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I seem to get much better results if I replace BinormalDistribution[{Sqrt[dt], Sqrt[dt]}, \[Rho]] with BinormalDistribution[{Sqrt[dt], Sqrt[dt]}, \[Rho] dt] This is very strange because the Mathematica documentation clearly states that BinormalDistribution takes the correlation $\rho$ as input, whereas the covariance is given by $\rho \, dt$. I will ...

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Thanks for the responses. I'm still puzzling over this. Here is an implementation which uses both Milstein discretization as well as antithetic variables. The code constructs the volatility skew for a T = 574 day call with initial forward price G0 = 570.856 and rate of interest r = 0.05327. The volatility skew is clearly crazy: it is concave with a ...

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The issue I have with these approaches is that they use the unconditional distribution to eliminate the latent volatility. However, when the volatility process has very weak mean reversion one would need a very long and clean sample to make robust parameter identification from the unconditional density. They just throw away all the information from the ...

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Some simple improvements: 1) Replace the Euler discretization approximation of the volatility to a Milstein discretization approximation. See e.g. these notes by Rouah. 2) 100 Paths is a very low number of paths, and leads to a big standard error in your estimate. So this should be increased by a factor of ~100. 3) You should use some form of variance ...

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change the discretization and use the QE-M approach: Andersen (2006) the bias is way smaller than the one of the simple Euler. further u can try to use control variates/anthitetic numbers to reduce the sample variance.

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