Hi, I am reading Andersen (2008), "Efficient Simulation of the Heston Stochastic Volatility Model". In this paper, he used QE scheme to model the square root process Vs in Heston model. My question is: is it true that when h goes into zero, the calculated asset price XT will converge to its true price? That's, is it weak convergent? Or there is some bias? Many thanks.

Can't answer your question on convergence rate but the experiments by Joerg Kienitz and myself show QE outperforms all other standard FD schemes.

QuoteOriginally posted by: outrunI just finished implementing Euler with full truncation (with a lot of help from the people here) described in A Comparison of Biased Simulation Schemes for Stochastic Volatility Models and that is proven to have strong convergence (see section 4.3)Well, I was reading your very nice paper SEVERAL WEEKS ago, and it is quite interesting. Wilmott forum is a small world, isn't it? haha, I finished my master in Netherlands. ^_^Many thanks.

QuoteWilmott forum is a small world, isn't it? haha, I finished my master in Netherlands. ^_^Wilmott is a hotbed of Dutch posters!

QuoteOriginally posted by: CuchulainnQuoteWilmott forum is a small world, isn't it? haha, I finished my master in Netherlands. ^_^Wilmott is a hotbed of Dutch posters!Well, That is very nice. I used to presume most of them were from USA or UK. ^_^I would like to test the weak order by experiments, which critiera to use, please? I see that from the definition of week error, it is |E(f(Xnh)-Ef(XT)|, where there is a wild choice of function f satisfying a certain smooth property. I mean, which f(x) is usually used to produce best experimental result? What is the difference? Many thanks .

QuoteOriginally posted by: fmfreshmanQuoteOriginally posted by: CuchulainnQuoteWilmott forum is a small world, isn't it? haha, I finished my master in Netherlands. ^_^Wilmott is a hotbed of Dutch posters!Well, That is very nice. I used to presume most of them were from USA or UK. ^_^I would like to test the weak order by experiments, which critiera to use, please? I see that from the definition of week error, it is |E(f(Xnh)-Ef(XT)|, where there is a wild choice of function f satisfying a certain smooth property. I mean, which f(x) is usually used to produce best experimental result? What is the difference? Many thanks .Small population, big impact.

QuoteOriginally posted by: fmfreshmanQuoteOriginally posted by: CuchulainnQuoteWilmott forum is a small world, isn't it? haha, I finished my master in Netherlands. ^_^Wilmott is a hotbed of Dutch posters!Well, That is very nice. I used to presume most of them were from USA or UK. ^_^I would like to test the weak order by experiments, which critiera to use, please? I see that from the definition of week error, it is |E(f(Xnh)-Ef(XT)|, where there is a wild choice of function f satisfying a certain smooth property. I mean, which f(x) is usually used to produce best experimental result? What is the difference? Many thanks .You can try f(x) = (5+3x^4)/(2+5*x) and comprare results with : http://cermics.enpc.fr/reports/CERMICS- ... 05-279.pdf page 26

Desmond Higham proved some convergence results for Heston.Things have moved on quite a bit since 2008 when the "biased simulations schemes" was written.See eg http://ssrn.com/abstract=1617187

QuoteOriginally posted by: CuchulainnCan't answer your question on convergence rate but the experiments by Joerg Kienitz and myself show QE outperforms all other standard FD schemes.Did you implement van Haastrecht and Pelsser's NCI method and Glasserman and Kim's Gamma Expansion?

QuoteOriginally posted by: QuantCentralQuoteOriginally posted by: CuchulainnCan't answer your question on convergence rate but the experiments by Joerg Kienitz and myself show QE outperforms all other standard FD schemes.Did you implement van Haastrecht and Pelsser's NCI method and Glasserman and Kim's Gamma Expansion?No. Did you have links to these?

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: QuantCentralQuoteOriginally posted by: CuchulainnCan't answer your question on convergence rate but the experiments by Joerg Kienitz and myself show QE outperforms all other standard FD schemes.Did you implement van Haastrecht and Pelsser's NCI method and Glasserman and Kim's Gamma Expansion?No. Did you have links to these?van Haastrecht and Pelsser's NCI methodGlasserman and Kim's Gamma Expansion

Thanks!