Representations for conditional expectations and applications to pricing and hedging of financial products in Lévy and jump-diffusion setting

Abstract

In this article, we derive expressions for conditional expectations in terms of regular expectations without conditioning but involving some weights. For this purpose, we apply two approaches: the conditional density method and the Malliavin method. We use these expressions for the numerical estimation of the price of American options and their deltas in a Lévy and jump-diffusion setting. Several examples of applications to financial and energy markets are given including numerical examples.

Keywords:

• Conditional expectation
• Monte Carlo methods
• conditional density method
• Malliavin calculus
• Pricing
• Lévy processes
• American option
• reduction of variance

MATHEMATICS SUBJECT CLASSIFICATION:

• 65C05
• 60H07
• 60H35
• 60H30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The financial support from the Agency for Innovation by Science and Technology in Flanders (IWT, grant number 111262) is gratefully acknowledged by Catherine Daveloose. Asma Khedher thanks the KPMG Center of Excellence in Risk Management for the financial support. Part of the research by Asma Khedher and Michèle Vanmaele was carried out during their stay at the CAS - Centre of Advanced Study of the Norwegian Academy of Science and Letter with the support from the research program SEFE. Michèle Vanmaele also acknowledges the Research Foundation Flanders (FWO) and the Special Research Fund (BOF) of the Ghent University for providing the possibility to go on sabbatical leave to CAS.