Re: Heston and ExactVariance
Posted by
Dimathematician on
Oct 02, 2009; 5:59am
URL: http://quantlib.414.s1.nabble.com/Heston-and-ExactVariance-tp13047p13054.html
A better name or a better scheme :)? The Broadie Kaya scheme could be added of course. As
far 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
<[hidden email]>
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
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