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Stock price dynamics and option valuations under volatility feedback effect

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  • Kanniainen, Juho
  • Piché, Robert

Abstract

According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price–dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations under the volatility feedback effect by modeling the joint dynamics of stock price, dividends, and volatility in continuous time. Most importantly, our model predicts the negative effect of an increase in squared return volatility on the value of deep-in-the-money call options and, furthermore, attempts to explain the volatility puzzle. We theoretically demonstrate a mechanism by which the market price of diffusion return risk, or an equity risk-premium, affects option prices and empirically illustrate how to identify that mechanism using forward-looking information on option contracts. Our theoretical and empirical results support the relevance of the volatility feedback effect. Overall, the results indicate that the prevailing practice of ignoring the time-varying dividend yield in option pricing can lead to oversimplification of the stock market dynamics.

Suggested Citation

  • Kanniainen, Juho & Piché, Robert, 2013. "Stock price dynamics and option valuations under volatility feedback effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 722-740.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:722-740
    DOI: 10.1016/j.physa.2012.10.004
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    as
    1. Campbell, John Y. & Hentschel, Ludger, 1992. "No news is good news *1: An asymmetric model of changing volatility in stock returns," Journal of Financial Economics, Elsevier, vol. 31(3), pages 281-318, June.
    2. Wu, Guojun, 2001. "The Determinants of Asymmetric Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 14(3), pages 837-859.
    3. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. "General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
    4. George J. Jiang & Pieter J. van der Sluis, 1999. "Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates," Review of Finance, European Finance Association, vol. 3(3), pages 273-310.
    5. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Do Call Prices and the Underlying Stock Always Move in the Same Direction?," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 549-584.
    6. Bollerslev, Tim & Gibson, Michael & Zhou, Hao, 2011. "Dynamic estimation of volatility risk premia and investor risk aversion from option-implied and realized volatilities," Journal of Econometrics, Elsevier, vol. 160(1), pages 235-245, January.
    7. Masaaki Kijima, 2002. "Monotonicity And Convexity Of Option Prices Revisited," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 411-425, October.
    8. Raberto, Marco & Cincotti, Silvano, 2005. "Modeling and simulation of a double auction artificial financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 34-45.
    9. Bakshi, Gurdip & Chen, Zhiwu, 2005. "Stock valuation in dynamic economies," Journal of Financial Markets, Elsevier, vol. 8(2), pages 111-151, May.
    10. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    11. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    12. Pindyck, Robert S, 1984. "Risk, Inflation, and the Stock Market," American Economic Review, American Economic Association, vol. 74(3), pages 335-351, June.
    13. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2005. "There is a risk-return trade-off after all," Journal of Financial Economics, Elsevier, vol. 76(3), pages 509-548, June.
    14. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    15. 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..
    16. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2010. "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3141-3189, August.
    17. John Y. Campbell, Robert J. Shiller, 1988. "The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 195-228.
    18. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    19. Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," The Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
    20. Tim Bollerslev & Julia Litvinova & George Tauchen, 2006. "Leverage and Volatility Feedback Effects in High-Frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 353-384.
    21. Brennan, Michael J. & Xia, Yihong, 2001. "Stock price volatility and equity premium," Journal of Monetary Economics, Elsevier, vol. 47(2), pages 249-283, April.
    22. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    23. Bekaert, Geert & Engstrom, Eric & Xing, Yuhang, 2009. "Risk, uncertainty, and asset prices," Journal of Financial Economics, Elsevier, vol. 91(1), pages 59-82, January.
    24. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    25. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    26. Tim Bollerslev & Natalia Sizova & George Tauchen, 2011. "Volatility in Equilibrium: Asymmetries and Dynamic Dependencies," Review of Finance, European Finance Association, vol. 16(1), pages 31-80.
    27. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
    28. Lin Peng & Turan G. Bali, 2006. "Is there a risk-return trade-off? Evidence from high-frequency data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1169-1198.
    29. Campbell, John Y, 1993. "Intertemporal Asset Pricing without Consumption Data," American Economic Review, American Economic Association, vol. 83(3), pages 487-512, June.
    30. Gurdip Bakshi & Liuren Wu, 2010. "The Behavior of Risk and Market Prices of Risk Over the Nasdaq Bubble Period," Management Science, INFORMS, vol. 56(12), pages 2251-2264, December.
    31. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    32. Juho Kanniainen, 2009. "Can properly discounted projects follow geometric Brownian motion?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 435-450, December.
    33. repec:bla:jfinan:v:59:y:2004:i:3:p:1405-1440 is not listed on IDEAS
    34. Giovanni Barone Adesi & Robert F. Engle & Loriano Mancini, 2014. "A GARCH Option Pricing Model with Filtered Historical Simulation," Palgrave Macmillan Books, in: Giovanni Barone Adesi (ed.), Simulating Security Returns: A Filtered Historical Simulation Approach, chapter 4, pages 66-108, Palgrave Macmillan.
    35. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    36. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, vol. 50(9), pages 1204-1221, September.
    37. Ang, Andrew & Liu, Jun, 2007. "Risk, return, and dividends," Journal of Financial Economics, Elsevier, vol. 85(1), pages 1-38, July.
    38. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    39. Cochrane, John H, 1992. "Explaining the Variance of Price-Dividend Ratios," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 243-280.
    40. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
    41. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    42. Peter Carr & Liuren Wu, 2009. "Variance Risk Premiums," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1311-1341, March.
    43. Florescu, Ionuţ & Pãsãricã, Cristian Gabriel, 2009. "A study about the existence of the leverage effect in stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 419-432.
    44. Jingzhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time- Changed Levy Processes," Finance 0401002, University Library of Munich, Germany.
    45. Christoffersen, Peter & Dorion, Christian & Jacobs, Kris & Wang, Yintian, 2010. "Volatility Components, Affine Restrictions, and Nonnormal Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 483-502.
    46. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    47. Bali, Turan G., 2008. "The intertemporal relation between expected returns and risk," Journal of Financial Economics, Elsevier, vol. 87(1), pages 101-131, January.
    48. Bakshi, Gurdip & Ju, Nengjiu & Ou-Yang, Hui, 2006. "Estimation of continuous-time models with an application to equity volatility dynamics," Journal of Financial Economics, Elsevier, vol. 82(1), pages 227-249, October.
    49. Bali, Turan G. & Engle, Robert F., 2010. "The intertemporal capital asset pricing model with dynamic conditional correlations," Journal of Monetary Economics, Elsevier, vol. 57(4), pages 377-390, May.
    50. McDonald, Robert L & Siegel, Daniel R, 1985. "Investment and the Valuation of Firms When There Is an Option to Shut Down," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 331-349, June.
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