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A New Stochastic Volatility Model better and More General than Heston

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 Ahsan Amin, CEO at Infiniti Derivatives Technologies

 Wednesday, July 2, 2014

A New Stochastic Volatility Model better and more general than Heston The model is based on my paper "Solution of Stochastic Volatility Models Using Variance Transition Probabilities and Path Integrals", which can be downloaded from http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2149231 The asset price diffusion is lognormal like in Heston dX/X=sigma(t)sqrt(V(t))dz(t) correlated variance diffusion is given as dV(t)=kappa(theta-V(t))dt+epsilon V(t)^gamma dz(t) with a general volatility exponent gamma. The model is lognormal with mean reverting volatility structure correlated with the asset price that includes correlated heston as a special case but is more general in the exponent of volatility, gamma, in the diffusion of stochastic variance.Heston has this volatility exponent set at half, while a lognormal mean reverting stochastic variance would have this exponent set at one and our model can take any value of this exponent between half and one and can also find a suitable value of this volatility exponent from the option price data so that the model is in good calibration with the option prices data. We can easily price hundreds of possible options at different maturities along the strike price spectrum up to five years in simply a time of the order of a second using this new technique. The way we price the options using our technique, it is very easily possible to simultaneously fit both implied volatility skew and option price skew using this model. We will like to emphasize that this general model cannot be solved by transform techniques.


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1 comments on article "A New Stochastic Volatility Model better and More General than Heston"

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 Julian Cook, Head of Quantitative Research. Fenics Group. GFI NY

 Wednesday, July 9, 2014



I'm interested in your motivation for building a generalized stochastic model? The usual approach is to build a local-stochastic volatility model, since you can fit the smile exactly by construction.. having said that a pure stochastic model would be preferable (well cleaner anyway)

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