Signature Volatility Models: Pricing and Hedging with Fourier
Eduardo Abi Jaber, Louis-Amand Gérard
Source abstract
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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