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Black–Scholes option pricing within Itô and Stratonovich conventions

Author

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  • Perelló, J
  • Porrà, J.M
  • Montero, M
  • Masoliver, J

Abstract

Options are financial instruments designed to protect investors from the stock market randomness. In 1973, Black, Scholes and Merton proposed a very popular option pricing method using stochastic differential equations within the Itô 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 Itô 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

  • Perelló, J & Porrà, J.M & Montero, M & Masoliver, J, 2000. "Black–Scholes option pricing within Itô and Stratonovich conventions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 260-274.
    • Handle: RePEc:eee:phsmap:v:278:y:2000:i:1:p:260-274
    DOI: 10.1016/S0378-4371(99)00612-3
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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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