Choosing Stochastic Volatility Models and Comparing Their Pricing
Summary
The discussion recommends several directions for comparing stochastic volatility models used in option research, including published comparisons, Fourier-based smile modeling, extensions with stochastic interest rates, and Bergomi-style variance curve models. It also highlights work deriving a second-order expansion of the implied volatility smile in volatility of volatility that applies across stochastic volatility models.
A central point is that vanilla option prices alone may not distinguish these models: a sufficiently flexible volatility surface interpolation can reproduce vanilla prices, so fit quality primarily reflects calibration. To investigate differences in model dynamics, the response recommends pricing path-dependent products, especially forward-start options. These suggestions are research directions rather than a complete benchmark: the document provides no implementation details, data, or empirical comparison results, and model usefulness depends on the products and dynamics under study.
Key ideas
- Potential model families and references include Bergomi variance curve approaches and stochastic volatility models with stochastic rates.
- Smile expansions can provide a way to compare model implications across stochastic volatility specifications.
- Vanilla option fit largely evaluates calibration when a volatility surface can be interpolated directly.
- Path-dependent options, particularly forward-start options, can expose differences in model dynamics.
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# Ideas about Stochastic volatility models # Ideas about Stochastic volatility models 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 ! ## Answer by user16891 (score 4) https://quant.stackexchange.com/a/19345 - Comparing stochastic volatility models through Monte Carlo simulations(2006) - Applications of Fourier Transform to Smile Modeling(2010) - Extension of Stochastic Volatility Equity Models with Hull-White Interest Rate Process - Comparison Of Stochastic Volatility Models. The second reference is very good in this context. I hope you can download it. ## Answer by AFK (score 4) https://quant.stackexchange.com/a/21234 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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