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Ito’s Lemma and Its Applications

In: Derivative Security Pricing

Author

Listed:
  • Carl Chiarella

    (University of Technology Sydney)

  • Xue-Zhong He

    (University of Technology Sydney)

  • Christina Sklibosios Nikitopoulos

    (University of Technology Sydney)

Abstract

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.

Suggested Citation

  • Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Ito’s Lemma and Its Applications," Dynamic Modeling and Econometrics in Economics and Finance, in: Derivative Security Pricing, edition 127, chapter 0, pages 111-143, Springer.
    • Handle: RePEc:spr:dymchp:978-3-662-45906-5_6
    DOI: 10.1007/978-3-662-45906-5_6
    as

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