Talk:Stochastic volatility

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 $$\omega/\theta$$ instead of $$\omega$$ (It's the value of $$\nu_t$$ that would make the coefficient on $$dt$$ zero). Since the text specifically calls $$\omega$$ 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)

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)

Volatility (finance)
The initial sentence of this article makes it look as if it's about a concept in finance rather than about stochastic volatility in general. We need to distinguish if from the other article titled Volatility (finance), or else merge the two articles. Michael Hardy (talk) 16:41, 6 February 2009 (UTC)

Standard deviation of dW
The article states "dW is a standard gaussian with zero mean and unit standard deviation."

That is incorrect. dW has a variance of dt. And the integral of dW from 0 to T (W(T)) has a variance of T. — Preceding unsigned comment added by 209.167.126.66 (talk) 16:06, 30 August 2011 (UTC)

Form of 3/2 model
My source for the 3/2 model, Lewis "Option Valuation Under Stochastic Volatility" (2000) has a different form for the 3/2 SDE. Please see page 5. Theta is not outside the bracket in the drift term. This means that the real 3/2 can have a drift term with V and no V^2. The way that it was being shown on this page made that impossible. I've now changed it to reflect what's in Lewis. — Preceding unsigned comment added by 124.189.64.231 (talk) 01:05, 13 July 2013 (UTC)