Option Pricing with Orthogonal Polynomial Expansions
Mathematical Finance, Forthcoming
40 Pages Posted: 29 Nov 2017 Last revised: 9 Jun 2019
Date Written: May 20, 2019
We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accurately as the Fourier transform based method in the nested affine case. We also derive and numerically validate series representations for option Greeks. We depict an extension of our approach to exotic options whose payoffs depend on a finite number of prices.
Keywords: Greeks, Option Pricing, Orthogonal Polynomials, Parameter Sensitivity, Polynomial Diffusion Models, Stochastic Volatility
JEL Classification: C32, G12, G13
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