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 be $3.00 or $1.50? Some people I've been working with on this problem think the answer is $3.00 and some think $1.50. Which is it? And why? Thanks!
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 be $3.00 or $1.50? Some people I've been working with on this problem think the answer is $3.00 and some think $1.50. Which is it? And why? Thanks!
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