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Leverage Effect, Volatility Feedback, and Self-Exciting Market Disruptions

Published online by Cambridge University Press:  04 October 2017

Peter Carr  and
Liuren Wu
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Abstract

Equity index volatility variation and its interaction with the index return can come from three distinct channels. First, index volatility increases with the market’s aggregate financial leverage. Second, positive shocks to systematic risk increase the cost of capital and reduce the valuation of future cash flows, generating a negative correlation between the index return and its volatility, regardless of financial leverage. Finally, large negative market disruptions show self-exciting behaviors. This article proposes a model that incorporates all three channels and examines their relative contribution to index option pricing and stock option pricing for different types of companies.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 52 , Issue 5 , October 2017 , pp. 2119 - 2156
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2017 

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Footnotes

1

The authors thank Gurdip Bakshi, Hendrik Bessembinder (the editor), Peter Christoffersen (the referee), Bruno Dupire, Peter Fraenkel, Jingzhi Huang, John Hull, Dilip Madan, Tom McCurdy, George Panayotov, Matthew Richardson, and Allen White, as well as participants at Applied Quantitative Research; Bloomberg; New York University; Rutgers University; the University of Toronto; the 2008 Princeton Implied Volatility Models conference; the 2010 Computational Optimization Models in Statistics, Econometrics and Finance (COMISEF) Latest Developments in Heavy-Tailed Distributions conference; the 2010 China International Conference in Finance; the 2010 Annual Meeting of the Brazilian Finance Society; the 2011 American Finance Association annual meeting; and the 2011 CUNY Macro and Finance Colloquium for comments. We also thank Sergey Nadtochiy for research assistance and Richard Holowczak for computing support. Wu gratefully acknowledges the support by a grant from the City University of New York PSC-CUNY Research Award Program.

