Is there a link between these two models? how can i arrive to the VG from Heston's model?

there is no direct link, namely you can not arrive at VG from Heston. But Carr et al extended a few Levy models to Stochastic Levy models by time change the original process by a Heston/CIR integral. See the paper at http://www.math.nyu.edu/research/carrp/ ... pfinal.pdf

QuoteOriginally posted by: bingfeithere is no direct link, namely you can not arrive at VG from Heston. But Carr et al extended a few Levy models to Stochastic Levy models by time change the original process by a Heston/CIR integral. See the paper at http://www.math.nyu.edu/research/carrp/ ... l.pdfthank you very much

But with a particular definition of the volatility process in Heston model, or with some hypothesis on the process, can i arrive to a gamma distribution of the volatility as in Madan Seneta?

The SV models assume that the process is of the formdS_t/S_t = m_t dt + s_t dW_tHeston is just a special case. In all of them the asset process has continuous sample paths (even if s_t is discontinuous, e.g. regime switching), and by construction the increments are not `iid.'The VG process is purely discontinuous, and the increments are `iid'Therefore I cannot see how one can yield the other. They seem to be sort of opposites...Is that right?K.

My prof told me it's possible, but i don't know how i can do; he says i must make some hypothesis on Heston modelQuoteOriginally posted by: RezThe SV models assume that the process is of the formdS_t/S_t = m_t dt + s_t dW_tHeston is just a special case. In all of them the asset process has continuous sample paths (even if s_t is discontinuous, e.g. regime switching), and by construction the increments are not `iid.'The VG process is purely discontinuous, and the increments are `iid'Therefore I cannot see how one can yield the other. They seem to be sort of opposites...Is that right?K.

Is there anybody with an idea?

your prof is wrong... the Heston model is markovian in 2 variables and diffusive.the vg model is markovian in 1 variable and pure jump. best guess is that he's suggesting sending two parameters in the Heston model to some limit in such a way that it converges to a jumpy process

Maybe..i try to keep the same equation for the price of stock, but something different for the variance. I hope

Any new ideas??

QuoteOriginally posted by: mjyour prof is wrong... the Heston model is markovian in 2 variables and diffusive.the vg model is markovian in 1 variable and pure jump. best guess is that he's suggesting sending two parameters in the Heston model to some limit in such a way that it converges to a jumpy processIn which way?

Could you tell me please?QuoteOriginally posted by: mjyour prof is wrong... the Heston model is markovian in 2 variables and diffusive.the vg model is markovian in 1 variable and pure jump. best guess is that he's suggesting sending two parameters in the Heston model to some limit in such a way that it converges to a jumpy process

You might at least look at:Chourdakis Kyriakos 'Option pricing using the fractional FFT' J. Comp. Finance Winter 04/05 <FRFT, examples with VG Variance-Gamma, Heston stochastic volatility> Christoffersen Peter, Steve Heston, Kris Jacobs 'Option Valuation with Conditional Skewness'7/04 <S&P 500, GARCH, Jump, Stochastic Volatility> Heston Steven 'Invisible Parameters in Option Prices' JofF 7/93<log-gamma, double sided Gamma, negative binomial distribution>

Thanks a lot QuoteOriginally posted by: jfuquaYou might at least look at:Chourdakis Kyriakos 'Option pricing using the fractional FFT' J. Comp. Finance Winter 04/05 <FRFT, examples with VG Variance-Gamma, Heston stochastic volatility> Christoffersen Peter, Steve Heston, Kris Jacobs 'Option Valuation with Conditional Skewness'7/04 <S&P 500, GARCH, Jump, Stochastic Volatility> Heston Steven 'Invisible Parameters in Option Prices' JofF 7/93<log-gamma, double sided Gamma, negative binomial distribution>