Ito's Calculus and the Derivation of the Black-Scholes Option-Pricing Model

HANDBOOK OF QUANTITATIVE FINANCE, C. F. Lee, Alice C. Lee, eds., Springer, 2009

63 Pages Posted: 18 Oct 2007 Last revised: 12 Feb 2009

See all articles by George Chalamandaris

George Chalamandaris

Athens University of Economics and Business - Department of Accounting and Finance

A. (Tassos) G. Malliaris

Loyola University Chicago

Date Written: 2009

Abstract

The purpose of this paper is to develop certain relatively recent mathematical discoveries known generally as stochastic calculus, or more specifically as Ito's Calculus and to also illustrate their application in the pricing of options. The mathematical methods of stochastic calculus are illustrated in alternative derivations of the celebrated Black-Scholes-Merton model. The topic is motivated by a desire to provide an intuitive understanding of certain probabilistic methods that have found significant use in financial economics.

Keywords: Ito, Calculus, Derivation, Black, Scholes, Option, Pricing

JEL Classification: C02, C60, G13

Suggested Citation

Chalamandaris, George and Malliaris, A. (Tassos) G., Ito's Calculus and the Derivation of the Black-Scholes Option-Pricing Model (2009). HANDBOOK OF QUANTITATIVE FINANCE, C. F. Lee, Alice C. Lee, eds., Springer, 2009, Available at SSRN: https://ssrn.com/abstract=1022386

George Chalamandaris

Athens University of Economics and Business - Department of Accounting and Finance ( email )

76 Patission Street
GR-104 34 Athens
Greece

A. (Tassos) G. Malliaris (Contact Author)

Loyola University Chicago ( email )

16 E. Pearson Ave
Quinlan School of Business
Chicago, IL 60611
United States
312-915-6063 (Phone)

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