Non-parametric partial importance sampling for financial derivative pricing

• Verfasst von: Neddermeyer, Jan Christoph [VerfasserIn]
• Titel: Non-parametric partial importance sampling for financial derivative pricing
• Verf.angabe: Jan C. Neddermeyer
• Jahr: 2011
• Umfang: 14 S.
• Fussnoten: First published online: 11 May 2010 ; Gesehen am 15.09.2022
• Titel Quelle: Enthalten in: Quantitative finance
• Ort Quelle: London : Taylor & Francis, 2001
• Jahr Quelle: 2011
• Band/Heft Quelle: 11(2011), 8, Seite 1193-1206
• ISSN Quelle: 1469-7696
• DOI: doi:10.1080/14697680903496485
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Financial engineering
• Sach-SW: Monte Carlo methods
• Sach-SW: Option pricing via simulation
• Sach-SW: Path-dependent options
• Sach-SW: Pricing of derivatives securities
• K10plus-PPN: 1817214799

Abstract

Importance sampling is a promising variance reduction technique for Monte Carlo simulation-based derivative pricing. Existing importance sampling methods are based on a parametric choice of the proposal. This article proposes an algorithm that estimates the optimal proposal non-parametrically using a multivariate frequency polygon estimator. In contrast to parametric methods, non-parametric estimation allows for close approximation of the optimal proposal. Standard non-parametric importance sampling is inefficient for high-dimensional problems. We solve this issue by applying the procedure to a low-dimensional subspace, which is identified through principal component analysis and the concept of the effective dimension. The mean square error properties of the algorithm are investigated and its asymptotic optimality is shown. Quasi-Monte Carlo is used for further improvement of the method. It is easy to implement, particularly it does not require any analytical computation, and it is computationally very efficient. We demonstrate through path-dependent and multi-asset option pricing problems that the algorithm leads to significant efficiency gains compared with other algorithms in the literature.