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!

Financial Management: Theory & Practice
16th Edition
ISBN:9781337909730
Author:Brigham
Publisher:Brigham
Chapter8: Financial Options And Applications In Corporate Finance
Section: Chapter Questions
Problem 5MC: In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM). (1)...
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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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