The Leverage Effect Puzzle under Semi-nonparametric Stochastic Volatility Models

References

• Aït-Sahalia, Y. (2002), “Maximum-Likelihood Estimation of Discretely-Sampled Diffusions: A Closed-Form Approximation Approach,” Econometrica, 70, 223–262.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y. (2008), “Closed-Form Likelihood Expansions for Multivariate Diffusions,” Annals of Statistics, 36, 906–937.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., Fan, J., Laeven, R. J., Wang, C. D., and Yang, X. (2017), “Estimation of the Continuous and Discontinuous Leverage Effects,” Journal of the American Statistical Association, 112, 1744–1758. DOI: 10.1080/01621459.2016.1240082.
   PubMed Web of Science ®Google Scholar
• Aït-Sahalia, Y., Fan, J., and Li, Y. (2013): “The Leverage Effect Puzzle: Disentangling Sources of Bias at High Frequency,” Journal of Financial Economics, 109, 224–249. DOI: 10.1016/j.jfineco.2013.02.018.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., Hansen, L. P., and Scheinkman, J. (2010), “Operator Methods for Continuous-Time Markov Processes,” in Handbook of Financial Econometrics (Vol. 1, 1st ed.), eds. Y. Aït-Sahalia, and L. P. Hansen, pp. 1–66, San Diego: North-Holland.
   Google Scholar
• Aït-Sahalia, Y., and Jacod, J. (2012), “Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data,” Journal of Economic Literature, 50, 1007–50. DOI: 10.1257/jel.50.4.1007.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., and Jacod, J. (2014), High Frequency Financial Econometrics (1st ed.), Princeton: Princeton University Press.
   Google Scholar
• Aït-Sahalia, Y., and Kimmel, R. (2007), “Maximum Likelihood Estimation of Stochastic Volatility Models,” Journal of Financial Economics, 83, 413–452. DOI: 10.1016/j.jfineco.2005.10.006.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., and Mykland, P. A. (2003), “The Effects of Random and Discrete Sampling When Estimating Continuous-Time Diffusions,” Econometrica, 71, 483–549. DOI: 10.1111/1468-0262.t01-1-00416.
   Web of Science ®Google Scholar
• Aït-Sahalia, Y., and Mykland, P. A. (2004), “Estimators of Diffusions with Randomly Spaced Discrete Observations: A General Theory,” Annals of Statistics, 32, 2186–2222.
   Web of Science ®Google Scholar
• Andersen, T. G., Benzoni, L., and Lund, J. (2002), “An Empirical Investigation of Continuous-Time Equity Return Models,” The Journal of Finance, 57, 1239–1284. DOI: 10.1111/1540-6261.00460.
   Web of Science ®Google Scholar
• Bandi, F. M., and Renò, R. (2012), “Time-Varying Leverage Effects,” Journal of Econometrics, 169, 94–113. DOI: 10.1016/j.jeconom.2012.01.010.
   Web of Science ®Google Scholar
• Bandi, F. M., and Renò, R. (2018), “Nonparametric Stochastic Volatility,” Econometric Theory, 34, 1207–1255.
   Web of Science ®Google Scholar
• Bollerslev, T., Litvinova, J., and Tauchen, G. (2006), “Leverage and Volatility Feedback Effects in High-Frequency Data,” Journal of Financial Econometrics, 4, 353–384. DOI: 10.1093/jjfinec/nbj014.
   Google Scholar
• Chernov, M., Gallant, A. R., Ghysels, E., and Tauchen, G. T. (2003), “Alternative Models for Stock Price Dynamics,” Journal of Econometrics, 116, 225–257. DOI: 10.1016/S0304-4076(03)00108-8.
   Web of Science ®Google Scholar
• Chesney, M., and Scott, L. O. (1989), “Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model,” Journal of Financial and Quantitative Analysis, 24, 267–284. DOI: 10.2307/2330812.
   Web of Science ®Google Scholar
• Christoffersen, P., Jacobs, K., Mimouni, K. (2010), “Volatility Dynamics for the S \& P500: Evidence from Realized Volatility, Daily Returns, and Option Prices,” Review of Financial Studies, 23, 3141–3189.
   Web of Science ®Google Scholar
• Duffie, D., Pan, J., and Singleton, K. (2000), “Transform Analysis and Asset Pricing for Affine Jump-Diffusions,” Econometrica, 68, 1343–1376. DOI: 10.1111/1468-0262.00164.
   Web of Science ®Google Scholar
• Feller, W. (1952), “The Parabolic Differential Equations and the Associated Semi-Groups of Transformations,” Annals of Mathematics, 55, 468–519. DOI: 10.2307/1969644.
   Web of Science ®Google Scholar
• Gallant, A. R., Hsu, C.-T., and Tauchen, G. T. (1999), “Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance,” The Review of Economics and Statistics, 81, 617–631. DOI: 10.1162/003465399558481.
   Web of Science ®Google Scholar
• Hansen, L. P., and Scheinkman, J. A. (1995), “Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes,” Econometrica, 63, 767–804. DOI: 10.2307/2171800.
   Web of Science ®Google Scholar
• Heston, S. L. (1993), “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options,” Review of Financial Studies, 6, 327–43. DOI: 10.1093/rfs/6.2.327.
   Web of Science ®Google Scholar
• Jacod, J., Li, Y., Mykland, P., Podolskij, M., and Vetter, M. (2009), “Microstructure Noise in the Continuous Case: The Pre-averaging Approach,” Stochastic Processes and Their Applications, 119, 2149–2276. DOI: 10.1016/j.spa.2008.11.004.
