Numerical valuation of basket credit derivatives in structural jump-diffusion models

Journal of Computational Finance

Volumn 15, Issue 4, 2012, Pages 115-158

  Bujok, Karolina ^a   Reisinger, Christoph ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84973662788     PISSN: 14601559     EISSN: 17552850     Source Type: Journal    
DOI: 10.21314/JCF.2012.249     Document Type: Article

References (34)

1. Bielecki, T., and Rutkowski, M. (2002). Credit Risk: Modeling, Valuation and Hedging. Springer.
2. Black, F., and Cox, J. (1976).Valuing corporate securities: some effects of bond indenture provisions. Journal of Finance 31(2), 351-367.
3. Brigo, D., and Mercurio, F. (2007). Interest Rate Models: Theory and Practice. Springer.
4. Broadie, M., Glasserman, P., and Kou, S. (1997).A continuity correction for discrete barrier options. Mathematical Finance 7(4), 325-349.
5. Bujok, K. (2012). Numerical solution of a class of SPDEs in finance. Doctoral Thesis, University of Oxford. (In preparation.)
6. Bush, N., Hambly, B., Haworth, H., Jin, L., and Reisinger, C. (2011). Stochastic evolution equations in portfolio credit modelling. SIAM Journal on Financial Mathematics 2(1), 627-664.
7. Carmona, R., Fouque, J.-P., and Vestal, D. (2009). Interacting particle systems for the computation of rare credit portfolio losses. Finance and Stochastics 13(4), 613-633.
8. Coleman, T., and Li, Y. (1994).On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. Mathematical Programming 67(2), 189-224.
9. Coleman, T., and Li, Y. (1996). An interior trust region approach for nonlinear minimization subject to bounds. SIAM Journal on Optimization 6(2), 418-445.
10. Duffie, D., and Lando, D. (2001).Termstructures of credit spreads with incomplete accounting information. Econometrica 69(3), 633-664.
11. Fang, F., Jönsson, H., Oosterlee, C., and Schoutens, W. (2010). Fast valuation and calibration of credit default swaps under Lévy dynamics.The Journal of Computational Finance 14(2), 57-86.
12. Finger, C., Finkelstein, V., Pan, G., Lardy, J.-P., Ta, T., and Tierney, J. (2002). CreditGrades. Technical Document, RiskMetrics Group.
13. Fouque, J., Wignall, B., and Zhou, X. (2008). Modeling correlated defaults: first passage model under stochastic volatility. The Journal of Computational Finance 11(3), 43-78.
14. Giles, M. (2008). Multi-level Monte Carlo path simulation.Operations Research 56(3), 607-617.
15. Giles, M., and Carter, R. (2006). Convergence analysis of Crank-Nicolson and Rannacher time-marching. The Journal of Computational Finance 9(4), 89-112.
16. Haworth, H., and Reisinger, C. (2007). Modelling basket credit default swaps with default contagion. The Journal of Credit Risk 3(4), 31-67.
17. Hilberink, B., and Rogers, L. (2002). Optimal capital structure and endogenous default. Finance and Stochastics 6(2), 237-263.
18. Hu, X., and Ye, Z. (2007). Valuing credit derivatives in a jump-diffusion model. Applied Mathematics and Computation 190(1), 627-632.
19. Hull, J., Predescu, M., and White, A. (2010). The valuation of correlation-dependent credit derivatives using a structural model. The Journal of Credit Risk 6(3), 99-132.
20. Kaebe, C., Maruhn, J. H., and Sachs, E.W. (2009). Adjoint based Monte Carlo calibration of financial market models. Journal of Finance and Stochastics 13, 351-379.
21. Kiesel, R., and Scherer, M. (2007). Dynamic credit portfolio modelling in structural models with jumps. Preprint, Universität Ulm.
22. Kou, S. (2002). A jump-diffusion model for option pricing. Management Science 48(8), 1086-1101.
23. Kou, S., and Wang, H. (2003). First passage times of a jump diffusion process. Advances in Applied Probability 35(2), 504-531.
24. Kurtz, T., and Xiong, J. (1999). Particle representations for a class of nonlinear SPDEs. Stochastic Processes and Applications 83, 103-126.
25. Lipton, A., and Sepp, A. (2009). Credit value adjustment for credit default swaps via the structural default model. The Jounal of Credit Risk 5(2), 123-146.
26. Merton, R. (1974). On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance 29(2), 684-673.
27. Merton, R. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3(1), 125-144.
28. Pooley, D. M., Vetzal, K. R., and Forsyth, P. A. (2003). Remedies for non-smooth payoffs in option pricing. The Journal of Computational Finance 6(4), 25-40.
29. Ramezani, C., and Zeng, Y. (2007). Maximum likelihood estimation of the double exponential jump-diffusion process. Annals of Finance 3(4), 487-507.
30. Rannacher, R. (1984). Finite element solution of diffusion problems with irregular data. Numerische Mathematik 43(2), 309-327.
31. Schönbucher, P. (2003). Credit Derivatives Pricing Models: Models, Pricing and Implementation. Wiley.
32. Tavella, D., and Randall, C. (2000). Pricing Financial Instruments: The Finite Difference Method. Wiley.
33. Willemann, S. (2007). Fitting the CDO correlation skew: a tractable structural jump-diffusion model. The Journal of Credit Risk 3(1), 63-90.
34. Zhou, C. (1997). A jump-diffusion approach to modelling credit risk and valuing defaultable securities. Discussion Paper, Finance and Economics Series, Board of Governors of Federal Reserve System.