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Alaster1213
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Heston Model: Zhu scheme

July 7th, 2012, 6:51 am

Hi everyone, I am trying to use Monte Carlo for heston model. I have implemented several schemes including QE-M, Alfonsi, Zhu etc. Now, I am trying to combine Zhu scheme with asset price process in Andersen(2007), and I have followed the martingale correction in Gauthier and Possamai (2010), "Efficient Simulation of the Double Heston Model".downloadUnfortunately, I can't get the correct option price after using martingale correction.Does anybody have any idea about this?Thanks
 
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Alan
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Heston Model: Zhu scheme

July 7th, 2012, 4:15 pm

In my experience, problems with MC's and "sqrt" models are typically due to repeated hits on V=0.So, I would first try to get your scheme working well for relatively short time horizons with the Feller condition(s) satisfied (so nohits in the continuum limit) and forget that 'martingale correction'. The 'full truncation' method should work ok.Then, try cases when the Feller condition(s) are violated but T < 3, say, again without the martingale correction.If your real interest lies in setups more difficult than this, MC may not be the way to go at all, and youshould probably elaborate on what you are trying to accomplish.
Last edited by Alan on July 6th, 2012, 10:00 pm, edited 1 time in total.
 
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Cuchulainn
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Heston Model: Zhu scheme

July 8th, 2012, 4:01 pm

QuoteIn my experience, problems with MC's and "sqrt" models are typically due to repeated hits on V=0.Standard numerical methods (FDM, e.g. Euler...) for SDE do not converge monotonically. i.e. increasing NT, NSIM does not imply better convergence. This is lack of predictability.Is FDM the right approach? In the engineering literature SFEM is used, even Karhunen-Loeve.
Last edited by Cuchulainn on July 7th, 2012, 10:00 pm, edited 1 time in total.
 
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Alan
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Heston Model: Zhu scheme

July 8th, 2012, 4:20 pm

I don't think anybody can say until we know what the OP is trying to accomplish.
 
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Lapsilago
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Heston Model: Zhu scheme

July 8th, 2012, 7:30 pm

Have you applied the exact sampling scheme proposed by Broadie and Kaya.If you could give the vals of the variables you use we can compare prices...
 
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Alaster1213
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Heston Model: Zhu scheme

July 8th, 2012, 8:02 pm

Thanks for all reply,Comparing to the price from closed-form formula, the price from Zhu scheme (before martingale correction) is quite close. The problem is I think there is something wrong with the martingale correction part, which I have followed Gauthier and Possamai(2010).I want to do the martingale correction for efficiency comparison.
 
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mj
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Heston Model: Zhu scheme

August 2nd, 2012, 8:29 am

Have you tried Chan--Joshi?http://ssrn.com/abstract=1617187Code downloadable from markjoshi.com