   Web of Science ®Google Scholar
• Jing, B.-Y., Liu, Z., and Kong, X.-B. (2014), “On the Estimation of Integrated Volatility with Jumps and Microstructure Noise,” Journal of Business & Economic Statistics, 32, 457–467. DOI: 10.1080/07350015.2014.906350.
   Web of Science ®Google Scholar
• Jones, C. S. (2003), “The Dynamics of Stochastic Volatility: Evidence From Underlying and Options Markets,” Journal of Econometrics, 116, 181–224. DOI: 10.1016/S0304-4076(03)00107-6.
   Web of Science ®Google Scholar
• Kalnina, I., and Xiu, D. (2017), “Nonparametric Estimation of the Leverage Effect: A Trade-off between Robustness and Efficiency,” Journal of the American Statistical Association, 112, 384–396. DOI: 10.1080/01621459.2016.1141687.
   Web of Science ®Google Scholar
• Karatzas, I., and Shreve, S. E. (1991), Brownian Motion and Stochastic Calculus, New York: Springer-Verlag.
   Google Scholar
• Karlin, S., and Taylor, H. M. (1981), A Second Course in Stochastic Processes (2nd ed.), New York: Academic Press
   Google Scholar
• Kessler, M. (1997), “Estimation of an Ergodic Diffusion from Discrete Observations,” Scandinavian Journal of Statistics, 24, 211–229. DOI: 10.1111/1467-9469.00059.
   Web of Science ®Google Scholar
• Li, C. (2013a), “Maximum-Likelihood Estimation for Diffusion Processes via Closed-Form Density Expansions,” Annals of Statistics, 41, 1350–1380.
   Web of Science ®Google Scholar
• Li, C. (2013b), “Supplement to “Maximum-Likelihood Estimation for Diffusion Processes via Closed-form Density Expansions”,” Annals of Statistics, 41, 1350–1380.
   Web of Science ®Google Scholar
• Li, C., and Li, X. (2015), “A Closed-form Expansion Approach for Pricing Discretely Monitored Variance Swaps,” Operations Research Letters, 43, 450–455. DOI: 10.1016/j.orl.2015.06.003.
   Web of Science ®Google Scholar
• Mykland, P., and Wang, C. D. (2014), “The Estimation of Leverage Effect with High Frequency Data,” Journal of the American Statistical Association, 109, 197–215. DOI: 10.1080/01621459.2013.864189.
   Web of Science ®Google Scholar
• Mykland, P. A., and Zhang, L. (2012), “The Econometrics of High Frequency Data,” in Statistical Methods for Stochastic Differential Equations, 124, eds. M. Kessler, A. Linder, and M. Sørensen, pp. 109–190, New York: Chapman and Hall/CRC.
   Google Scholar
• Nelson, D. B. (1990), “ARCH Models as Diffusion Approximations,” Journal of Econometrics, 45, 7–38. DOI: 10.1016/0304-4076(90)90092-8.
   Web of Science ®Google Scholar
• Nualart, D. (2006), The Malliavin Calculus and Related Topics (2nd ed.), Probability and Its Applications, Berlin: Springer.
   Google Scholar
• Oksendal, B. (2010), Stochastic Differential Equations: An Introduction with Applications (6th ed.), Berlin, Heidelberg: Springer-Verlag.
   Google Scholar
• Tao, M., Wang, Y., Yao, Q., and Zou, J. (2011), “Large Volatility Matrix Inference via Combining Low-Frequency and High-Frequency Approaches,” Journal of the American Statistical Association, 106, 1025–1040. DOI: 10.1198/jasa.2011.tm10276.
   Web of Science ®Google Scholar
• Tao, M., Wang, Y., and Zhou, H. (2013), “Optimal Sparse Volatility Matrix Estimation for High-Dimensional Itô Processes with Measurement Errors,” The Annals of Statistics, 41, 1816–1864. DOI: 10.1214/13-AOS1128.
   Web of Science ®Google Scholar
• Todorov, V., and Tauchen, G. E. (2011), “Volatility Jumps,” Journal of Business and Economic Statistics, 29, 356–371. DOI: 10.1198/jbes.2010.08342.
   Web of Science ®Google Scholar
• Vetter, M. (2015), “Estimation of Integrated Volatility of Volatility with Applications to Goodness-of-Fit Testing,” Bernoulli, 21, 2393–2418. DOI: 10.3150/14-BEJ648.
   Web of Science ®Google Scholar
• Xiu, D. (2010), “Quasi-Maximum Likelihood Estimation of Volatility with High Frequency Data,” Journal of Econometrics, 159, 235–250. DOI: 10.1016/j.jeconom.2010.07.002.
   Web of Science ®Google Scholar
• Xiu, D., Aït-Sahalia, Y., and Fan, J. (2010), “High-Frequency Covariance Estimates with Noisy and Asynchronous Data,” Journal of the American Statistical Association, 105, 1504–1517. DOI: 10.1198/jasa.2010.tm10163.
   Web of Science ®Google Scholar
• Zhang, L., Mykland, P. A., and Aït-Sahalia, Y. (2005), “A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High-Ffrequency Data,” Journal of the American Statistical Association, 100, 1394–1411. DOI: 10.1198/016214505000000169.
   Web of Science ®Google Scholar