Skip to main content Accesibility Help

Good Volatility, Bad Volatility, and Option Pricing

  • Bruno Feunou and Cédric Okou

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.

Corresponding author
*Feunou (corresponding author),, Bank of Canada; Okou,, Université du Québec à Montréal School of Management.
Hide All

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.

Hide All
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.
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.
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Labys, P.. “Modeling and Forecasting Realized Volatility.” Econometrica, 71 (2003), 579625.
Andersen, T. G.; Bondarenko, O.; and Gonzalez-Perez, M. T.. “Exploring Return Dynamics via Corridor Implied Volatility.” Review of Financial Studies, 28 (2015), 29022945.
Andersen, T. G.; Fusari, N.; and Todorov, V.. “Parametric Inference and Dynamic State Recovery from Option Panels.” Econometrica, 83 (2015), 10811145.
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.
Bakshi, G., and Madan, D.. “Spanning and Derivative Security Valuation.” Journal of Financial Economics, 55 (2000), 205238.
Bandi, F., and Renò, R.. “Price and Volatility Co-Jumps.” Journal of Financial Economics, 119 (2016), 107146.
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).
Barndorff-Nielsen, O. E., and Shephard, N.. “Power and Bipower Variation with Stochastic Volatility and Jumps.” Journal of Financial Econometrics, 2 (2004), 137.
Bates, D.Post-’87 Crash Fears in the S&P 500 Futures Option Market.” Journal of Econometrics, 96 (2000), 181238.
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637654.
Bollerslev, T.; Li, S.; and Zhao, B.. “Good Volatility, Bad Volatility, and the Cross-Section of Stock Returns.” Working Paper, Duke University (2017).
Bollerslev, T.; Tauchen, G.; and Zhou, H.. “Expected Stock Returns and Variance Risk Premia.” Review of Financial Studies, 22 (2009), 44634492.
Carr, P., and Madan, D.. “Optimal Positioning in Derivative Securities.” Quantitative Finance, 1 (2001), 1937.
Christoffersen, P.; Elkamhi, R.; Feunou, B.; and Jacobs, K.. “Option Valuation with Conditional Heteroskedasticity and Nonnormality.” Review of Financial Studies, 23 (2010), 21392183.
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.
Christoffersen, P.; Feunou, B.; and Jeon, Y.. “Option Valuation with Observable Volatility and Jump Dynamics.” Journal of Banking & Finance, 61 (2015), S101S120.
Christoffersen, P.; Heston, S.; and Jacobs, K.. “Capturing Option Anomalies with a Variance-Dependent Pricing Kernel.” Review of Financial Studies, 26 (2013), 19632006.
Corsi, F.; Fusari, N.; and Vecchia, D. L.. “Realizing Smiles: Options Pricing with Realized Volatility.” Journal of Financial Economics, 107 (2013), 284304.
Darolles, S.; Gourieroux, C.; and Jasiak, J.. “Structural Laplace Transform and Compound Autoregressive Models.” Journal of Time Series Analysis, 27 (2006), 477503.
Duffie, D.; Pan, J.; and Singleton, K.. “Transform Analysis and Option Pricing for Affine Jump-Diffusions.” Econometrica, 68 (2000), 13431377.
Feunou, B.; Jahan-Parvar, M. R.; and Okou, C.. “Downside Variance Risk Premium.” Journal of Financial Econometrics, 16 (2018), 341383.
Feunou, B.; Jahan-Parvar, M. R.; and Tédongap, R.. “Modeling Market Downside Volatility.” Review of Finance, 17 (2013), 443481.
Feunou, B.; Jahan-Parvar, M. R.; and Tédongap, R.. “Which Parametric Model for Conditional Skewness?European Journal of Finance, 22 (2016), 12371271.
Guo, H.; Wang, K.; and Zhou, H.. “Good Jumps, Bad Jumps, and Conditional Equity Premium.” Working Paper, University of Cincinnati (2015).
Hansen, P. R., and Lunde, A.. “Realized Variance and Market Microstructure Noise.” Journal of Business and Economic Statistics, 24 (2006), 127161.
Heston, S. L., and Nandi, S.. “A Closed-Form GARCH Option Valuation Model.” Review of Financial Studies, 13 (2000), 585625.
Huang, J.-Z., and Wu, L.. “Specification Analysis of Option Pricing Models Based on Time-Changed Lévy Processes.” Journal of Finance, 59 (2004), 14051439.
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).
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.
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).
Stentoft, L.“Option Pricing Using Realized Volatility.” CREATES Research Paper (2008).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Financial and Quantitative Analysis
  • ISSN: 0022-1090
  • EISSN: 1756-6916
  • URL: /core/journals/journal-of-financial-and-quantitative-analysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
Type Description Title
Supplementary materials

Feunou and Okou supplementary material
Feunou and Okou supplementary material 1

 Unknown (771 KB)
771 KB


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed