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.
Exact Solutions for a GBM-type Stochastic Volatility Model having a Stationary Distribution
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abstract
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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A lognormal type stochastic volatility model with quadratic drift
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.