Optimal Portfolios with Credit Default Swaps



Using a continuous-time, stochastic, and dynamic framework, this study derives a closed-form solution for the optimal investment problem for an agent with hyperbolic absolute risk aversion preferences for maximising the expected utility of his or her final wealth. The agent invests in a frictionless, complete market in which a riskless asset, a (defaultable) bond, and a credit default swap written on the bond are listed. The model is calibrated to market data of six European countries and assesses the behaviour of an investor exposed to different levels of sovereign risk. A numerical analysis shows that it is optimal to issue credit default swaps in a larger quantity than that of bonds, which are optimally purchased. This speculative strategy is more aggressive in countries characterised by higher sovereign risk. This result is confirmed when the investor is endowed with a different level of risk aversion. Finally, we solve a static version of the optimisation problem and show that the speculative/hedging strategy is definitely different with respect to the dynamic one.


Credit default swap Optimal dynamic programming Hyperbolic absolute risk aversion 

JEL Classification

G11 G20 G12 


  1. Aizenman J, Hutchison M, Jinjarak Y (2013) What is the risk of european sovereign debt defaults? Fiscal space, cds spreads and market pricing of risk. J Int Money Financ 34:37–59. The European Sovereign Debt Crisis: Background & PerspectiveCrossRefGoogle Scholar
  2. Badaoui S, Cathcart L, El-Jahel L (2013) Do sovereign credit default swaps represent a clean measure of sovereign default risk? a factor model approach. J Bank Financ 37(7):2392–2407CrossRefGoogle Scholar
  3. Biffis E (2005) Affine processes for dynamic mortality and actuarial valuations. Insurance: Mathematics and Economics 37(3):443–468Google Scholar
  4. Björk T (2009) Arbitrage theory in continuous time, 3rd Edn. Oxford University PressGoogle Scholar
  5. Calice G, Chen J, Williams J (2013) Liquidity spillovers in sovereign bond and cds markets: an analysis of the eurozone sovereign debt crisis. J Econ Behav Organ 85:122–143. Financial Sector Performance and RiskCrossRefGoogle Scholar
  6. Calice G, Ioannidis C, Williams J (2012) Credit derivatives and the default risk of large complex financial institutions. J Financ Serv Res 42:85–107CrossRefGoogle Scholar
  7. Chiarella C, ter Ellen S, He X-Z, Wu E (2015) Fear or fundamentals? heterogeneous beliefs in the european sovereign cds market. Journal of Empirical Finance 32:19–34CrossRefGoogle Scholar
  8. Dahl M (2004) Stochastic mortality in life insurance: Market reserves and mortality-linked insurance contracts. Insurance: Mathematics and Economics 35 (1):113–136Google Scholar
  9. Delatte A -L, Gex M, López-Villavicencio A (2012) Has the cds market influenced the borrowing cost of european countries during the sovereign crisis? J Int Money Financ 31(3):481–497CrossRefGoogle Scholar
  10. Dewachter H, Iania L, Lyrio M, de Sola Perea M (2015) A macro-financial analysis of the euro area sovereign bond market. J Bank Financ 50:308–325CrossRefGoogle Scholar
  11. Duffie D, Singleton KJ (2003) Credit Risk – Pricing, Measurement, and Management. Princeton Series in FinanceGoogle Scholar
  12. Fontana A, Scheicher M (2016) An analysis of euro area sovereign cds and their relation with government bonds. J Bank Financ 62:126–140CrossRefGoogle Scholar
  13. Haugh D, Ollivaud P, Turner D (2009) What drives sovereign risk premiums? An analysis of recent evidence from the euro area. Economics department working papers, OECDGoogle Scholar
  14. Hull JC, White AD (2000) Valuing credit default swaps i – no counterparty default risk. J Deriv 8(1):29–40CrossRefGoogle Scholar
  15. Juurikkala O (2012) Credit default swaps and the eu short selling regulation: a critical analysis. European Company and Financial Law Review 9(3):307–341CrossRefGoogle Scholar
  16. Karatzas I, Shreve ES (1998) Methods of Mathematical Finance. Springer-VerlagGoogle Scholar
  17. Øksendal B (2000) Stochastic differential equations - an introduction with applications, 5th Edn. Springer–VerlagGoogle Scholar
  18. Kubler F, Schmedders K (2001) Incomplete markets, transitory shocks, and welfare. Rev Econ Dyn 4(4):747–766CrossRefGoogle Scholar
  19. Lando D (1998) On cox processes and credit risky securities. Rev Deriv Res 2:99–120Google Scholar
  20. Menoncin F (2008) The role of longevity bonds in optimal portfolios. Insurance: Mathematics and Economics 42:343–358Google Scholar
  21. Menoncin F (2009) Death bonds with stochastic force of mortality. Actuarial and financial mathematics conference - interplay between finance and insurance. In: Vanmaele M, Deelstra G, De Schepper A, Dhaene J, Van Goethem P (eds)Google Scholar
  22. Menoncin F, Regis L (2015) Longevity assets and pre-retirement consumption/portfolio decisions. EIC working paper series 2, IMT luccaGoogle Scholar
  23. Sgherri S, Zoli E (2009) Euro area sovereign risk during the crisis. Imf working paper no. 09/222, international monetary fundGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Economics, Management, and Quantitative MethodsUniversity of MilanMilanItaly
  2. 2.Department of Economics and ManagementUniversity of BresciaBresciaItaly

Personalised recommendations