Re: [Quantlib-dev] Heston and ExactVariance

[Dima <dim...@go...>]

A better name or a better scheme :)? The Broadie Kaya scheme could be added
of course. Asfar as I understand you're sampling from chi square as they do.
But then you use this variance
in the next step for the asset. They do a full sampling of the variance from
t to t+\Delta for the
asset. And then I get lost since you do multiply with rho/sigma... in the
drift and subtract...
Do you have a source for your approach? Thanks



2009/10/1 Klaus Spanderen <kl...@sp...>

> Hi
>
> your are right, exact variance is not the exact simulation alogrithm as
> proposed by Broadie and Kaya. "exact variance" here means that the variance
> part of the Heston process is sampled from the "correct" non-central chi
> square distribution.
>
> May be we should change the name of the scheme. Do you have a better one?
>
> best regards
>  Klaus
>
>
> ----- original message --------
>
> Subject: [Quantlib-dev] Heston and ExactVariance
> Sent: Thu, 01 Oct 2009
> From: Dima
>
> Hi All,
>
> I appologize for the frequency of the initialized discussions, but I'm
> browsing through a lot of
> QuantLib code and need to discuss the issues. I hope that nobody is annoyed
> and the
> discussions add some value to the library.
>
> I had a look at Heston and the exact variance method. There were some
> questions on Wilmott
> about what the code does and some user requests. As far as I can see this
> is not the method
> proposed by Broadie and Kaya in "Exact Simulation of stochastic
> volatility..." which is what
> is commonly understood as the exact simulation approach. Which might be
> misleading. And
> I didn't find out what is actually done and if there is some approximation
> happening. Can anyone
> elaborate?
>
> As a side note: I don't think it is good coding practice to pass normal
> random variables to "evolve"
> and transform them to other variables within the code. What is often done
> is: take normal, take
> cdf to get uniform, take inverse of other cdf to get a sample of the random
> number corresponding
> to this cdf. Don't know how good the random variables are if generated in
> that way, also the interface
> will be hard to understand. I think there should rather be a way to pass
> the random variables directly.
>
> Best regards, Dima
>
>
> --- original message end ----
>
>
>