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Total return swap valuation with counterparty risk and interest rate risk. (English) Zbl 1406.91454

Summary: We study the pricing of total return swap (TRS) under the contagion models with counterparty risk and the interest rate risk. We assume that interest rate follows Heath-Jarrow-Morton (HJM) forward interest rate model and obtain the Libor market interest rate. The cases where default is related to the interest rate and independent of interest rate are considered. Using the methods of change of measure and the “total hazard construction”, the joint default probabilities are obtained. Furthermore, we obtain the closed-form formulas of TRS under different contagion models, respectively.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G30 Interest rates, asset pricing, etc. (stochastic models)
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[1] Merton, R. C., On the pricing of corporate debt: the risk structure of interest rates, The Journal of Finance, 29, 2, 449-470 (1974)
[2] Black, F.; Cox, J. C., Valuing corporate securities: some effects of bond indenture provisions, The Journal of Finance, 31, 2, 351-367 (2007)
[3] Geske, R., The valuation of corporate liabilities as compound options, The Journal of Financial and Quantitative Analysis, 12, 4, 541-552 (1977)
[4] Artzner, P.; Delbaen, F., Default risk insurance and incomplete markets, Mathematical Finance, 5, 3, 187-195 (1995) · Zbl 0866.90047
[5] Duffie, D.; Schroder, M.; Skiadas, C., Recursive valuation of defaultable securities and the timing of resolution of uncertainty, The Annals of Applied Probability, 6, 4, 1075-1090 (1996) · Zbl 0868.90008
[6] Jarrow, R. A.; Turnbull, S. M., Pricing options on financial securities subject to default risk, The Journal of Finance, 50, 1, 53-86 (1995)
[7] Madan, D. B.; Unal, H., Pricing the risks of default, Review of Derivatives Research, 2, 2-3, 121-160 (1998) · Zbl 1274.91426
[8] Duffie, D.; Lando, D., Term structures of credit spreads with incomplete accounting information, Econometrica, 69, 3, 633-664 (2001) · Zbl 1019.91022
[9] Jarrow, R. A.; Lando, D.; Turnbull, S. M., A Markov model for the term structure of credit risk spreads, The Review of Financial Studies, 10, 2, 481-523 (1997)
[10] Litterman, R. B.; Iben, T., Corporate Bond Valuation and Term Structure of Credit Spreads, Financial Anal, The Journal of Portfolio Management, 17, 3, 52-64 (1991)
[11] Duffie, D.; Singleton, K. J., Modeling term structures of defaultable bonds, Review of Financial Studies, 12, 4, 687-720 (1999)
[12] Lando, D., On cox processes and credit risky securities, Review of Derivatives Research, 2, 2-3, 99-120 (1998) · Zbl 1274.91459
[13] Collin-Dufresne, P.; Solnik, B., On the term structure of default premia in the swap and LIBOR markets, The Journal of Finance, 56, 3, 1095-1115 (2001)
[14] Duffee, G. R., Estimating the price of default risk, Review of Financial Studies, 12, 1, 197-226 (1999)
[15] Jarrow, R. A.; Yu, F., Counterparty risk and the pricing of defaultable securities, The Journal of Finance, 56, 5, 1765-1799 (2001)
[16] Elliott, R. J.; Jeanblanc, M.; Yor, M., On models of default risk, Mathematical Finance, 10, 2, 179-195 (2000) · Zbl 1042.91038
[17] Jamshidian, F., Valuation of Credit Default Swaps and Swaptions (2003), The Hague, The Netherlands: NIB Capital Bank, The Hague, The Netherlands · Zbl 1063.91034
[18] Ye, Z. X.; Zhuang, R. X., Pricing of total return swap, Chinese Journal of Applied Probability and Statistics, 28, 1, 79-86 (2012) · Zbl 1265.91072
[19] Das, S. R.; Sundaram, R. K., An integrated model for hybrid securities, Management Science, 53, 9, 1439-1451 (2007) · Zbl 1232.91687
[20] Harrison, J. M.; Kreps, D. M., Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, 20, 3, 381-408 (1979) · Zbl 0431.90019
[21] Harrison, J. M.; Pliska, S. R., Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and Their Applications, 11, 3, 215-260 (1981) · Zbl 0482.60097
[22] Heath, D.; Jarrow, R.; Morton, A., Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation, Econometrica, 60, 1, 77-105 (1992) · Zbl 0751.90009
[23] Shreve, S. E., Stochastic Calculus for Finance: Continuous-Time Models (2004), New York, NY, USA: Springer, New York, NY, USA · Zbl 1068.91041
[24] Leung, S. Y.; Kwok, Y. K., Credit default swap valuation with counterparty risk, The Kyoto Economic Review, 74, 1, 25-45 (2005)
[25] Bai, Y.-F.; Hu, X.-H.; Ye, Z.-X., A model for dependent default with hyperbolic attenuation effect and valuation of credit default swap, Applied Mathematics and Mechanics, 28, 12, 1643-1649 (2007) · Zbl 1231.62186
[26] Wang, A.-J.; Ye, Z.-X., The pricing of credit risky securities under stochastic interest rate model with default correlation, Applications of Mathematics, 58, 6, 703-727 (2013) · Zbl 1299.91162
[27] Hao, R.-L.; Ye, Z.-X., The intensity model for pricing credit securities with jump diffusion and counterparty risk, Mathematical Problems in Engineering, 2011 (2011) · Zbl 1213.91171
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