University of Oxford
It is a pleasure to introduce the latest issue of The Journal of Computational Finance.
This issue’s first two papers provide different angles on using so-called neural stochastic differential equations – that is, SDEs with coefficients parameterized by artificial neural networks – for modelling financial derivatives. In the first of these, “Robust pricing and hedging via neural stochastic differential equations”, Patrick Gierjatowicz, Marc Sabate-Vidales, David Šiška, Łukasz Szpruch and Zǎn Zǔrič follow the martingale model approach with overparameterized models of local stochastic volatility type to learn the dynamics of the underlying asset from observed option prices with different maturities. Hedge ratios are obtained as control variates, and the set of calibrated models allows the inherent model risk of more exotic contracts to be assessed.
In contrast, our second paper, “Estimating risks of European option books using neural stochastic differential equation market models” by Samuel N. Cohen, myself and Sheng Wang, follows a market model approach, where the neural SDE dynamics of a factor model for the whole option surface are learned from historical option price time series. The model outperforms standard filtered historical simulation in a detailed comparison of value-at-risk predictions.
In the third paper in the issue, “Least squares Monte Carlo methods in stochastic Volterra rough volatility models”, Henrique Guerreiro and João Guerra introduce a least-squares Monte Carlo method for options on the Chicago Board Options Exchange Volatility Index (VIX) that is applicable to models with state-dependent and non-Markovian volatility of volatility. The performance and market fit are demonstrated in careful numerical tests.
The last paper in this issue, “Analytical conversion between implied volatilities based on different dividend models” by Vladimir Lucic and Vladimir Jovanovi´c, addresses a practical problem that is often overlooked in the literature: namely, the treatment of dividends in implied volatility calculations. The authors derive a new generic formula and demonstrate its stability in numerical tests.
I trust that you will find the papers in this volume of interest.
The authors propose a model called neural SDE and demonstrate how this model can make it possible to find robust bounds for the prices of derivatives and the corresponding hedging strategies.
Estimating risks of European option books using neural stochastic differential equation market models
The authors investigate how arbitrage-free neural stochastic differential equation market models can produce realistic scenarios for the joint dynamics of multiple European options on a single underlying and demonstrate how they can be used as a risk…
The authors offer a VIX pricing algorithm for stochastic Volterra rough volatility models where the volatility is dependent of the vol-of-vol which reproduces key features of real-world data.
The authors propose an explicit formula for the conversion of implied volatilities corresponding to dividend modelling assumptions which covers a wide range of strikes and maturities.