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Use of Bayesian Estimates to determine the Volatility Parameter Input in the Black-Scholes and Binomial Option Pricing Models

Author

Listed:
  • Shu Wing Ho

    (The University of Auckland, Department of Statistics, Auckland, New Zealand)

  • Alan Lee

    (The University of Auckland, Department of Statistics, Auckland, New Zealand)

  • Alastair Marsden

    (The University of Auckland, Department of Accounting and Finance, Auckland, New Zealand)

Abstract

The valuation of options and many other derivative instruments requires an estimation of exante or forward looking volatility. This paper adopts a Bayesian approach to estimate stock price volatility. We find evidence that overall Bayesian volatility estimates more closely approximate the implied volatility of stocks derived from traded call and put options prices compared to historical volatility estimates sourced from IVolatility.com (“IVolatility”). Our evidence suggests use of the Bayesian approach to estimate volatility can provide a more accurate measure of ex-ante stock price volatility and will be useful in the pricing of derivative securities where the implied stock price volatility cannot be observed.

Suggested Citation

  • Shu Wing Ho & Alan Lee & Alastair Marsden, 2011. "Use of Bayesian Estimates to determine the Volatility Parameter Input in the Black-Scholes and Binomial Option Pricing Models," JRFM, MDPI, vol. 4(1), pages 1-23, December.
    • Handle: RePEc:gam:jjrfmx:v:4:y:2011:i:1:p:74-96:d:28374
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    References listed on IDEAS

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    Cited by:

    1. Kumar Yashaswi, 2021. "Posterior Cramer-Rao Lower Bound based Adaptive State Estimation for Option Price Forecasting," Papers 2112.03193, arXiv.org.
    2. Cangrejo Esquivel, Álvaro Javier & Tovar Cuevas, José Rafael & García, Isabel Cristina & Manotas Duque, Diego Fernando, 2022. "Estimación clásica y bayesiana de la volatilidad en el modelo de Black-Scholes [Classical and Bayesian estimation of volatility in the Black-Scholes model]," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 34(1), pages 237-262, December .
    3. Hanno Gottschalk & Elpida Nizami & Marius Schubert, 2016. "Option Pricing in Markets with Unknown Stochastic Dynamics," Papers 1602.04848, arXiv.org, revised Jan 2017.
    4. Abdulwahab Animoku & Ömür Uğur & Yeliz Yolcu-Okur, 2018. "Modeling and implementation of local volatility surfaces in Bayesian framework," Computational Management Science, Springer, vol. 15(2), pages 239-258, June.

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