Hostname: page-component-54dcc4c588-trf7k Total loading time: 0 Render date: 2025-10-10T01:47:05.689Z Has data issue: false hasContentIssue false
  • English
  • Français

ARBITRAGE-FREE OPTION PRICING MODELS

Part of: Mathematical economics

Published online by Cambridge University Press:  09 October 2009

DENIS BELL  and
SCOTT STELLJES
DENIS BELL*
Affiliation:
Department of Mathematics and Statistics, University of North Florida, 1 UNF Drive, Jacksonville, FL 32224, USA (email: DBell@unf.edu)
SCOTT STELLJES
Affiliation:
Department of Mathematics and Statistics, University of North Florida, 1 UNF Drive, Jacksonville, FL 32224, USA
*
✉For correspondence; e-mail: ahmet@math.missouri.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We describe a scheme for constructing explicitly solvable arbitrage-free models for stock price. This is used to study a model similar to one introduced by Cox and Ross, where the volatility of the stock is proportional to the square root of the stock price. We derive a formula for the value of a European call option based on this model and give a procedure for estimating parameters and for testing the validity of the model.

Keywords

arbitage-freeBlack–Scholes formulaEuropean call option

MSC classification

Secondary: 91B25: Asset pricing models

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 2 , October 2009 , pp. 145 - 152
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

Research partially supported by NSF grant DMS-0451194.

References

[1]Black, F. and Scholes, M. J., ‘The pricing of options and corporate liabilities’, J. Political Economy 81(3) (1973), 635–654.CrossRefGoogle Scholar
[2]Cox, J. C. and Ross, S. A., ‘The valuation of options for alternative stochastic processes’, J. Financial Economics 3 (1976), 145–166.CrossRefGoogle Scholar
[3]Delbaen, F. and Shirakawa, H., ‘A note of option pricing for constant elasticity of variance model’, Preprint No. 96-03, 1996.Google Scholar
[4]Gikhman, I. I. and Skorohod, A. V., Stochastic Differential Equations (Springer, Berlin, 1972).CrossRefGoogle Scholar
[5]Karatzas, I. and Shreve, S., Methods of Mathematical Finance (Springer, New York, 1998).Google Scholar
[6]Klebaner, F., Introduction to Stochastic Calculus with Applications, 2nd edn (Imperial College Press, London, 2005).Google Scholar
[7]Rogers, L. C. G. and Williams, D., Diffusions, Markov Processes, and Martingales, Vol. 2 (Wiley, New York, 1987).Google Scholar