American options in the rough Heston model

Abstract: Rough volatility models have emerged as compelling alternatives to classical semimartingale models to capture important stylized features of the implied volatility surface and the time series of realized volatility. The rough Heston model is particularly appealing because its affine structure facilitates the pricing of European options using Fourier techniques. In this work we consider the problem of pricing American options in the rough Heston model. The complexity of the problem stems from the absence of a Markovian-semimartingale structure in the model. To overcome this difficulty we work with a Markovian multi-factor semimartingale stochastic volatility model, which approximates the rough Heston model. In this approximated model, American options can be priced using a backward approach and simulation-based methods. We prove the convergence of American options prices in the multi-factor model towards the prices in the rough Heston model. The proof relies on the explicit expression of the conditional characteristic function of the joint forward process and the spot price, which is a consequence of the affine structure of the model. We illustrate with some numerical examples the behavior of American option prices with respect to some parameters in the model. This is joint work with Etienne Chevalier and Elizabeth Zuniga.

Zoom link: https://univr.zoom.us/j/82694434356