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Synthetic Options and Implied Volatility for the Corporate Bond Market

Published online by Cambridge University Press:  15 February 2022

Steven Shu-Hsiu Chen ,
Hitesh Doshi  and
Sang Byung Seo Open the ORCID record for Sang Byung Seo [Opens in a new window]
Steven Shu-Hsiu Chen
Affiliation:
A. R. Sanchez, Jr. School of Business, Texas A&M International University shu-hsiu.chen@tamiu.edu
Hitesh Doshi
Affiliation:
Bauer College of Business, University of Houston hdoshi@bauer.uh.edu
Sang Byung Seo*
Affiliation:
Wisconsin School of Business, University of Wisconsin–Madison
*
sang.seo@wisc.edu (corresponding author)
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Abstract

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We synthetically create option contracts on a corporate bond index using CDX swaptions, overcoming the limitations that stem from the lack of traded corporate bond options. Our approach allows us to estimate forward-looking moments concerning the corporate bond market in a model-free manner. By constructing an aggregate volatility measure and the associated variance risk premium, we examine the role of volatility risk in the corporate bond market. We highlight that the ex ante conditional second and higher moments we estimate from synthetic corporate bond options carry important implications for credit risk models, providing an extra basis for testing their validity.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 58 , Issue 3 , May 2023 , pp. 1295 - 1325
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of the Michael G. Foster School of Business, University of Washington

Footnotes

We thank the anonymous referee and Hendrik Bessembinder (the editor) for their valuable comments and suggestions. We are also grateful to Daniel Andrei, Patrick Augustin, Turan Bali, Daniel Bauer, Fousseni Chabi-Yo, Hui Chen, Ing-Haw Cheng, James Choi, Jesse Davis, Jan Ericsson, Mathieu Fournier, Mohammad Ghaderi, Robert Goldstein, Kris Jacobs, Alexandre Jeanneret, Mete Kilic, Praveen Kumar, Yuguo Liu, Piotr Orlowski, Paola Pederzoli, Erwan Quintin, Mark Ready, Ivan Shaliastovich, Viktor Todorov, Aurelio Vasquez, and seminar participants at the 2020 Western Finance Association meeting, 2019 HEC-McGill Winter Finance Workshop, Bank of Italy, University of Houston, and University of Wisconsin–Madison for helpful comments. An earlier version of this article was circulated under the titles “Corporate Bond VIX” and “Ex Ante Risk in the Corporate Bond Market: Evidence from Synthetic Options.”

