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A Bayesian Approach to Modeling Stock Return Volatility for Option Valuation

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  • Karolyi, G. Andrew

Abstract

New measures of stock return volatility are developed to increase the precision of stock option price estimates. With Bayesian statistical methods, volatility estimates for a given stock are developed using prior information on the cross-sectional patterns in return volatilities for groups of stocks sorted on size, financial leverage, and trading volume. Call option values computed with the Bayesian procedure generally improve prediction accuracy for market prices of call options relative to those computed using implied volatility, standard historical volatility, or even the actual ex post volatility that occurred during each option's life. Although the Bayesian methods produce biased call price estimators, they do reduce the systematic tendency of standard pricing approaches to overprice (underprice) options on high (low) volatility stocks. Little bias improvement is observed with respect to the time to maturity and moneyness of the call options.

Suggested Citation

  • Karolyi, G. Andrew, 1993. "A Bayesian Approach to Modeling Stock Return Volatility for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(4), pages 579-594, December.
  • Handle: RePEc:cup:jfinqa:v:28:y:1993:i:04:p:579-594_00
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    Cited by:

    1. Tim Bollerslev & Benjamin Hood & John Huss & Lasse Heje Pedersen, 2018. "Risk Everywhere: Modeling and Managing Volatility," Review of Financial Studies, Society for Financial Studies, vol. 31(7), pages 2729-2773.
    2. Lisha Lin & Yaqiong Li & Rui Gao & Jianhong Wu, 2019. "The Numerical Simulation of Quanto Option Prices Using Bayesian Statistical Methods," Papers 1910.04075, arXiv.org.
    3. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, December.
    4. Jiang, George J. & Tian, Yisong S., 2010. "Forecasting Volatility Using Long Memory and Comovements: An Application to Option Valuation under SFAS 123R," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(2), pages 503-533, April.
    5. Darsinos, T. & Satchell, S.E., 2001. "Bayesian Analysis of the Black-Scholes Option Price," Cambridge Working Papers in Economics 0102, Faculty of Economics, University of Cambridge.
    6. Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, vol. 72(2), pages 291-318, May.
    7. Kent Wang, 2010. "Forecasting volatilities in equity, bond and money markets: A market-based approach," Australian Journal of Management, Australian School of Business, vol. 35(2), pages 165-180, August.
    8. Contreras, P. & Satchell, S.E., 2003. "A Bayesian Confidence Interval for Value-at-Risk," Cambridge Working Papers in Economics 0348, Faculty of Economics, University of Cambridge.
    9. Darsinos, T. & Satchell, S.E., 2001. "Bayesian Forecasting of Options Prices: A Natural Framework for Pooling Historical and Implied Volatiltiy Information," Cambridge Working Papers in Economics 0116, Faculty of Economics, University of Cambridge.
    10. Lin, Lisha & Li, Yaqiong & Gao, Rui & Wu, Jianhong, 2021. "The numerical simulation of Quanto option prices using Bayesian statistical methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    11. Henryk Gzyl & German Molina & Enrique ter Horst, 2009. "Assessment and propagation of input uncertainty in tree‐based option pricing models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 275-308, May.
    12. 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.
    13. Yang, Seungho & Oh, Gabjin, 2020. "A Bayesian estimation of exponential Lévy models for implied volatility smile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    14. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    15. Chen, Ding & Guo, Biao & Zhou, Guofu, 2023. "Firm fundamentals and the cross-section of implied volatility shapes," Journal of Financial Markets, Elsevier, vol. 63(C).
    16. Henryk Gzyl & Enrique ter Horst & Samuel W. Malone, 2008. "Bayesian parameter inference for models of the Black and Scholes type," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(6), pages 507-524, November.
    17. George J. Jiang & Pieter J. van der Sluis, 1998. "Pricing Stock Options under Stochastic Volatility and Stochastic Interest Rates with Efficient Method of Moments Estimation," Tinbergen Institute Discussion Papers 98-067/4, Tinbergen Institute.
    18. 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 .
    19. Gao, Rui & Li, Yaqiong & Lin, Lisha, 2019. "Bayesian statistical inference for European options with stock liquidity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 312-322.
    20. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.

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