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I've read even in recent papers, and on page 21 of the book "The Volatility Surface" by Jim Gatheral (2006), all the debate over whether to reflect or truncate negative variances whilst simulating the Heston process and the subsequent ramifications of what doing that entails, etc.

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It seems the solution is so simple it might have escaped them, but why not just reject the sample if it results in variance going negative and drawing another entirely different sample?

The pseudo-random generator is supposed to generate identically distributed independent increments. So, there is no chance of an infinite sequence of draws causing the algorithm to cease to terminate since usually in my testing the very next draw, or perhaps the next is sufficient to draw a sample avoiding the negative variance situation; this should not bias the process theoretically in any way.

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  • $\begingroup$ Can you pls mention at least one source with the name of the article, authors, page number(s) and publication date in regards to the summary you have made in the first paragraph of your post? $\endgroup$
    – Alper
    Feb 19, 2023 at 9:51
  • $\begingroup$ Wouldn’t this lead to bias? $\endgroup$
    – Bob Jansen
    Feb 19, 2023 at 11:54
  • $\begingroup$ @Alper sure, let me find them $\endgroup$
    – crow
    Feb 19, 2023 at 21:01
  • $\begingroup$ @BobJansen i dont think so, why would it? since the samples are IID then it should make no difference $\endgroup$
    – crow
    Feb 19, 2023 at 21:01
  • $\begingroup$ Because you’re rejecting those samples that go towards zero only. Imagine you do antithetic sampling, you would throw away some samples and keep the negation. $\endgroup$
    – Bob Jansen
    Feb 20, 2023 at 1:56

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