Review of Quantitative Finance and Accounting

, Volume 52, Issue 4, pp 1065–1084 | Cite as

Debt rollover-induced local volatility model

  • Oleg SokolinskiyEmail author
Original Research


This paper introduces a structural scenario-based model with debt rollover risk and a higher-fidelity treatment of the bankruptcy procedure. The emerging stock price process is a generalized Brownian motion with state-dependent local volatility, and the resultant implied volatility smile is due exclusively to structural features (debt rollover and credit risks). Therefore, the model reinforces structural foundations of local volatility option pricing models. The paper advocates a joint modeling and calibration framework for multiple classes of derivatives on the firm’s asset value. In particular, an empirical application to Solar City equity and stock option valuation demonstrates the versatility and efficiency gains of the suggested model.


Option pricing Rollover risk Credit risk Local volatility Volatility smile Reorganization 

JEL Classification



  1. Bao J, Pan J (2013) Bond illiquidity and excess volatility. Rev Financ Stud 26(12):3068–3103. CrossRefGoogle Scholar
  2. Barone G (2011) Equity options, credit default swaps and leverage: a simple stochastic-volatility model for equity and credit derivatives. SSRN.
  3. Bharath S, Shumway T (2008) Forecasting default with the merton distance to default model. Rev Financ Stud 21(3):1339–1369CrossRefGoogle Scholar
  4. Black F, Cox J (1976) Valuing corporate securities: some effects of bond indenture provisions. J Finance 31(2):351–367CrossRefGoogle Scholar
  5. Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81:631–659CrossRefGoogle Scholar
  6. Brigo D, Morini M, Pallavicini A (2013) Counterpary credit risk, collateral and funding. Wiley finance. Wiley, New YorkCrossRefGoogle Scholar
  7. Brigo D, Tarenghi M (2004) Credit default swap calibration and equity swap valuation under counterparty risk with a tractable structural model. FEA 2004 Conference at MIT.
  8. Brigo D, Tarenghi M (2005) Credit default swap calibration and counterparty risk valuation with a scenario based first passage model. Working paper.
  9. Broadie M, Chernov M, Sundaresan S (2007) Optimal debt and equity values in the presence of chapter 7 and chapter 11. J Finance 62(3):1341–1377CrossRefGoogle Scholar
  10. Broadie M, Kaya O (2007) A binomial lattice method for pricing corporate debt and modeling chapter 11 proceedings. J Financ Quant Anal 42(2):279–312CrossRefGoogle Scholar
  11. Chen N, Kou S (2009) Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk. Math Finance 19(3):343–378CrossRefGoogle Scholar
  12. Chen RR, Lee CF, Lee HH (2009) Empirical performance of the constant elasticity variance option pricing model. Rev Paci Basin Financ Markets Policies 12(02):177–217CrossRefGoogle Scholar
  13. Chen TK, Liao HH, Lu CW (2011) A flow-based corporate credit model. Rev Quant Finance Account 36(4):517–532. CrossRefGoogle Scholar
  14. Chen CJ, Panjer H (2009) A bridge from ruin theory to credit risk. Rev Quant Finance Account 32(4):373–403. CrossRefGoogle Scholar
  15. Chiu WC, Wang CW, Wu WN, Lin CJ (2017) Impact of rollover risk and corporate policy on extreme risk in the Taiwanese manufacturing industry. Rev Pac Basin Finance Markets Policies 20(03):1750019CrossRefGoogle Scholar
  16. Couch R, Dothan M, Wu W (2012) Interest tax shields: a barrier options approach. Rev Quant Finance Account 39(1):123–146. CrossRefGoogle Scholar
  17. Cremers M, Driessen J, Maenhout P, Weinbaum D (2008) Individual stock-option prices and credit spreads. J Bank Finance 32:2706–2715. CrossRefGoogle Scholar
  18. Derman E, Kani I (1994) Riding on a smile. Risk 7:32–39Google Scholar
  19. Derman E, Kani I (1998) Stochastic implied trees: arbitrage pricing with stochastic term and strike structure of volatility. Int J Theor Appl Finance 1(01):61–110CrossRefGoogle Scholar
