Ito, Stratonovich and Friends

17 Pages Posted: 24 Apr 2017 Last revised: 2 Jun 2017

Date Written: May 18, 2017

Abstract

This exposition should provide you with the bigger picture of stochastic calculus, especially stochastic integrals. It heuristically and pedagogically develops key concepts and intuitions of one of the most important fields of applied mathematics today, namely quantitative finance. It demystifies ideas that a normally either too starkly dumbed down or hidden under highly technical details, so this text tries to fill a missing link in the literature where there seems to be no middle ground as of today. Additionally, the paper gives two results which cannot (to the best of my knowledge) readily be found in the classical literature: an illustration of the Ito correction term within binomial trees and a Taylor expansion for the Stratonovich integral.

Keywords: Stochastic process, stochastic calculus, stochastic integral, Ito integral, Stratonovich integral, stochastic differential equation (SDE), Jensen’s inequality, Ito’s lemma, Ito correction, Binomial tree, Taylor expansion, martingale, option pricing, convexity.

JEL Classification: C60, C65, G12, G13

Suggested Citation

von Jouanne-Diedrich, Holger, Ito, Stratonovich and Friends (May 18, 2017). Available at SSRN: https://ssrn.com/abstract=2956257 or http://dx.doi.org/10.2139/ssrn.2956257

Holger Von Jouanne-Diedrich (Contact Author)

Technical University Aschaffenburg ( email )

Germany

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