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.
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