Fast Derivative Valuation from Volatility Surfaces using Machine Learning

TL;DR

This paper presents a machine learning framework using Gaussian Process Regression to rapidly and accurately price derivatives based on volatility surfaces, significantly speeding up traditional valuation methods for real-time applications.

Contribution

The authors develop a novel ML approach that models derivative valuations from volatility surface parameters, enabling near-instantaneous pricing with high accuracy, surpassing conventional computational methods.

Findings

Achieves 0.5% relative error for variance swap fair strike

Attains 1.7% to 3.5% relative error for American put prices and Greeks

Provides 3-4 orders of magnitude speedup over finite-difference methods

Abstract

We introduce a fast and flexible Machine Learning (ML) framework for pricing derivative products whose valuation depends on volatility surfaces. By parameterizing volatility surfaces with the 5-parameter stochastic volatility inspired (SVI) model augmented by a one-factor term structure adjustment, we first generate numerous volatility surfaces over realistic ranges for these parameters. From these synthetic market scenarios, we then compute high-accuracy valuations using conventional methodologies for two representative products: the fair strike of a variance swap and the price and Greeks of an American put. We then train the Gaussian Process Regressor (GPR) to learn the nonlinear mapping from the input risk factors, which are the volatility surface parameters, strike and interest rate, to the valuation outputs. Once trained, We use the GPR to perform out-of-sample valuations and compare the results against valuations using conventional methodologies. Our ML model achieves very accurate results of $0.5\%$ relative error for the fair strike of variance swap and $1.7\% \sim 3.5\%$ relative error for American put prices and first-order Greeks. More importantly, after training, the model computes valuations almost instantly, yielding a three to four orders of magnitude speedup over Crank-Nicolson finite-difference method for American puts, enabling real-time risk analytics, dynamic hedging and large-scale scenario analysis. Our approach is general and can be extended to other path-dependent derivative products with early-exercise features, paving the way for hybrid quantitative engines for modern financial systems.