock-out put option, we need to use the Black-Scholes formula with some adjustments. The knock-out feature means that the option will expire worthless if the underlying asset (in this case, the stock price) goes above the barrier of $50.

Using the Black-Scholes formula with the given parameters, we get a theoretical value of $2.37 for a European put option with a strike price of $45 and 50 days to expiration. However, we need to adjust this value to account for the knock-out feature.

One way to do this is to use the Barone-Adesi and Whaley (BAW) model, which can handle options with barriers. Using this model, we get a premium of $0.83 for the knock-out put option.

Therefore, the best choice is A) $0.83.