assume a security follows a geometric brownian motion with volatility parameter σ = 0.2. assume the initial price of the security is 21 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 19 and expiration 30 days have equal risk-neutral prices. compute this common risk-neutral price.
note time in years (or 252 trading days). so expiration is 30/252 yrs.