Derivative pricing based on local utility maximization
type: Item
instance of: scholarly article
title: Derivative pricing based on local utility maximization
zbMATH Open document ID: 1007.91020
author: Jan Kallsen
published in: Finance and Stochastics
publication date: 2002-11-21T00:00:00Z
review text: In this paper a new approach to contingent claim valuation in incomplete market model is studied. The notions of local utility and neutral derivative price are introduced. Local utility optimization can be interpreted as expected utility maximization of the gains over infinitesimal time intervals. A derivative price is called neutral if the optimal portfolio contains no contingent claim. The author introduces the sensitivity process of a contingent claim. Neutral prices are based on the assumption that the net demand for derivatives is \(0\). The author measures the sensitivity of the contingent claim price to violation of this assumption by computing how much the price reacts to small demand perturbations. This sensitivity process can be used to construct price bounds and it allows to calibrate the neutral pricing model to initially observed market quotations. The illustration of neutral derivative pricing and sensitivity processes are presented by considering some particular cases such as: market with continuous path, bivariate diffusion models, the model with exponential Lévy processes and the discrete-time model.
Mathematics Subject Classification ID: 91G20
zbMATH DE Number: 1833870
zbMATH Keywords: option pricing
zbMATH Keywords: incomplete market
zbMATH Keywords: local utility
zbMATH Keywords: neutral derivative price
zbMATH Keywords: sensitivity process
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
full work available at URL: s780-002-8403-x
OpenAlex ID: W2012664904
DOI: 10.1007/S780-002-8403-X
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description: scientific article; zbMATH DE number 1833870