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

George Chalamandaris and Anastasios Malliaris

Chapter 27 in Handbook of Financial Econometrics, Mathematics, Statistics, and Machine Learning:(In 4 Volumes), 2020, pp 1025-1074 from World Scientific Publishing Co. Pte. Ltd.

Abstract: The purpose of this chapter is to develop certain relatively recent mathematical discoveries known generally as stochastic calculus, or more specifically as Itô’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: Financial Econometrics; Financial Mathematics; Financial Statistics; Financial Technology; Machine Learning; Covariance Regression; Cluster Effect; Option Bound; Dynamic Capital Budgeting; Big Data (search for similar items in EconPapers)
JEL-codes: C01 C1 G32 (search for similar items in EconPapers)
Date: 2020
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