Least-Square Monte-Carlo

Axes that matter: PCA with a difference ArXiv ID: 2503.06707 “View on arXiv” Authors: Unknown Abstract We extend the scope of differential machine learning and introduce a new breed of supervised principal component analysis to reduce dimensionality of Derivatives problems. Applications include the specification and calibration of pricing models, the identification of regression features in least-square Monte-Carlo, and the pre-processing of simulated datasets for (differential) machine learning. Keywords: differential machine learning, principal component analysis, derivatives pricing, least-square Monte-Carlo, dimensionality reduction ...

KANOP: A Data-Efficient Option Pricing Model using Kolmogorov-Arnold Networks ArXiv ID: 2410.00419 “View on arXiv” Authors: Unknown Abstract Inspired by the recently proposed Kolmogorov-Arnold Networks (KANs), we introduce the KAN-based Option Pricing (KANOP) model to value American-style options, building on the conventional Least Square Monte Carlo (LSMC) algorithm. KANs, which are based on Kolmogorov-Arnold representation theorem, offer a data-efficient alternative to traditional Multi-Layer Perceptrons, requiring fewer hidden layers to achieve a higher level of performance. By leveraging the flexibility of KANs, KANOP provides a learnable alternative to the conventional set of basis functions used in the LSMC model, allowing the model to adapt to the pricing task and effectively estimate the expected continuation value. Using examples of standard American and Asian-American options, we demonstrate that KANOP produces more reliable option value estimates, both for single-dimensional cases and in more complex scenarios involving multiple input variables. The delta estimated by the KANOP model is also more accurate than that obtained using conventional basis functions, which is crucial for effective option hedging. Graphical illustrations further validate KANOP’s ability to accurately model the expected continuation value for American-style options. ...