References

Acharya, V. V.; Amihud, Y.; and Bharath, S. T.. “Liquidity Risk of Corporate Bond Returns: Conditional Approach.” Journal of Financial Economics, 110 (2013), 358–386.CrossRefGoogle Scholar
Aït-Sahalia, Y., and Duarte, J.. “Nonparametric Option Pricing Under Shape Restrictions.” Journal of Econometrics, 116 (2003), 9–47.CrossRefGoogle Scholar
Aït-Sahalia, Y.; Karaman, M.; and Mancini, L.. “The Term Structure of Variance Swaps and Risk Premia.” Working Paper, Princeton University (2018).Google Scholar
Aït-Sahalia, Y., and Lo, A. W.. “Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices.” Journal of Finance, 53 (1998), 499–547.CrossRefGoogle Scholar
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Labys, P.. “Modeling and Forecasting Realized Volatility.” Econometrica, 71 (2003), 579–625.CrossRefGoogle Scholar
Andersen, T. G.; Fusari, N.; and Todorov, V.. “The Risk Premia Embedded in Index Options.” Journal of Financial Economics, 117 (2015), 558–584.CrossRefGoogle Scholar
Bai, J.; Bali, T. G.; and Wen, Q.. “Do the Distributional Characteristics of Corporate Bonds Predict Their Future Returns?” Working Paper, Georgetown University (2016).CrossRefGoogle Scholar
Bai, J.; Bali, T. G.; and Wen, Q.. “Common Risk Factors in the Cross-Section of Corporate Bond Returns.” Journal of Financial Economics, 131 (2019), 619–642.CrossRefGoogle Scholar
Bai, J., and Collin-Dufresne, P.. “The CDS-Bond Basis.” Financial Management, 48 (2019), 417–439.CrossRefGoogle Scholar
Bakshi, G., and Kapadia, N.. “Delta-Hedged Gains and the Negative Market Volatility Risk Premium.” Review of Financial Studies, 16 (2003), 527–566.CrossRefGoogle 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), 101–143.CrossRefGoogle Scholar
Bakshi, G., and Madan, D.. “Spanning and Derivative-Security Valuation.” Journal of Financial Economics, 55 (2000), 205–238.CrossRefGoogle Scholar
Bakshi, G.; Madan, D.; and Panayotov, G.. “Returns of Claims on the Upside and the Viability of U-Shaped Pricing Kernels.” Journal of Financial Economics, 97 (2010), 130–154.CrossRefGoogle Scholar
Bekaert, G., and Wu, G.. “Asymmetric Volatility and Risk in Equity Markets.” Review of Financial Studies, 13 (2000), 1–42.CrossRefGoogle Scholar
Bollerslev, T.; Litvinova, J.; and Tauchen, G.. “Leverage and Volatility Feedback Effects in High-Frequency Data.” Journal of Financial Econometrics, 4 (2006), 353–384.CrossRefGoogle 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
Bongaerts, D.; de Jong, F.; and Driessen, J.. “An Asset Pricing Approach to Liquidity Effects in Corporate Bond Markets.” Review of Financial Studies, 30 (2017), 1229–1269.CrossRefGoogle Scholar
Breeden, D. T., and Litzenberger, R. H.. “Prices of State-Contingent Claims Implicit in Option Prices.” Journal of Business, 51 (1978), 621–651.CrossRefGoogle Scholar
Britten-Jones, M., and Neuberger, A.. “Option Prices, Implied Price Processes, and Stochastic Volatility.” Journal of Finance, 55 (2000), 839–866.CrossRefGoogle Scholar
Campbell, J. Y., and Hentschel, L.. “No News Is Good News: An Asymmetric Model of Changing Volatility in Stock Returns.” Journal of Financial Economics, 31 (1992), 281–318.CrossRefGoogle Scholar
Carr, P., and Madan, D.. “Towards a Theory of Volatility Trading.” In Risk Book on Volatility, Jarrow, R., ed. New York: Risk (1998).Google Scholar
Carr, P., and Madan, D.. “Optimal Positioning in Derivative Securities.” Quantitative Finance, 1 (2001), 19–37.CrossRefGoogle Scholar
Carr, P., and Wu, L.. “A Tale of Two Indices.” Journal of Derivatives, 13 (2006), 13–29.CrossRefGoogle Scholar
Carr, P., and Wu, L.. “Variance Risk Premiums.” Review of Financial Studies, 22 (2009), 1311–1341.CrossRefGoogle Scholar
Chabi-Yo, F. “Pricing Kernels with Stochastic Skewness and Volatility Risk.” Management Science, 58 (2012), 624–640.CrossRefGoogle Scholar
Chabi-Yo, F.; Garcia, R.; and Renault, E.. “State Dependence Can Explain the Risk Aversion Puzzle.” Review of Financial Studies, 21 (2007), 973–1011.CrossRefGoogle Scholar
Choi, J., and Kim, Y.. “Anomalies and Market (Dis)Integration.” Journal of Monetary Economics, 100 (2018), 16–34.CrossRefGoogle Scholar
Choi, Y. S.; Doshi, H.; Jacobs, K.; and Turnbull, S. M.. “Pricing Structured Products with Economic Covariates.” Journal of Financial Economics, 135 (2019), 754–773.CrossRefGoogle Scholar
Christoffersen, P.; Heston, S.; and Jacobs, K.. “Capturing Option Anomalies with a Variance-Dependent Pricing Kernel.” Review of Financial Studies, 26 (2013), 1963–2006.CrossRefGoogle Scholar
Christoffersen, P.; Jacobs, K.; and Pan, X. N.. “The State Price Density Implied by Crude Oil Futures and Option Prices.” Review of Financial Studies, 35 (2022), 1064–1103.CrossRefGoogle Scholar
Collin-Dufresne, P.; Goldstein, R. S.; and Yang, F.. “On the Relative Pricing of Long-Maturity Index Options and Collateralized Debt Obligations.” Journal of Finance, 67 (2012), 1983–2014.CrossRefGoogle Scholar
