Hedging option books using neural-SDE market models

Abstract

We study the capability of arbitrage-free neural-SDE market models to yield effective strategies for hedging options. In particular, we derive sensitivity-based and minimumvariance-based hedging strategies using these models and examine their performance when applied to various option portfolios using real-world data. Through backtesting analysis over typical and stressed market periods, we show that neural-SDE market models achieve lower hedging errors than Black-Scholes delta and delta-vega hedging consistently over time, and are less sensitive to the tenor choice of hedging instruments. In addition, hedging using market models leads to similar performance to hedging using Heston models, while the former tends to be more robust during stressed market periods.

Continuous‐time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations

“…Neural network SDEs-sometimes referred to as neural-SDEs-are SDEs where the drift and/or volatility of the SDE is a neural network. Neural SDEs have recently become of great interest in mathematical finance (Arribas et al, 2020;Cohen et al, 2023Cohen et al, , 2022Cohen et al, , 2022bGierjatowicz et al, 2020;Ni et al, 2021).…”

“…We now consider a slightly more complex model where the intensity dynamics are given by a neural network. Neural network (or "neural SDEs") have been widely studied in the financial mathematics literature (Arribas et al, 2020;Cohen et al, 2023Cohen et al, , 2022Cohen et al, , 2022bGierjatowicz et al, 2020;Ni et al, 2021). Neural network Hawkes processes (or "neural Hawkes processes") have also been recently studied and implemented in a number of papers for modeling order book data (Kumar, 2021;Lu and Abergel, 2018;Shi & Cartlidge, 2022).…”