References

Adrian, T., and Shin, H. S.. “Liquidity and Leverage.” Journal of Financial Intermediation, 19 (2010), 418–437.CrossRefGoogle Scholar
Aït-Sahalia, Y.; Cacho-Diaz, J.; and Laeven, R. J.. “Modeling Financial Contagion Using Mutually Exciting Jump Processes.” Journal of Financial Economics, 117 (2015), 585–606.Google Scholar
Andersen, T. G.; Fusari, N.; and Todorov, V.. “The Risk Premia Embedded in Index Options.” Journal of Financial Economics, 117 (2015), 558–584.Google Scholar
Azizpour, S.; Giesecke, K.; and Schwenkler, G.. “Exploring the Sources of Default Clustering.” Journal of Financial Economics, forthcoming (2017).Google Scholar
Backus, D., and Chernov, M.. “Disasters Implied by Equity Index Options.” Journal of Finance, 66 (2011), 1969–2012.Google Scholar
Baele, L.; Driessen, J.; Londono, J. M.; and Spalt, O. G.. “Cumulative Prospect Theory and the Variance Premium.” Working Paper, Tilburg University (2014).CrossRefGoogle Scholar
Bai, J., and Wu, L.. “Anchoring Corporate Credit Default Swap Spreads to Firm Fundamentals.” Journal of Financial and Quantitative Analysis, 51 (2016), 1521–1543.CrossRefGoogle Scholar
Bakshi, G.; Cao, C.; and Chen, Z.. “Empirical Performance of Alternative Option Pricing Models.” Journal of Finance, 52 (1997), 2003–2049.CrossRefGoogle Scholar
Bakshi, G.; Carr, P.; and Wu, L.. “Stochastic Risk Premiums, Stochastic Skewness in Currency Options, and Stochastic Discount Factors in International Economies.” Journal of Financial Economics, 87 (2008), 132–156.CrossRefGoogle Scholar
Bakshi, G.; Ju, N.; and Ou-Yang, H.. “Estimation of Continuous-Time Models with an Application to Equity Volatility.” Journal of Financial Economics, 82 (2006), 227–249.Google Scholar
Bakshi, G., and Kapadia, N.. “Delta-Hedged Gains and the Negative Market Volatility Risk Premium.” Review of Financial Studies, 16 (2003a), 527–566.Google Scholar
Bakshi, G., and Kapadia, N.. “Volatility Risk Premium Embedded in Individual Equity Options: Some New Insights.” Journal of Derivatives, 11 (2003b), 45–54.Google Scholar
Bakshi, G., and Madan, D.. “A Theory of Volatility Spread.” Management Science, 52 (2006), 1945–1956.CrossRefGoogle Scholar
Bakshi, G.; Panayotov, G.; and Skoulakis, G.. “Improving the Predictability of Real Economic Activity and Asset Returns with Forward Variances Inferred from Option Portfolios.” Journal of Financial Economics, 100 (2011), 475–495.CrossRefGoogle Scholar
Bakshi, G., and Wu, L.. “The Behavior of Risk and Market Prices of Risk over the Nasdaq Bubble Period.” Management Science, 56 (2010), 2251–2264.CrossRefGoogle Scholar
Bates, D. S.“Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options.” Review of Financial Studies, 9 (1996), 69–107.CrossRefGoogle Scholar
Bates, D. S.“Post-’87 Crash Fears in the S&P 500 Futures Option Market.” Journal of Econometrics, 94 (2000), 181–238.Google Scholar
Beckers, S.“The Constant Elasticity of Variance Model and Its Implications for Option Pricing.” Journal of Finance, 35 (1980), 661–673.CrossRefGoogle Scholar
Bekaert, G., and Wu, G.. “Asymmetric Volatilities and Risk in Equity Markets.” Review of Financial Studies, 13 (2000), 1–42.Google Scholar
Birru, J., and Figlewski, S.. “Anatomy of a Meltdown: The Risk Neutral Density for the S&P 500 in the Fall of 2008.” Journal of Financial Markets, 15 (2012), 151–180.Google Scholar
Black, F.“Studies of Stock Price Volatility Changes.” In Proceedings of the 1976 American Statistical Association, Business and Economical Statistics Section, Alexandria, VA: American Statistical Association (1976).Google Scholar
Black, F., and Cox, J. C.. “Valuing Corporate Securities: Some Effects of Bond Indenture Provisions.” Journal of Finance, 31 (1976), 351–367.CrossRefGoogle Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–654.Google Scholar
Bollerslev, T.; Gibson, M.; and Zhou, H.. “Dynamic Estimation of Volatility Risk Premia and Investor Risk Aversion from Option-Implied and Realized Volatilities.” Journal of Econometrics, 160 (2011), 235–245.Google Scholar
Bollerslev, T.; Tauchen, G.; and Zhou, H.. “Expected Stock Returns and Variance Risk Premia.” Review of Financial Studies, 22 (2009), 4463–4492.CrossRefGoogle Scholar
Broadie, M.; Chernov, M.; and Johannes, M.. “Model Specification and Risk Premia: Evidence from Futures Options.” Journal of Finance, 62 (2007), 1453–1490.Google Scholar
Campbell, J. Y., and Hentschel, L.. “No News Is Good News: An Asymmetric Model of Changing Volatility in Stock Returns.” Review of Economic Studies, 31 (1992), 281–318.Google Scholar
Carr, P., and Sun, J.. “A New Approach for Option Pricing under Stochastic Volatility.” Review of Derivatives Research, 10 (2007), 87–150.Google Scholar
Carr, P., and Wu, L.. “Time-Changed Lévy Processes and Option Pricing.” Journal of Financial Economics, 71 (2004), 113–141.Google Scholar
Carr, P., and Wu, L.. “Variance Risk Premiums.” Review of Financial Studies, 22 (2009), 1311–1341.Google Scholar
Chacko, G., and Viceira, L.. “Spectral GMM Estimation of Continuous-Time Processes.” Journal of Econometrics, 116 (2003), 259–292.Google Scholar
Christoffersen, P. F.; Heston, S. L.; and Jacobs, K.. “The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well.” Management Science, 55 (2009), 1914–1932.Google Scholar
Christoffersen, P.; Jacobs, K.; and Mimouni, K.. “Volatility Dynamics for the S&P 500: Evidence from Realized Volatility, Daily Returns, and Option Prices.” Review of Financial Studies, 23 (2010), 3141–3189.CrossRefGoogle Scholar
Christoffersen, P.; Jacobs, K.; Ornthanalai, C.; and Wang, Y.. “Option Valuation with Long-Run and Short-Run Volatility Components.” Journal of Financial Economics, 90 (2008), 272–297.Google Scholar
