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Good Volatility, Bad Volatility, and Option Pricing

Published online by Cambridge University Press:  13 September 2018

Abstract

Advances in variance analysis permit the splitting of the total quadratic variation of a jump-diffusion process into upside and downside components. Recent studies establish that this decomposition enhances volatility predictions and highlight the upside/downside variance spread as a driver of the asymmetry in stock price distributions. To appraise the economic gain of this decomposition, we design a new and flexible option pricing model in which the underlying asset price exhibits distinct upside and downside semivariance dynamics driven by the model-free proxies of the variances. The new model outperforms common benchmarks, especially the alternative that splits the quadratic variation into diffusive and jump components.

Type
Research Article
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2018 

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Footnotes

1

We are indebted to Jennifer Conrad (the editor) and an anonymous referee for helpful comments that improved the article. We pay a special tribute to Peter Christoffersen, colleague and friend, who passed away on June 22, 2018, and whose guidance and support greatly shaped this research agenda. Our hearts and thoughts go out to his family. We also thank Diego Amaya, Christian Dorion, Yoontae Jeon, and seminar participants at HEC Montréal and Université Paris Nanterre for fruitful discussions. We gratefully acknowledge financial support from the Bank of Canada, the Université du Québec à Montréal (UQAM) research funds, and the Canadian Derivatives Institute (CDI). The views expressed in this article are those of the authors. No responsibility for them should be attributed to the Bank of Canada.

References

Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Ebens, H.. “The Distribution of Realized Stock Return Volatility.” Journal of Financial Economics, 61 (2001), 4376.Google Scholar
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Labys, P.. “The Distribution of Realized Exchange Rate Volatility.” Journal of the American Statistical Association, 96 (2001), 4255.Google Scholar
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Labys, P.. “Modeling and Forecasting Realized Volatility.” Econometrica, 71 (2003), 579625.Google Scholar
Andersen, T. G.; Bondarenko, O.; and Gonzalez-Perez, M. T.. “Exploring Return Dynamics via Corridor Implied Volatility.” Review of Financial Studies, 28 (2015), 29022945.Google Scholar
Andersen, T. G.; Fusari, N.; and Todorov, V.. “Parametric Inference and Dynamic State Recovery from Option Panels.” Econometrica, 83 (2015), 10811145.Google Scholar
Bakshi, G.; Kapadia, N.; and Madan, D.. “Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options.” Review of Financial Studies, 16 (2003), 101143.Google Scholar
Bakshi, G., and Madan, D.. “Spanning and Derivative Security Valuation.” Journal of Financial Economics, 55 (2000), 205238.Google Scholar
Bandi, F., and Renò, R.. “Price and Volatility Co-Jumps.” Journal of Financial Economics, 119 (2016), 107146.Google Scholar
Barndorff-Nielsen, O. E.; Kinnebrock, S.; and Shephard, N.. “Measuring Downside Risk: Realised Semivariance.” In Volatility and Time Series Econometrics: Essays in Honor of Robert F. Engle, Bollerslev, T., Russell, J., and Watson, M., eds. Oxford, UK: Oxford University Press (2010).Google Scholar
Barndorff-Nielsen, O. E., and Shephard, N.. “Power and Bipower Variation with Stochastic Volatility and Jumps.” Journal of Financial Econometrics, 2 (2004), 137.Google Scholar
Bates, D.Post-’87 Crash Fears in the S&P 500 Futures Option Market.” Journal of Econometrics, 96 (2000), 181238.Google Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637654.Google Scholar
Bollerslev, T.; Li, S.; and Zhao, B.. “Good Volatility, Bad Volatility, and the Cross-Section of Stock Returns.” Working Paper, Duke University (2017).Google Scholar
Bollerslev, T.; Tauchen, G.; and Zhou, H.. “Expected Stock Returns and Variance Risk Premia.” Review of Financial Studies, 22 (2009), 44634492.Google Scholar
Carr, P., and Madan, D.. “Optimal Positioning in Derivative Securities.” Quantitative Finance, 1 (2001), 1937.Google Scholar
Christoffersen, P.; Elkamhi, R.; Feunou, B.; and Jacobs, K.. “Option Valuation with Conditional Heteroskedasticity and Nonnormality.” Review of Financial Studies, 23 (2010), 21392183.Google Scholar
Christoffersen, P.; Feunou, B.; Jacobs, K.; and Meddahi, N.. “The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation.” Journal of Financial and Quantitative Analysis, 49 (2014), 663697.Google Scholar
Christoffersen, P.; Feunou, B.; and Jeon, Y.. “Option Valuation with Observable Volatility and Jump Dynamics.” Journal of Banking & Finance, 61 (2015), S101S120.Google Scholar
Christoffersen, P.; Heston, S.; and Jacobs, K.. “Capturing Option Anomalies with a Variance-Dependent Pricing Kernel.” Review of Financial Studies, 26 (2013), 19632006.Google Scholar
Corsi, F.; Fusari, N.; and Vecchia, D. L.. “Realizing Smiles: Options Pricing with Realized Volatility.” Journal of Financial Economics, 107 (2013), 284304.Google Scholar
Darolles, S.; Gourieroux, C.; and Jasiak, J.. “Structural Laplace Transform and Compound Autoregressive Models.” Journal of Time Series Analysis, 27 (2006), 477503.Google Scholar
Duffie, D.; Pan, J.; and Singleton, K.. “Transform Analysis and Option Pricing for Affine Jump-Diffusions.” Econometrica, 68 (2000), 13431377.Google Scholar
Feunou, B.; Jahan-Parvar, M. R.; and Okou, C.. “Downside Variance Risk Premium.” Journal of Financial Econometrics, 16 (2018), 341383.Google Scholar
Feunou, B.; Jahan-Parvar, M. R.; and Tédongap, R.. “Modeling Market Downside Volatility.” Review of Finance, 17 (2013), 443481.Google Scholar
Feunou, B.; Jahan-Parvar, M. R.; and Tédongap, R.. “Which Parametric Model for Conditional Skewness?European Journal of Finance, 22 (2016), 12371271.Google Scholar
Guo, H.; Wang, K.; and Zhou, H.. “Good Jumps, Bad Jumps, and Conditional Equity Premium.” Working Paper, University of Cincinnati (2015).Google Scholar
Hansen, P. R., and Lunde, A.. “Realized Variance and Market Microstructure Noise.” Journal of Business and Economic Statistics, 24 (2006), 127161.Google Scholar
Heston, S. L., and Nandi, S.. “A Closed-Form GARCH Option Valuation Model.” Review of Financial Studies, 13 (2000), 585625.Google Scholar
Huang, J.-Z., and Wu, L.. “Specification Analysis of Option Pricing Models Based on Time-Changed Lévy Processes.” Journal of Finance, 59 (2004), 14051439.Google Scholar
Mincer, J., and Zarnowitz, V.. “The Evaluation of Economic Forecasts.” In Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, Mincer, J., ed. Cambridge, MA: National Bureau of Economic Research (1969).Google Scholar
Patton, A. J., and Sheppard, K.. “Good Volatility, Bad Volatility: Signed Jumps and the Persistence of Volatility.” Review of Economics and Statistics, 97 (2015), 683697.Google Scholar
Renault, E.Econometric Models of Option Pricing Errors.” In Advances in Economics and Econometrics: Theory and Applications, Seventh World Congress, Kreps, D. M. and Wallis, K. F., eds. Cambridge, UK: Cambridge University Press (1997).Google Scholar
Stentoft, L.“Option Pricing Using Realized Volatility.” CREATES Research Paper (2008).Google Scholar
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