  20. Du D (2011) Explaining credit spreads and volatility smirk: a unified framework. Working paperGoogle Scholar
  21. Dupire B (1994) Pricing with a smile. Risk 7:18–20Google Scholar
  22. Gatheral J (2006) The volatility surface: a practitioner’s guide. Wiley finance. Wiley, New YorkGoogle Scholar
  23. Geske R (1979) The valuation of compound options. J Financ Econ 7:63–82CrossRefGoogle Scholar
  24. Hull J, Nelken I, White A (2004/2005) Mertons model, credit risk and volatility skews. J Credit Risk 1(1):3–27Google Scholar
  25. Ju HS, Chen RR, Yeh SK, Yang TH (2015) Evaluation of conducting capital structure arbitrage using the multi-period extended Geske–Johnson model. Rev Quant Finance Account 44(1):89–111. CrossRefGoogle Scholar
  26. Lee SY, Chung YF (2009) Extending the maturity of a defaulting debtthe longstaff model revisited. Rev Pac Basin Financ Markets Policies 12(01):125–140CrossRefGoogle Scholar
  27. Lee KW, Lee CF (2009) Cash holdings, corporate governance structure and firm valuation. Rev Pac Basin Financ Markets Policies 12(03):475–508CrossRefGoogle Scholar
  28. Lee HH, Shih K, Wang K (2016) Measuring sovereign credit risk using a structural model approach. Rev Quant Finance Account 47(4):1097–1128. CrossRefGoogle Scholar
  29. Lee C, Wu TP, Chen RR (2004) The constant elasticity of variance models: new evidence from s&p 500 index options. Rev Pac Basin Financ Markets Policies 7(02):173–190CrossRefGoogle Scholar
  30. Leland H (1994) Corporate debt value, bond covenants, and optimal capital structure. J Finance 49(4):1213–1252CrossRefGoogle Scholar
  31. Liang G, Lutkebohmert E, Wei W (2015) Funding liquidity, debt tenor structure, and creditors belief: an exogenous dynamic debt run model. Math Financ Econ 9:271–302. CrossRefGoogle Scholar
  32. Makarov R, Metzler A, Ni Z (2013) Modelling default risk with occupation times. Finance Res Lett 13:54–65. CrossRefGoogle Scholar
  33. Merton R (1974) On the pricing of corporate debt: the risk structure of interest rates. J Finance 29:449–470Google Scholar
  34. Perrakis S, Zhong R (2015) Rollover risk and volatility risk in credit spread models: a unified approach. J Bank Finance 55:215–231. CrossRefGoogle Scholar
  35. Perrakis S, Zhong R (2014) Credit spreads and state-dependent volatility: theory and empirical evidence. Working paper SSRN. or
  36. Qu C (2009) Pricing corporate bonds in structural models under CEV process. Acta Math Appl Sin. Google Scholar
  37. Rebonato R (2004) Volatility correlation, second edition. Wiley, New YorkCrossRefGoogle Scholar
  38. Riddiough TJ, Thompson HE (1996) Valuing debt in a complex capital structure. Rev Quant Finance Account 6(3):203–221. CrossRefGoogle Scholar
  39. Schönbucher P (2003) Credit derivatives pricing models: models, pricing and implementation, first edition. Wiley, New YorkGoogle Scholar
  40. Shreve S (2004) Stochastic calculus for finance II: continuous-time models. Springer finance textbook. Springer, BerlinGoogle Scholar
  41. Toft K, Prucyk B (1997) Options on leveraged equity: theory and empirical tests. J Finance 52(3):1151–1180CrossRefGoogle Scholar
  42. Vassalou M, Xing Y (2004) Default risk in equity returns. J Finance 59(2):831–868CrossRefGoogle Scholar
  43. Wang AT, Yang SY (2007) A simplified firm value-based risky discount bond pricing model. Rev Pac Basin Financ Markets Policies 10(03):445–468CrossRefGoogle Scholar
  44. Wilmott P (2007) Paul Wilmott introduces quantitative finance, second edition. Wiley, New YorkGoogle Scholar
  45. Xe Z, Xiong W (2012) Rollover risk and credit risk. J Finance 67(2):391–429CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Rutgers Business School - Newark and New BrunswickPiscatawayUSA

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