Efficient calculation of the Greeks for exponential Lévy processes: an application of measure valued differentiation

Pflug, G. ORCID: https://orcid.org/0000-0001-8215-3550 & Thoma, P. (2016). Efficient calculation of the Greeks for exponential Lévy processes: an application of measure valued differentiation. Quantitative Finance 16 (2) 247-257. 10.1080/14697688.2015.1114364.

[thumbnail of Efficient calculation of the Greeks for exponential Levy processes.pdf]
Preview
Text
Efficient calculation of the Greeks for exponential Levy processes.pdf - Accepted Version
Available under License Creative Commons Attribution.

Download (401kB) | Preview

Abstract

Monte Carlo simulation methods have become more and more important in the financial sector in the past years. In this paper, we introduce a new simulation method for the estimation of the derivatives of prices of financial contracts with respect to (w.r.t.) certain distributional parameters called the ‘Greeks’. In particular, we assume that the underlying financial process is a Lévy-type process in discrete time. Our method is based on the Measure-Valued Differentiation (MVD) approach, which allows representation of derivatives as differences of two processes, called the phantoms. We discuss the applicability of MVD for different types of option pay-offs in combination with different types of models of the underlying and provide a framework for the applicability of MVD for path-dependent pay-off functions, as Lookback Options or Asian Options.

Item Type: Article
Uncontrolled Keywords: Asian options; Estimation of the Greeks; Exotic options; Lookback option; Lévy-Processes; Measure valued differentiation
Research Programs: Risk & Resilience (RISK)
Risk, Policy and Vulnerability (RPV)
Depositing User: Luke Kirwan
Date Deposited: 15 Feb 2016 11:08
Last Modified: 27 Aug 2021 17:25
URI: https://pure.iiasa.ac.at/11927

Actions (login required)

View Item View Item