Collin-Dufresne, P., and Goldstein, R. S.. “Do Credit Spreads Reflect Stationary Leverage Ratios?” Journal of Finance, 56 (2001), 1929–1957.CrossRefGoogle Scholar
Cox, J. C.“The Constant Elasticity of Variance Option Pricing Model.” Journal of Portfolio Management, 23 (1996), 15–17.Google Scholar
Cremers, M.; Driessen, J.; and Maenhout, P. J.. “Explaining the Level of Credit Spreads: Option-Implied Jump Risk Premia in a Firm Value Model.” Review of Financial Studies, 21 (2008), 2209–2242.Google Scholar
Ding, X.; Giesecke, K.; and Tomecek, P. I.. “Time-Changed Birth Processes and Multi-Name Credit Derivatives.” Operations Research, 57 (2009), 990–1005.Google Scholar
Drechsler, I., and Yaron, A.. “What’s Vol Got to Do with It?” Review of Financial Studies, 24 (2011), 1–45.Google Scholar
Du, D.“General Equilibrium Pricing of Options with Habit Formation and Event Risks.” Journal of Financial Economics, 99 (2011), 400–426.Google Scholar
Duffie, D.; Pan, J.; and Singleton, K.. “Transform Analysis and Asset Pricing for Affine Jump Diffusions.” Econometrica, 68 (2000), 1343–1376.Google Scholar
Dumas, B.; Fleming, J.; and Whaley, R. E.. “Implied Volatility Functions: Empirical Tests.” Journal of Finance, 53 (1998), 2059–2106.Google Scholar
Dupire, B.“Pricing with a Smile.” Risk, 7 (1994), 18–20.Google Scholar
Egloff, D.; Leippold, M.; and Wu, L.. “The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments.” Journal of Financial and Quantitative Analysis, 45 (2010), 1279–1310.Google Scholar
Emanuel, D. C., and MacBeth, J. D.. “Further Results on the Constant Elasticity of Variance Call Option Pricing Model.” Journal of Financial and Quantitative Analysis, 17 (1982), 533–554.Google Scholar
Eraker, B.“Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices.” Journal of Finance, 59 (2004), 1367–1404.Google Scholar
Eraker, B.; Johannes, M.; and Polson, N.. “The Impact of Jumps in Equity Index Volatility and Returns.” Journal of Finance, 58 (2003), 1269–1300.Google Scholar
Figlewski, S.“Estimating the Implied Risk Neutral Density for the U.S. Market Portfolio.” In Volatility and Time Series Econometrics: Essays in Honor of Robert F. Engle, Bollerslev, T., Russell, J. R., and Watson, M., eds. Oxford, UK: Oxford University Press (2009).Google Scholar
Figlewski, S., and Wang, X.. “Is the ‘Leverage Effect’ a Leverage Effect?” Working Paper, New York University and City University of Hong Kong (2000).Google Scholar
Hasanhodzic, J., and Lo, A.. “Black’s Leverage Effect Is Not Due to Leverage.” Working Paper, Boston University and MIT (2010).Google Scholar
Heston, S. L.“Closed-Form Solution for Options with Stochastic Volatility, with Application to Bond and Currency Options.” Review of Financial Studies, 6 (1993), 327–343.CrossRefGoogle Scholar
Heston, S. L., and Nandi, S.. “A Closed-Form GARCH Option Valuation Model.” Review of Financial Studies, 13 (2000), 585–625.Google Scholar
Heston, S. L. H.“A Simple New Formula for Options with Stochastic Volatility.” Working Paper, University of Maryland (1997).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), 1405–1440.Google Scholar
Hurd, T., and Li, C.. “In Search of Hybrid Models for Credit Risk: From Leland-Toft to Carr-Linetsky.” Working Paper, McMaster University (2008).Google Scholar
Ishida, I., and Engle, R. F.. “Modeling Variance of Variance: The Square Root, the Affine, and the CEV GARCH Models.” Working Paper, New York University (2002).Google Scholar
Javaheri, A. Inside Volatility Arbitrage: The Secrets of Skewness. London, UK: John Wiley & Sons (2005).Google Scholar
Jones, C. S.“The Dynamics of Stochastic Volatility: Evidence from Underlying and Options Markets.” Journal of Econometrics, 116 (2003), 181–224.Google Scholar
Kalman, R. E.“A New Approach to Linear Filtering and Prediction Problems.” Transactions of the ASME—Journal of Basic Engineering, 82 (1960), 35–45.Google Scholar
Leland, H. E.“Risky Debt, Bond Covenants and Optimal Capital Structure.” Journal of Finance, 49 (1994), 1213–1252.Google Scholar
Leland, H. E., and Toft, K. B.. “Optimal Capital Structure, Endogenous Bankruptcy and the Term Structure of Credit Spreads.” Journal of Finance, 51 (1996), 987–1019.Google Scholar
Lewis, A. L. Option Valuation under Stochastic Volatility. Newport Beach, CA: Finance Press (2000).Google Scholar
Medvedev, A., and Scaillet, O.. “Approximation and Calibration of Short-Term Implied Volatilities under Jump-Diffusion Stochastic Volatility.” Review of Financial Studies, 20 (2007), 427–459.Google Scholar
Merton, R. C.“On the Pricing of Corporate Debt: The Risk Structure of Interest Rates.” Journal of Finance, 29 (1974), 449–470.Google Scholar
Pan, J.“The Jump-Risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study.” Journal of Financial Economics, 63 (2002), 3–50.Google Scholar
Ross, S.“The Recovery Theorem.” Journal of Finance, 70 (2015), 615–648.Google Scholar
Santa-Clara, P., and Yan, S.. “Crashes, Volatility, and the Equity Premium: Lessons from S&P 500 Options.” Review of Economics and Statistics, 92 (2010), 435–451.Google Scholar
Schroder, M.“Computing the Constant Elasticity of Variance Option Pricing Formula.” Journal of Finance, 44 (1989), 211–219.Google Scholar
Wu, L., and Zhu, J.. “Simple Robust Hedging with Nearby Contracts.” Journal of Financial Econometrics, 15 (2016), 1–35.CrossRefGoogle Scholar
Zhou, H.“Variance Risk Premia, Asset Predictability Puzzles, and Macroeconomic Uncertainty.” Working Paper, Federal Reserve Board (2010).Google Scholar
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