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arXiv · 2402.01820

Signature volatility models: pricing and hedging with Fourier

Eduardo Abi Jaber·Louis-Amand Gérard
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Abstract

We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is remarkably universal, as it includes, but is not limited to, the celebrated Stein-Stein, Bergomi, and Heston models, together with some path-dependent variants. Second, we derive the joint characteristic functional of the log-price and integrated variance provided that some infinite dimensional extended tensor algebra valued Riccati equation admits a solution. This allows us to price and (quadratically) hedge certain European and path-dependent options using Fourier inversion techniques. We highlight the efficiency and accuracy of these Fourier techniques in a comprehensive numerical study.

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Eduardo Abi Jaber, Louis-Amand Gérard. 2024-02-02. Signature volatility models: pricing and hedging with Fourier. https://doi.org/10.1137/24m1636952

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