Itô’s Calculus: Derivation of the Black–Scholes Option Pricing Model

Cheng-Few Lee (), Hong-Yi Chen () and John Lee ()
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Cheng-Few Lee: Rutgers University, Department of Finance and Economics, Rutgers Business School
Hong-Yi Chen: National Chengchi University, Department of Finance
John Lee: Center for PBBEF Research

Chapter Chapter 20 in Financial Econometrics, Mathematics and Statistics, 2019, pp 517-540 from Springer

Abstract: Abstract The purpose of this chapter is to develop certain relatively mathematical discoveries known generally as stochastic calculusStochastic calculus, or more specifically as Itô’s calculus and to also illustrate their application in the pricing of options. The mathematical methods of stochastic calculusStochastic 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: Black–Scholes option pricing model; Expected terminal option price; Itô lemma; Option pricing; Stochastic differential equation approach; Stock-price behavior (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-9429-8_20

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DOI: 10.1007/978-1-4939-9429-8_20

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