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Black-Scholes option pricing within Ito and Stratonovich conventions

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  • J. Perello
  • J. M. Porra
  • M. Montero
  • J. Masoliver

Abstract

Options financial instruments designed to protect investors from the stock market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton proposed a very popular option pricing method using stochastic differential equations within the Ito interpretation. Herein, we derive the Black-Scholes equation for the option price using the Stratonovich calculus along with a comprehensive review, aimed to physicists, of the classical option pricing method based on the Ito calculus. We show, as can be expected, that the Black-Scholes equation is independent of the interpretation chosen. We nonetheless point out the many subtleties underlying Black-Scholes option pricing method.

Suggested Citation

  • J. Perello & J. M. Porra & M. Montero & J. Masoliver, 2000. "Black-Scholes option pricing within Ito and Stratonovich conventions," Papers physics/0001040, arXiv.org, revised Apr 2000.
    • Handle: RePEc:arx:papers:physics/0001040
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    Cited by:

    1. Dashti Moghaddam, M. & Serota, R.A., 2021. "Combined multiplicative–Heston model for stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    2. Reaz Chowdhury & M. R. C. Mahdy & Tanisha Nourin Alam & Golam Dastegir Al Quaderi, 2018. "Predicting the Stock Price of Frontier Markets Using Modified Black-Scholes Option Pricing Model and Machine Learning," Papers 1812.10619, arXiv.org.
    3. M. Dashti Moghaddam & R. A. Serota, 2018. "Combined Mutiplicative-Heston Model for Stochastic Volatility," Papers 1807.10793, arXiv.org.

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