Fast Derivative Valuation from Volatility Surfaces using Machine Learning

2025-05-29

AI Summary

This paper addresses the inefficiency and inflexibility of real-time pricing and Greeks computation for volatility-surface-dependent derivatives—such as variance swaps and American put options. We propose a novel machine learning framework integrating the Stochastic Volatility Inspired (SVI) parameterization with Gaussian Process Regression (GPR). Our approach innovatively couples SVI surface parameters with term-structure dynamics and employs GPR to directly learn the nonlinear mapping from risk factors to prices and first-order Greeks (Delta, Gamma). Trained on synthetic data and rigorously validated against Crank–Nicolson finite-difference benchmarks, the model achieves millisecond-scale inference: relative pricing error is 0.5% for variance swaps and 1.7%–3.5% for American puts and their Greeks. Computational speed improves by three to four orders of magnitude over conventional numerical methods, enabling real-time risk management and large-scale scenario analysis.

Technology Category

• Machine Learning: Learning with Manifolds
• Reasoning under Uncertainty: Stochastic Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Fast ML pricing of derivatives using volatility surfaces
• Accelerating valuation for variance swaps and American puts
• Enabling real-time risk analytics and dynamic hedging

Innovation

• Machine Learning framework for derivative pricing
• Gaussian Process Regressor for valuation mapping
• Real-time risk analytics with speedup