IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v4y2011i1p74-96d28374.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/4/1/74/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/4/1/74/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Elton, Edwin J & Gruber, Martin J & Urich, Thomas J, 1978. "Are Betas Best?," Journal of Finance, American Finance Association, vol. 33(5), pages 1375-1384, December.
    2. Choudhary, Preeti, 2011. "Evidence on differences between recognition and disclosure: A comparison of inputs to estimate fair values of employee stock options," Journal of Accounting and Economics, Elsevier, vol. 51(1-2), pages 77-94, February.
    3. Blume, Marshall E, 1975. "Betas and Their Regression Tendencies," Journal of Finance, American Finance Association, vol. 30(3), pages 785-795, June.
    4. Jacquier, Eric & Jarrow, Robert, 2000. "Bayesian analysis of contingent claim model error," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 145-180.
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    6. 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.
    7. Gael M. Martin & Catherine S. Forbes & Vance L. Martin, 2005. "Implicit Bayesian Inference Using Option Prices," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 437-462, May.
    8. Jorion, Philippe, 1995. "Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-528, June.
    9. Catherine S. Forbes & Gael M. Martin & Jill Wright, 2007. "Inference for a Class of Stochastic Volatility Models Using Option and Spot Prices: Application of a Bivariate Kalman Filter," Econometric Reviews, Taylor & Francis Journals, vol. 26(2-4), pages 387-418.
    10. 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.
    11. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    12. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    13. Steven Li & Qianqian Yang, 2009. "The relationship between implied and realized volatility: evidence from the Australian stock index option market," Review of Quantitative Finance and Accounting, Springer, vol. 32(4), pages 405-419, May.
    14. Klemkosky, Robert C & Martin, John D, 1975. "The Adjustment of Beta Forecasts," Journal of Finance, American Finance Association, vol. 30(4), pages 1123-1128, September.
    15. Latane, Henry A & Rendleman, Richard J, Jr, 1976. "Standard Deviations of Stock Price Ratios Implied in Option Prices," Journal of Finance, American Finance Association, vol. 31(2), pages 369-381, May.
    16. Eubank, Arthur A, Jr & Zumwalt, J Kenton, 1979. "An Analysis of the Forecast Error Impact of Alternative Beta Adjustment Techniques and Risk Classes," Journal of Finance, American Finance Association, vol. 34(3), pages 761-776, June.
    17. Bauwens, Luc & Lubrano, Michel, 2002. "Bayesian option pricing using asymmetric GARCH models," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 321-342, August.
    18. Choudhary, Preeti, 2011. "Evidence on differences between recognition and disclosure: A comparison of inputs to estimate fair values of employee stock options," Journal of Accounting and Economics, Elsevier, vol. 51(1), pages 77-94.
    19. Szakmary, Andrew & Ors, Evren & Kyoung Kim, Jin & Davidson, Wallace III, 2003. "The predictive power of implied volatility: Evidence from 35 futures markets," Journal of Banking & Finance, Elsevier, vol. 27(11), pages 2151-2175, November.
    20. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    21. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    22. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-681.
    23. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    24. Beckers, Stan, 1981. "Standard deviations implied in option prices as predictors of future stock price variability," Journal of Banking & Finance, Elsevier, vol. 5(3), pages 363-381, September.
    25. Vasicek, Oldrich A, 1973. "A Note on Using Cross-Sectional Information in Bayesian Estimation of Security Betas," Journal of Finance, American Finance Association, vol. 28(5), pages 1233-1239, December.
    26. Satchell, Stephen, 2007. "Forecasting Expected Returns in the Financial Markets," Elsevier Monographs, Elsevier, edition 1, number 9780750683210.
    27. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    28. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
    29. David B. Flynn & Simone D. Grose & Gael M. Martin & Vance L. Martin, 2003. "Pricing Australian S&P200 Options: A Bayesian Approach Based on Generalized Distributional Forms," Monash Econometrics and Business Statistics Working Papers 6/03, Monash University, Department of Econometrics and Business Statistics.
    30. Barone-Adesi, Giovanni & Whaley, Robert E., 1986. "The valuation of American call options and the expected ex-dividend stock price decline," Journal of Financial Economics, Elsevier, vol. 17(1), pages 91-111, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Tak Kuen Siu, 2024. "Bayesian Lower and Upper Estimates for Ether Option Prices with Conditional Heteroscedasticity and Model Uncertainty," JRFM, MDPI, vol. 17(10), pages 1-32, September.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    2. Imlak Shaikh & Puja Padhi, 2013. "On the Linkages among Ex-ante and Ex-post Volatility: Evidence from NSE Options Market (India)," Global Business Review, International Management Institute, vol. 14(3), pages 487-505, September.
    3. 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.
    4. Wilkens, Sascha & Roder, Klaus, 2006. "The informational content of option-implied distributions: Evidence from the Eurex index and interest rate futures options market," Global Finance Journal, Elsevier, vol. 17(1), pages 50-74, September.
    5. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    6. Imlak Shaikh & Puja Padhi, 2015. "On the Relationship of Ex-ante and Ex-post Volatility: A Sub-period Analysis of S&P CNX Nifty Index Options," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 14(2), pages 140-175, August.
    7. Chuang, Wen-I & Huang, Teng-Ching & Lin, Bing-Huei, 2013. "Predicting volatility using the Markov-switching multifractal model: Evidence from S&P 100 index and equity options," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 168-187.
    8. Steven Li & Qianqian Yang, 2009. "The relationship between implied and realized volatility: evidence from the Australian stock index option market," Review of Quantitative Finance and Accounting, Springer, vol. 32(4), pages 405-419, May.
    9. Viteva, Svetlana & Veld-Merkoulova, Yulia V. & Campbell, Kevin, 2014. "The forecasting accuracy of implied volatility from ECX carbon options," Energy Economics, Elsevier, vol. 45(C), pages 475-484.
    10. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    11. Puja Padhi & Imlak Shaikh, 2014. "On the relationship of implied, realized and historical volatility: evidence from NSE equity index options," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 15(5), pages 915-934, November.
    12. Dicle, Mehmet F. & Levendis, John, 2020. "Historic risk and implied volatility," Global Finance Journal, Elsevier, vol. 45(C).
    13. Barr, Kanlaya Jintanakul, 2009. "The implied volatility bias and option smile: is there a simple explanation?," ISU General Staff Papers 200901010800002026, Iowa State University, Department of Economics.
    14. Szakmary, Andrew & Ors, Evren & Kyoung Kim, Jin & Davidson, Wallace III, 2003. "The predictive power of implied volatility: Evidence from 35 futures markets," Journal of Banking & Finance, Elsevier, vol. 27(11), pages 2151-2175, November.
    15. Neely, Christopher J., 2009. "Forecasting foreign exchange volatility: Why is implied volatility biased and inefficient? And does it matter?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(1), pages 188-205, February.
    16. 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, October.
    17. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, October.
    18. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, June.
    19. Peter Christoffersen & Kris Jacobs & Gregory Vainberg, 2007. "Forward-Looking Betas," CREATES Research Papers 2007-39, Department of Economics and Business Economics, Aarhus University.
    20. Murad Samsudin, Najmi Ismail & Mohamad, Azhar & Sifat, Imtiaz Mohammad, 2021. "Implied volatility of structured warrants: Emerging market evidence," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 464-479.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jjrfmx:v:4:y:2011:i:1:p:74-96:d:28374. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.