Collin-Dufresne, P.; Junge, B.; and Trolle, A. B.. “How Integrated Are Credit and Equity Markets? Evidence from Index Options.” Working Paper, Swiss Finance Institute (2021).CrossRefGoogle Scholar
Coval, J. D.; Jurek, J. W.; and Stafford, E.. “Economic Catastrophe Bonds.” American Economic Review, 99 (2009), 628–666.CrossRefGoogle Scholar
Coval, J. D., and Shumway, T.. “Expected Option Returns.” Journal of Finance, 56 (2001), 983–1009.CrossRefGoogle Scholar
Drechsler, I., and Yaron, A.. “What’s Vol Got to Do with It.” Review of Financial Studies, 24 (2011), 1–45.CrossRefGoogle Scholar
Du, D.; Elkamhi, R.; and Ericsson, J.. “Time-Varying Asset Volatility and the Credit Spread Puzzle.” Journal of Finance, 74 (2019), 1841–1885.CrossRefGoogle Scholar
Duffie, D., and Singleton, K. J.. Credit Risk: Pricing, Management, and Measurement. Princeton Series in Finance. Princeton, NJ: Princeton University Press (2003).CrossRefGoogle Scholar
Dupire, B. “Pricing with a Smile.” Risk, 7 (1994), 18–20.Google Scholar
Dykstra, R. L. “An Algorithm for Restricted Least Squares Regression.” Journal of the American Statistical Association, 78 (1983), 837–842.CrossRefGoogle Scholar
Eom, Y. H.; Helwege, J.; and Huang, J.-Z.. “Structural Models of Corporate Bond Pricing: An Empirical Analysis.” Review of Financial Studies, 17 (2004), 499–544.CrossRefGoogle Scholar
Eraker, B., and Wu, Y.. “Explaining the Negative Returns to VIX Futures and ETNs: An Equilibrium Approach.” Journal of Financial Economics, 125 (2017), 72–98.CrossRefGoogle Scholar
Fama, E. F., and French, K. R.. “Common Risk Factors in the Returns on Bonds and Stocks.” Journal of Financial Economics, 33 (1993), 3–56.CrossRefGoogle Scholar
Feldhütter, P., and Schaefer, S. M.. “The Myth of the Credit Spread Puzzle.” Review of Financial Studies, 31 (2018), 2897–2942.Google Scholar
French, K. R.; Schwert, G. W.; and Stambaugh, R. F.. “Expected Stock Returns and Volatility.” Journal of Financial Economics, 19 (1987), 3–29.CrossRefGoogle Scholar
Gebhardt, W. R.; Hvidkjaer, S.; and Swaminathan, B.. “The Cross-Section of Expected Corporate Bond Returns: Betas or Characteristics?” Journal of Financial Economics, 75 (2005), 85–114.CrossRefGoogle Scholar
Huang, J.-Z., and Huang, M.. “How Much of the Corporate-Treasury Yield Spread Is due to Credit Risk?” Review of Asset Pricing Studies, 2 (2012), 153–202.CrossRefGoogle Scholar
Huang, J.-Z.; Shi, Z.; and Zhou, H.. “Specification Analysis of Structural Credit Risk Models.” Working Paper, Tsinghua University (2019).CrossRefGoogle Scholar
Jackwerth, J. C. “Recovering Risk Aversion from Option Prices and Realized Returns.” Review of Financial Studies, 13 (2000), 433–451.CrossRefGoogle Scholar
Jiang, G. J., and Tian, Y. S.. “The Model-Free Implied Volatility and Its Information Content.” Review of Financial Studies, 18 (2005), 1305–1342.CrossRefGoogle Scholar
Jostova, G.; Nikolova, S.; Philipov, A.; and Stahel, C. W.. “Momentum in Corporate Bond Returns.” Review of Financial Studies, 26 (2013), 1649–1693.CrossRefGoogle Scholar
Kelly, B. T.; Manzo, G.; and Palhares, D.. “Credit-Implied Volatility.” Working Paper, University of Chicago (2018).Google Scholar
Li, H., and Zhao, F.. “Nonparametric Estimation of State-Price Densities Implicit in Interest Rate Cap Prices.” Review of Financial Studies, 22 (2009), 4335–4376.CrossRefGoogle Scholar
Lin, H.; Wang, J.; and Wu, C.. “Liquidity Risk and Expected Corporate Bond Returns.” Journal of Financial Economics, 99 (2011), 628–650.CrossRefGoogle Scholar
Longstaff, F. A., and Rajan, A.. “An Empirical Analysis of the Pricing of Collateralized Debt Obligations.” Journal of Finance, 63 (2008), 529–563.CrossRefGoogle 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
Neuberger, A. “The Log Contract.” Journal of Portfolio Management, 20 (1994), 74–80.CrossRefGoogle Scholar
Newey, W., and West, K.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703–708.CrossRefGoogle Scholar
Rosenberg, J. V., and Engle, R. F.. “Empirical Pricing Kernels.” Journal of Financial Economics, 64 (2002), 341–372.CrossRefGoogle Scholar
Seo, S. B., and Wachter, J. A.. “Do Rare Events Explain CDX Tranche Spreads?” Journal of Finance, 73 (2018), 2343–2383.CrossRefGoogle Scholar
Song, Z., and Xiu, D.. “A Tale of Two Option Markets: Pricing Kernels and Volatility Risk.” Journal of Econometrics, 190 (2016), 176–196.CrossRefGoogle Scholar
Todorov, V. “Variance Risk-Premium Dynamics: The Role of Jumps.” Review of Financial Studies, 23 (2010), 345–383.CrossRefGoogle Scholar
Zhou, H. “Variance Risk Premia, Asset Predictability Puzzles, and Macroeconomic Uncertainty.” Annual Review of Financial Economics, 10 (2018), 481–497.CrossRefGoogle Scholar
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