Studies in valuation of derivative instruments.
Item
-
Title
-
Studies in valuation of derivative instruments.
-
Identifier
-
AAI9315505
-
identifier
-
9315505
-
Creator
-
Stebe, Peter Francis.
-
Contributor
-
Adviser: Ronald Anderson
-
Date
-
1993
-
Language
-
English
-
Publisher
-
City University of New York.
-
Subject
-
Economics, Finance | Economics, Theory
-
Abstract
-
In the first part of this paper, I discuss some aspects of the theory of the Black-Scholes equation and its derivation as explained in the Black-Scholes paper and in articles by R. Merton. Another solution to the Black-Scholes equation is obtained, which is shown to be the unique solution to the model if the Stratonovich integral is assumed in place of the Ito integral. The work is also done to show directly that if the log-normal distribution is assumed, the Black-Scholes formula is the time-discounted expected value of the European call option. In the second part of the paper the random walk model of financial asset price will be modified to reflect the fact that some traders take into account the profitability and salvage value of the underlying businesses so that the price of a going business will not become less than a certain non-zero minimum. Two models will be explored, in the first of which the price of the asset will be allowed to exceed any preset bound, and in the second of which the price will not be allowed to exceed a certain maximum. So that the models can reflect the change in the value of the security between interest or dividend payments, the upper and lower bounds are taken to be time dependent. The first is a modification to allow for the cases of tulips, Mississippi land, Tokyo real estate, and the like. I hope that the second model, in which the asset price varies between two bounds, will aid in the further study of market behavior along the lines suggested by P. Cootner, as discussed below. The two models could be obtained as the log-normal model of P. Samuelson is obtained in the continuous model of random walk by replacing dS by dS/S, the singularity at zero being replaced by singularities at the upper and lower bounds. This method of introduction is not used, because it can lead to difficulties in interpretation, as explored in the discussion in the early parts of the paper, and because a finite model is better suited to discussion of the economic issues involved. The models obtained are applied to the valuation of options.
-
Type
-
dissertation
-
Source
-
PQT Legacy CUNY.xlsx
-
degree
-
Ph.D.
