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I am currently working on comparing different models for modelling the volatility and then pricing vanilla options (I use option prices on real stocks in order to calibrate my models and then I compare them). I already implemented the Heston model (close form formula and Monte-Carlo) and the SABR models.

I was wondering if you have any ideas of which stochastic volatility models I can also use (if you have any paper about recent models for example). I have heard about Jacobi model but I was not able to find anything about this.

I had also in mind to compare with the result I obtain from the SVI model but as it is not really a stochastic volatility model, I would like to find something else I can work on.

Thank you in advance for your ideas !

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  • $\begingroup$ There are many good articles in this issue. What are you looking for exactly? $\endgroup$ – user16891 Aug 16 '15 at 11:26
  • $\begingroup$ I am looking for any stochastic volatility models that can be interesting to implement and compare. I am just a bit lost and I don't know what to look at for this. I have now implemented Heston and Sabr models, so I would like to stay on the same king of models but maybe more recent, which can be potentially used in the industry for option pricing on stocks. $\endgroup$ – Matt59 Aug 16 '15 at 13:32
  • $\begingroup$ Did you already look into jump models or central tendency models? $\endgroup$ – Phun Aug 16 '15 at 13:55
  • $\begingroup$ I had a look on models with jumps (such as Heston and Sabr with jumps in the price process and in the volatility process) but I don't know if it is really worthy to implement it. What do you mean by central tendency models ? (I have never heard about this I think) $\endgroup$ – Matt59 Aug 16 '15 at 13:58
  • $\begingroup$ Could you specify in what respect you are comparing the different models (fit to vanilla options, parameter stability, use for pricing exotic options, etc)? If your goal is to get the best fit of a model in terms of pricing errors for vanilla options, models with jumps in the asset price process are definitely advisable for the short end. $\endgroup$ – pbr142 Aug 16 '15 at 15:23
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You can look at Bergomi's variance curve model (see his Smile Dynamics articles).

Another interesting article is Bergomi and Guyon's smile in stochastic volatility model where they give a very nice second order expansion of the smile in vol of vol that is valid in all stochastic volatility models.

Also note there is no point in using a stochastic volatility model to price vanilla options. All you need to do is interpolate a volatility surface. So what you are comparing by looking at vanilla options is actually the quality of your calibration. If you want to see the differences between stoch vol models, you should price path dependant options (forward start options in particular).

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  1. Comparing stochastic volatility models through Monte Carlo simulations(2006)
  2. Applications of Fourier Transform to Smile Modeling(2010)
  3. Extension of Stochastic Volatility Equity Models with Hull-White Interest Rate Process
  4. Comparison Of Stochastic Volatility Models.

The second reference is very good in this context. I hope you can download it.

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  • $\begingroup$ Thank you for your references, I can have access to the second reference, I'll have a look on it. But I can't access the 3rd link you posted $\endgroup$ – Matt59 Aug 16 '15 at 16:45
  • $\begingroup$ ta.twi.tudelft.nl/mf/users/oosterle/oosterlee/Hybrid_SZHW.pdf $\endgroup$ – user16891 Aug 16 '15 at 17:22
  • $\begingroup$ Also "The Volatility Surface " by Jim Gatheral is useful.eu.wiley.com/WileyCDA/WileyTitle/productCd-0471792519.html $\endgroup$ – user16891 Aug 16 '15 at 17:29
  • $\begingroup$ Thank you, this is already the main book I used for the background theory about stochastic volatility modeling. That's the reason why I think to test some models as SVI (this is what Gatheral is working on with some teachers of my university) but as it is not, I am still trying to find some other stochastic volatility models. $\endgroup$ – Matt59 Aug 16 '15 at 17:39
  • $\begingroup$ Do you know Double Heston ? $\endgroup$ – user16891 Aug 16 '15 at 17:42

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