Talk:Stochastic volatility

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[edit] Form of Heston model

My source for the Heston equation was Inside Volatility Arbitrage, A. Javaheri, pg. 47, which it gives as

d\nu_t = (\omega - \theta\,\nu_t)dt + \xi \nu_t^p\,dB_t \,

where p = 0.5

I'm afraid I don't have access to the paper you cited to compare it - can you kindly point me to a publicly available copy? I do have access to Javaheri, perhaps we can get this straightened out. Thanks. Ronnotel 14:17, 27 February 2007 (UTC)

Both formulas are mathematically equivalent, but the equation you use has long run mean ω / θ instead of ω (It's the value of νt that would make the coefficient on dt zero). Since the text specifically calls ω the long run mean, I changed the formulas. As far as I know, there is no publicly available copy of Heston's original article, but since it was referred to in the article, I checked the original equation. It reads (in the original notation)

d\nu_t = \kappa(\theta-\nu_t)dt+\sigma\sqrt{\nu_{t}}\sigma dz(t).

Froufrou07 17:22, 27 February 2007 (UTC)

Fair enough. Btw, I consider this page a stub and I would appreciate any contribution you can make. Ronnotel 18:17, 27 February 2007 (UTC)

[edit] explicit solution

The explicit solution of the stochastic differential equation is missing a square root of time;

the dW term should be multiplied by sqrt(T)

Right?


No, because the variance of W_t is already sqrt(t). A. Pichler 19:50, 14 August 2007 (UTC)