Hello Evereyone!I am pricing barrier options analytically as well as using Monte Carlo simulation in Matlab(GUI). I am getting a big difference between both the option prices. Can anyone tell me how to minmize this difference?Thanks.Festivie

My first guess would be, that the analytic formula you use prices continously monitored barrier options, while you can't price those with MC - at least not without tricks. So you are comparing the price of a continously monitored barrier options with one of a discrete monitored one. There exists a "continuity correction" from Broadie, Glasserman and Kou which you can also find in Haug's book. You can also use the "reverse" correction to price continously barriers with MC.

Buba is right you need to correct for the probability that the path breaches the barrier between your dicsrete simulation dates. Brownian bridge is the key word here. Leif Andersen has a paper "Exact Exotics" on that. and I believe Phil. Dybvig has one on that too. good luck

Do you have any sources for that paper "Exact Exotics"?

QuoteOriginally posted by: festivieHello Evereyone!I am pricing barrier options analytically as well as using Monte Carlo simulation in Matlab(GUI). I am getting a big difference between both the option prices. Can anyone tell me how to minmize this difference?Thanks.FestivieIf you can give me the type of barrier option and the input data I am willing to try it using FDM schemes. And if using discrete monitoring we can use Kou to approximate as a continuous monitoring problem. What is also possible with FDM is to time-step and check at the monitoring dates, and we may get jumps in the solutions, but thet can be handled.

i believe the paper was published in RISK megazine so one can not find it in any public domain. i have an edition of risk seminal papers thats where i got the paper.

hi cuch,do you talk about how to handle jumps, e.g. Levy jumps with continous jump density, to price barriers in your new book? is it in a backward eqn or forward? (please answer, because i might buy one, ^_^ just kidding)

Should the differences be that big??

QuoteOriginally posted by: bingfeihi cuch,do you talk about how to handle jumps, e.g. Levy jumps with continous jump density, to price barriers in your new book? is it in a backward eqn or forward? (please answer, because i might buy one, ^_^ just kidding)bingfei,My book does discuss the Mertton jump model as a PIDE. The PDE part can be a barrier problem.It does not discuss Levy processes as such but I suppose you could modify the SDE and use Ito to get the stuff you want. I just did not look at this Levy aspect there.The PDEs are usually forward in time, backward is a simple matter of changing the sign.If you buy my book I'll sign it for you and it will make both my publisher and me very happy.

QuoteOriginally posted by: playerShould the differences be that big??Player,What differences?

The biaseg pricing a barrier using MC and then applying a bridge to it

you get an order dt^{0.5} biasi've got a paper on www.markjoshi.com on monte carlo jump barrier option pricing with a little discussion of this