New answers tagged heston
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 ...
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.
Heston gives an expression for the characteristic function, from which option prices can be computed. Therefore it can be calibrated (statically) on a set of vanilla option prices with different strikes and maturities. Hence this produces risk neutral parameters that can be used to price other more exotic products. However, it is a pain to estimate the ...
Gatheral (Amazon) has a quite extensive discussion on that, and dives into calibration issues. In summary, what you describe appears to be less of a modeling issue, and more of a calibration problem. This is primarily because the model functions (such as the Heston model) are not by nature convex in their input parameters. This is simply result of the fact ...
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