Ito’s Lemma and Its Applications

Carl Chiarella*, Xue Zhong He, Christina Sklibosios Nikitopoulos

*Corresponding author for this work

Research output: Chapter in Book or Report/Conference proceedingChapterpeer-review

1 Citation (Scopus)


This chapter introduces Ito’s lemma, which is one of the most important tools of stochastic analysis in finance. It relates the change in the price of the derivative security to the change in the price of the underlying asset. Applications of Ito’s lemma to geometric Brownian motion asset price process, the Ornstein–Uhlenbeck process, and Brownian bridge process are discussed in detail. Extension and applications of Ito’s lemma in several variables are also included.

Original languageEnglish
Title of host publicationDynamic Modeling and Econometrics in Economics and Finance
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages33
Publication statusPublished - 2015
Externally publishedYes

Publication series

NameDynamic Modeling and Econometrics in Economics and Finance
ISSN (Print)1566-0419
ISSN (Electronic)2363-8370


  • Asset Price
  • Bond Price
  • Colour Noise
  • Stochastic Differential Equation
  • Wiener Process


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