Dividends in the theory of derivative securities pricing
type: Item
instance of: scholarly article
title: Dividends in the theory of derivative securities pricing
zbMATH Open document ID: 1127.91031
author: Lars Tyge Nielsen
published in: Economic Theory
publication date: 2007-04-26T00:00:00Z
review text: This paper develops the fundamental aspects of the theory of martingale pricing of derivative securities where cumulative gains processes are Ito processes and the cumulative dividend processes of both the underliers and derivative securities are general, which include Itô's processes or processes with finite variation. It derives a general formula for changing the unit of account of a cumulative dividend process. The formula satisfies the unit-variance property and consistent properties: the two ways of changing units of a trading strategy's cumulative dividend process are equivalent; changing from one unit to the second and then to the third is the same as changing from the first to the third. The paper also points out the inappropriateness of Duffie and Zame changing units in the case of an Ito process for a cumulative dividend process. It adds to the literature by extending to a general dividend process not only for underliers, but also for derivative securities. It gives a general formula for valuing a dividend process as a sum of a claim to the total accumulated nominal dividends and a claim to a stream of interest payment.
reviewed by: Qin Lu
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 91B24
zbMATH DE Number: 5146554
zbMATH Keywords: cumulative dividend process
zbMATH Keywords: Itô process
zbMATH Keywords: unit of account
zbMATH Keywords: martingale valuation
MaRDI profile type: Publication
full work available at URL: s00199-006-0106-6
OpenAlex ID: W2094673370
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DOI: 10.1007/S00199-006-0106-6
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description: scientific article; zbMATH DE number 5146554