implied vol are deduced from a risk neutral worldreturns are not.So, mixing both measures may lead to some incoherent results.

Estimate jump-models? Try mixtures.

Hi,Let Y_t evolve according to:d Y_t = \kappa ( \theta - Y_t) dt + \gamma Y_t d W_t (Linear model, maybe known under another name)I'm looking for contionally expectation and variance.Any help will be greatly appreciated.

Thank you Etuka, your answer is very helpful

<t>Stochastix, Probably many thanks for your help!Stochastix:In the CIR context, we can write: (1)from which, we can deduce:. (2)Unfortunately, for the the log-ou process the conditional expectation of the volatility is: (3)where: (4)Here, we can clearly see that:1) the link between volatilities in ...

I certainly miss something important, but why should it be easy to compute moment of the integrated volatility if i know conditionnal moments?second, it's not easy at all to replicate CIR results for an LOG-OU process...the characteristic function in this case is not tractable at all.

<t>Thanks Stochastix,unfortunately,1) i can't find Lewis's paper2) Bollerslev and Zhou use:i/ a CIR volatility process, ii/ Cox, Ingersoll and Ross (1985) results for the integrated volatility which are based on characteristic function.My goal is to find Var(\bar{V}), when the volatility process is ...

Does anybody knows how to calculateV(1/T \int \sigma_s^2 ds) without using moment generating function or characteristic function.Thanks

Another question which seems to be closely related to this topic: Which tests are generally used to show i) stationarity (first and second order) andii) mean reversionin the volatility?

Noh Engle and Kan (1994) "Forecasting Volatility and Options prices of the S&P 500 Index" will provide you tools to make volatility forecast from a GARCH model.

Taylor, of course...

Nice formula but for b small it does not work well...Please can you tell me how did you get this formula?

For alpha in |N, it's ok, E(X^alpha) are non-centered moments for a Poisson and your algebra is ok.but for b small or alpha in |R ???Unfortunately, it seems to me that there are no analytical answer...

You're right only if you also assume that lambda is sufficiently large (lambda >15,20 for an error <1%).Do you have an idea for E[exp(-X^2)]?

<t>See the statistic's bible: Johnson and Kotz,cdf, N, can be approximate by (for x >=0)N(x) = 1-N'(x)(a_1*t+a_2*t^2+a_3*t^3),where N'(x) is the normal density function,a_1 = 0.4361836a_2 = -0.1201676a_3 = 0.9372980t = (1+0.33267*x)^(-1).maximum error less than 10e-5Or by:N(x) = 1 - [1+(a+b*x)^c]^k,...