Assume a security follows a geometric Brownian motion with volatility parameter sigma=0.2. Assume the initial price of the security is $25 and the interest rate is 0. It is known that the price of a down-and-in barrier option and a down-and-out barrier option with strike price $22 and expiration 30 days have equal risk-neutral prices. Compute this common risk-neutral price. (I attempted this problem and got a final answer of $1.50. Not sure if that is right.)

Assume a security follows a geometric Brownian motion with volatility parameter sigma=0.2. Assume the initial price of the security is $25 and the interest rate is 0. It is known that the price of a down-and-in barrier option and a down-and-out barrier option with strike price $22 and expiration 30 days have equal risk-neutral prices. Compute this common risk-neutral price. (I attempted this problem and got a final answer of $1.50. Not sure if that is right.)

Corporate Fin Focused Approach

5th Edition

ISBN:9781285660516

Author:EHRHARDT

Publisher:EHRHARDT

Chapter6: Risk And Return

Section: Chapter Questions

Problem 14P

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Assume a security follows a geometric Brownian motion with volatility parameter sigma=0.2. Assume the initial price of the security is $25 and the interest rate is 0. It is known that the price of a down-and-in barrier option and a down-and-out barrier option with strike price $22 and expiration 30 days have equal risk-neutral prices. Compute this common risk-neutral price. I was able to do this problem, but have a question about the interpretation of my answer. I got an answer of $3.00 for the cost of the call option, but how do I answer "compute this common risk-neutral price"? Do I have to divide the answer my 2 for each of the barrier options and say the answer is $1.50? Or because of the fact that it says common does that mean to take the combined value of $1.50+$1.50 to get $3.00 as the answer? I'm just not sure if my answer to the question is $3.00 or $1.50. Does it all depend on the word "common"? Thanks for some clarification.
I was asked to repost the question. It is as follows: Assume a security follows a geometric Brownian motion with volatility parameter sigma=0.2. Assume the initial price of the security is $25 and the interest rate is 0. It is known that the price of a down-and-in barrier option and a down-and-out barrier option with strike price $22 and expiration 30 days have equal risk-neutral prices. Compute this common risk-neutral price. In regards to the above question, I had this follow up question: I am working with the following equation: The risk neutral present value of a "down-and-in" option PLUS the present value of a "down-and-out" option is EQUAL to the risk neutral price of a traditional call option (using Black-Scholes formula). I have calculated the call option to be $3.00 using the Black-Scholes formula. If I am being asked to find the "common risk neutral price", given that the price of a down-and-in barrier option and a down-and-out barrier option are equal, would my answer…
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