Help!! I am at a loss on how to do thisQuestion : Option Pricing and Integration Consider a basic European Barrier Knock Up and In Call, whose price is given by the expectation call = exp ^(-rT) E[0,ST -K]+ for all ST >BWherer = local interest rateST = price at maturity time TK = strike price B = barrier Note B > K Derive the formula for pricing this option starting from standard geometric Brownian motion formula given below.ST =S0 exp{(r-g- (v^2)/2)T + vW(T)}Whereg = foreign interest rate or dividend rateT = maturity timeS0 = spot price at t=0 v = volatility W(T) = Wiener process = Z(T^1/2) and Z = N(0,1)Hints: · We are interested in the case where S(T) = B· Solve for this special barrier case in terms of Z, use this later on after the integration is solved· Split the expectation (S-K) into integrals S and K. · Solve each integral – easiest way is arrange each integral such that the subject of the integral is in the form of the standard marginal normal distribution. Then you can assume the integral of the marginal distribution is equation to the cumulative distribution. You will have to make use of the sum of squares property to do this.· Once the integral is solved then substitute in the special case for Z· Subtract Integral 2 form 1 to get the final formula, remember to discount the integral or expectationHelpful references: Zhang – Exotic OptionsExotic options : a guide to second generation options / Peter G. Zhang.

this is in my book... as well as any number of other books

Check out this paper by Rich: "The mathematical foundations of barrier option-pricing theory"

Hi, where can i find that paper?thanks

apologize for following up an old thread, but did someone have an electronic version of thispaper (or something equivalent)? Rich: "The mathematical foundations of barrier option-pricing theory"Regards,--Dan

I have used Heston Model and Monte-Carlo-Simulation to price the Barrier Options that were traded at EUWAX (down-and-out calls and up-and-out puts with barrier = Strike). And I have found that the violation between Model-Price and the Market-Price by at the Money Barrier Options (barrier in the near of S0) are higher than those in the Money and out the money Options. Does anybody have a explanation ?Thanks in advance

As noted below, the paper you want isDon Rich, "The Mathematical Foundations of Barrier Option Pricing"Advances in Futures and Options Research, Volume 7, pages 267-311,1994, ISBN 1-55938-748-3