Risky Swaps.

Gikhman, Ilya (2008): Risky Swaps.

Abstract

In [10] we presented a reduced form of risky bond pricing. At the default date a bond seller fail to continue fulfill his obligation and the price of the bond sharply drops down. If the face value of the defaulted bond for no-default scenarios is $1 then the bond price just after default is called its recovery rate (RR). Rating agencies and theoretical models are trying to predict RR for companies or sovereign countries. The main theoretical problem with a risky bond or with general debt problems is presenting the price given the RR. The problem of a credit default swap (CDS) pricing is somewhat an adjacent problem. Recall that the corporate bond price is inversely depends on interest rate. The credit risk on a debt investment is related to the loss if default occurs. There exist a possibility for a risky bond buyer to reduce his credit risk. This can be achieved by buying a protection from a protection seller. The bondholder would pay a fixed premium up to maturity or default, which one comes first. In exchange if default comes before maturity the protection buyer will receive the difference between the initially set face value of the bond and RR. This difference is called ‘loss given default’. This contract represents CDS. The counterparty that pays a fixed premium is called CDS buyer or protection buyer and the opposite party is the CDS seller. Note that in contrast to corporate bond CDS contract does not assume that buyer of the CDS is a holder of the underlying bond. Note that underlying to the swap can be any asset. It is called the reference asset or reference entity. Thus CDS is a credit instrument that separates credit risk from corresponding underlying entity. Thus the formal type of the CDS can be described as follows. The buyer of the credit swap pays fixed rate or coupon until maturity or default if it occurs sooner than maturity. In case of default protection buyer delivers cash or default asset in exchange of the face value of the defaulted debt. These are known as cash or physical settlements correspondingly.

• Item Type: MPRA Paper
• Language: English
• Keywords: Default, risk neutral valuation, credit default swap, constant maturity default swap, equity default swap, asset swap, total return swap, credit linked note, floating rate risky bond, counter party risk, credit spread
• Subjects: G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing

References

1. Bansal G., and Skarabot J. US Fixed Income Strategy. Global Structured Credit Products. Citigroup Global Markets. April 20, 2006. 2. Black F., Scholes M., The Pricing of Options and Corporate Liabilities. The Journal of Political Economy (May’ 1973). 3. Don Chance, Equity Swaps and Equity Investing, 07-2003 4. Duffie D., Credit Swap Valuation, Financial Analysts Journal, 1999, 73-87. 5. Gikhman I, On Black-Scholes Equation. ICFAI Jornal of Applied Finance, v.10, No.4, April 2004, p.47-74. 6. Gikhman I., Drawbacks in Options Definition http://papers.ssrn.com/sol3/papers.cfm?abstract_id=895679, 2006. 7. Gikhman I., Option valuation. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=900111, 2007 8. Gikhman I., Some basic remarks on options valuation. Actes de la 3Хme Conférence Internationale de Finance - IFC 3, Formalisation et Modélisation, Hors Série N°3, IFC3 - 3-5 March, 2005, Hammamet, Tunisia, p.121-136. 9. Gikhman I., Fixed-income pricing. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=958838, 2007. 10. Gikhman I., Corporate debt pricing 1. http://papers.ssrn.com/sol3/papers.cfm?abstract_id= 11. Hull J., and White A., Valuing credit default swaps I: No counterparty default risk, Working Paper, University of Toronto, 2000; Journal of Derivatives 8, Fall, 2000, 29-40. 12. Jarrow R. and Turnbull S., Pricing Options on Financial Securities Subject to Default Risk”, Working Paper, Graduate School of Management, Cornell University, 1992 13. R. Jarrow R. and Turnbull S., Pricing Options on Financial Securities Subject to Credit Risk”, Journal of Finance 50, 1995, 53-85. 14. Merton R., On the pricing of corporate debt: The risk structure of interest rates. 684-73, November 1973.( Presented at AFA Meetings NY December 1973. 15. The Lehman Brothers Guide to Exotic Credit Derivatives, 2003. 16. C. Pedersen, S. Sen, “Valuation of Constant Maturity Default Swaps”, Quantitative Credit Research Quarterly, Lehman Brothers, June 2004.