Dividends in the theory of derivative securities pricing
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.
scientific article; zbMATH DE number 5146554
scientific article