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Exact Solutions for a GBM-type Stochastic Volatility Model having a Stationary Distribution

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arxiv 1809.08635 v2 pith:FWAVDDLV submitted 2018-09-23 q-fin.CP

Alan L. Lewis This is my paper · ORCID
classification q-fin.CP
keywords volatilityexactmodelsolutionsdensitygbm-typestationarystochastic
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We find various exact solutions for a new stochastic volatility (SV) model: the transition probability density, European-style option values, and (when it exists) the martingale defect. This may represent the first example of an SV model combining exact solutions, GBM-type volatility noise, and a stationary volatility density.

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  1. A lognormal type stochastic volatility model with quadratic drift

    q-fin.MF 2019-08 conditional novelty 7.0 of 10

    A stochastic volatility model with Generalized Inverse Gaussian steady state is made tractable via a measure change to a polynomial diffusion, enabling fast option pricing with orthogonal polynomials.

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