Hello everyone,Sorry for my english I'm not good at it.Actually I have developped an algorithm to price Call and Put by the Heston Model.Then I use the Levenberg Marquardt Algorithm to calibrate data from the market.So I have a set of five parameters : kappa, rho, theta, v0, lambdaBut I don't know how to use it to price exotic products. All I can find on the web was formula based on BS products.I have some idea but I'm not sure like the only difference between the price of a call for Heston and BS is P1 and P2 whereas N(d1) and N(d2) maybe I have to use these probabilities in the exotics formula ? Can you help me for this ?Thanks for all

now with the calibrated parameters you could simulate paths of vol and underlying using monte-carlo and price exotics or path-dependents

Quotenow with the calibrated parameters you could simulate paths of vol and underlying using monte-carlo and price exotics or path-dependentsHave you got any documents or sources that I can consult to have a better idea. I found this forum :http://www.nabble.com/Question-on-Path- ... 24.htmlbut he doesn't tell us the mathematics behind.Thanks for your help amit7ul

Someone else can help please ?

First, is this a real exercise? (i.e., there is a real exotic you aretrying to value?). In that case, you are warned that what you are doing maybe very dangerous. I will assume that the answer is no, andthis is just a student exercise. Then, for some types of exotics, as amit7ulpointed out, the easiest way to proceed is to write a Monte Carlo (MC)program. If you have never done that, you should start withsimple Black-Scholes, then move up to the euro-style Hestonputs and calls that you can already value, and then finally do yourexotic. For options with early exericse opportunities, I suggest a PDEframework. For follow-up, you should post exactly what types of exoticsyou want to value, and your experience with MC and PDEmethods.

So do people in the industry still use Heston? If so, how do you account for 31/8/08 to 12/08? - VIX doesn't look like a CIR type process!!

How do you account for the volatility of that period? Well ex-post is easy.Predicting some of the burst before the fact is also possible. Ages ago when I worked for a money manager, I developed a simple volatility predictor thatcombined GARCH forecasts, VIX, and some exogenous variables. One ofthe latter was a dummy for recessions because if you know you'rein one, that raises market volatility both on the downside (early in) and the typical subsequent upside bounce(s). Setting the dummy to oneis a judgement call, though, because the official recession arbiterin the US (the NBER) is slow to call it. The point is, once you set it,all your vol. predictions take a jump upward. Not a panacea, but something useful.Obviously, forecasting is an art -- there are a zillion possible exogenous parameters-- how many are helpful?. Go find out. There are also forward looking vol. indicators, too, like VIX futures, vol. swaps, etc. In the end, there is a huge amount of noise in volatility, but still (unlike returns), it -is- somewhat predictable.

QuoteOriginally posted by: MonkeyDLuffyQuotenow with the calibrated parameters you could simulate paths of vol and underlying using monte-carlo and price exotics or path-dependentsHave you got any documents or sources that I can consult to have a better idea. I found this forum :http://www.nabble.com/Question-on-Path- ... 24.htmlbut he doesn't tell us the mathematics behind.Thanks for your help amit7ulMonkey,I think the paper "Efficient Simulation of the Heston Stochastic Volatility Model" by Leif Andersen is good, I think you might have already seen it.Also maybe you can refer to Jim Gatheralls book "The volatility surface", you will also find other models besides heston there, and also derivation of call/put premia formulae.Also, if this is a first timers exercise, I think using python/matlab for prototyping will be good.Cheers...

QuoteOriginally posted by: AlanHow do you account for the volatility of that period? Well ex-post is easy.Predicting some of the burst before the fact is also possible. I developed a simple volatility predictor thatcombined GARCH forecasts, VIX, and some exogenous variables.Hi Alan, can you suggest something to read on such forecasting, especially "combinations"....Thanks,Manik

Hi Manik,I would google "GARCH with exogenous" variables or some such. You can also search thisforum for more discussions on this topic by me. Of course, there is a huge literature onforecasting generally.