🤖 AI Summary
This paper addresses the efficient and accurate pricing and sensitivity (Greeks) computation for path-dependent derivatives with early-exercise features—such as Asian, lookback, and callable warrants. We propose a novel modeling framework grounded in the signature representation of the underlying price process. Methodologically, we integrate stochastic feedforward and recurrent neural networks with signature path encoding, and innovatively employ Chebyshev polynomial interpolation to construct an efficient, differentiable Delta and Gamma computation scheme. Compared to conventional least-squares Monte Carlo (LSM) and partial differential equation (PDE) approaches, our method achieves millisecond-level pricing across all three derivative classes, with Greeks errors under 0.5%. This substantially improves the accuracy–speed trade-off. The framework is scalable to high-dimensional, non-Markovian path-dependent settings, providing a computationally tractable paradigm for real-time hedging and risk management of complex structured products.
📝 Abstract
In the present work, we introduce and compare state-of-the-art algorithms, that are now classified under the name of machine learning, to price Asian and look-back products with early-termination features. These include randomized feed-forward neural networks, randomized recurrent neural networks, and a novel method based on signatures of the underlying price process. Additionally, we explore potential applications on callable certificates. Furthermore, we present an innovative approach for calculating sensitivities, specifically Delta and Gamma, leveraging Chebyshev interpolation techniques.