I posted the question below earlier today, and got an answer that pretty much matched what I had done myself. However, I do have a question. The answer that was provided to me was $3.00 for the common risk-neutral price. When I did the problem myself, I also got $3.00 at one point. But since both the options (down-and-in and down-and-out) have equal risk-neutral prices, don't I have to divide $3.00 by 2 to get $1.50 for the final answer? Hope my question makes sense! 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 posted the question below earlier today, and got an answer that pretty much matched what I had done myself. However, I do have a question. The answer that was provided to me was $3.00 for the common risk-neutral price. When I did the problem myself, I also got $3.00 at one point. But since both the options (down-and-in and down-and-out) have equal risk-neutral prices, don't I have to divide $3.00 by 2 to get $1.50 for the final answer? Hope my question makes sense!
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.
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