An Application of Genetic Network Programming Model for Pricing of Basket Default Swaps (BDS)

Document Type : Research Article


Department of Industrial Engineering & Management Systems, Amirkabir University of Technology, Tehran, Iran


The credit derivatives market has experienced remarkable growth over the past decade. As such, there is a growing interest in tools for pricing of the most prominent credit derivative, the credit default swap (CDS). In this paper, we propose a heuristic algorithm for pricing of basket default swaps (BDS). For this purpose, genetic network programming (GNP), which is one of the recent evolutionary methods with graph structure as a subgroup of machine learning methods, is applied to assess basket default swap spreads. Here GNP is an alternative way for modeling the default correlation structure among different reference entities in a basket default swap. In order to improve the efficiency of the proposed algorithm, GNP with vigorous connection (GNP-VC) is developed and used for the first time in this paper. To implement our model, we consider a basket consisting of 25 entities of the CDX.NA.IG.5Y index. We compare the heuristic results with the Monte Carlo ones and discuss the efficiency of the proposed algorithm. The impact of vigorous connection on the performance of GNP is also reported.


[1]Abid F., Naifar N., “The determinants of credit default swap rates: An explanatory study”, International Journal of Theoretical and Applied Finance, 9 (01):23-42, 2006.
[2]Bo L., Capponi A., “Counterparty risk for CDS: Default clustering effects”, Journal of Banking & Finance, 52:29- 42, 2015.
[3]Bomfim A. N. (2015) Understanding credit derivatives and related instruments. Academic Press,
[4]Choe G. H., Jang H. J., “Efficient algorithms for basket default swap pricing with multivariate Archimedean copulas”, Insurance: Mathematics and Economics, 48 (2):205-213, 2011.
[5]Collin.Dufresne P., Goldstein R., Hugonnier J., “A general formula for valuing defaultable securities”, Econometrica, 72 (5):1377-1407, 2004.
[6]Das S. R., Duffie D., Kapadia N., Saita L., “Common failings: How corporate defaults are correlated”, The Journal of Finance, 62 (1):93-117, 2007.
[7]Davis M., Lo V., “Modelling default correlation in bond portfolios”, Mastering risk, 2:141-151, 2001.
[8]Dong Y., Wang G., “Bilateral counterparty risk valuation for credit default swap in a contagion model using Markov chain”, Economic Modelling, 40 (0):91-100, 2014.
[19]Duffie D., “Credit swap valuation”, Financial Analysts Journal:73-87, 1999.
[10]Esfahanipour A., Goodarzi M., Jahanbin R., “Analysis and forecasting of IPO underpricing”, Neural Computing and Applications:27(3): 651-658, 2016.
[11]Fabozzi F. J., Cheng X., Chen R.-R., “Exploring the components of credit risk in credit default swaps”, Finance Research Letters, 4 (1):10-18, 2007.
[12]Frey R., Backhaus J., “Portfolio credit risk models with interacting default intensities: a Markovian approach”, Preprint, University of Leipzig, 2004.
[13]Frey R., Backhaus J., “Pricing and hedging of portfolio credit derivatives with interacting default intensities”, International Journal of Theoretical and Applied Finance, 11 (06):611-634, 2008.
[14]Frontczak R., Rostek S., “Modeling loss given default with stochastic collateral”, Economic Modelling, 44:162- 170, 2015.
[15]Glasserman P., “Tail approximations for portfolio credit risk”, The Journal of Derivatives, 12 (2):24-42, 2004.
[16]Gouriéroux C., Monfort A., Renne J.-P., “Pricing default events: Surprise, exogeneity and contagion”, Journal of Econometrics, 182 (2):397-411, 2014.
[17]Gregory J. (2003) Credit derivatives: The definitive guide. Risk books,
[18]Herbertsson A., Jang J., Schmidt T., “Pricing basket default swaps in a tractable shot noise model”, Statistics & Probability Letters, 81 (8):1196-1207, 2011.
[19]Hirasawa K., Okubo M., Katagiri H., Hu J., Murata J. Comparison between genetic network programming (GNP) and genetic programming (GP). In: Evolutionary Computation, 2001. Proceedings of the 2001 Congress on, 2001. IEEE, pp 1276-1282
[20] Jarrow R. A., Yu F., “Counterparty risk and the pricing of defaultable securities”, the Journal of Finance, 56 (5):1765-1799, 2001.
[21] Kackar R. N., “Off-line quality control, parameter design, and the Taguchi method”, Journal of Quality Technology, 17:176-188, 1985.
[22] Koopman S. J., Lucas A., Schwaab B., “Modeling frailty-correlated defaults using many macroeconomic covariates”, Journal of Econometrics, 162 (2):312-325, 2011.
[23] Koza J. R., “Genetic programming. On the programming of computers by means of natural selection”, Complex adaptive systems, Cambridge, MA: The MIT (Massachusetts Institute of Technology) Press, 1992, 1, 1992.
[24] Lee W.-C., “Redefinition of the KMV model’s optimal default point based on genetic algorithms–Evidence from Taiwan”, Expert Systems with Applications, 38 (8):10107-10113, 2011.
[25] Lee Y., Poon S.-H., “Forecasting and decomposition of portfolio credit risk using macroeconomic and frailty factors”, Journal of Economic Dynamics and Control, 41 (0):69-92, 2014.
[26] Leung S. Y., Kwok Y. K., “Credit default swap valuation with counterparty risk”, The Kyoto Economic Review, 75 (1):25-45, 2005.
[27] Li D., “On default correlation: a copula function approach”, Journal of Fixed Income, 9 (4):43-54, 2000.
[28] Lu F.-Q., Huang M., Ching W.-K., Siu T. K., “Credit portfolio management using two-level particle swarm optimization”, Information Sciences, 237:162-175, 2013.
[29] Mousavi S., Esfahanipour A., Zarandi M. H. F., “MGP-INTACTSKY: Multitree Genetic Programming-based learning of INTerpretable and ACcurate TSK sYstems for Dynamic Portfolio Trading”, Applied Soft Computing, 2015.
[30] Mousavi S., Esfahanipour A., Zarandi M. H. F., “A novel approach to dynamic portfolio trading system using multitree genetic programming”, Knowledge- Based Systems, 66:68-81, 2014.
[31] Oreski S., Oreski D., Oreski G., “Hybrid system with genetic algorithm and artificial neural networks and its application to retail credit risk assessment”, Expert systems with applications, 39 (16):12605-12617, 2012.
[32] Schlottmann F., Seese D., “A hybrid heuristic approach to discrete multi-objective optimization of credit portfolios”, Computational statistics & data analysis, 47 (2):373-399, 2004.
[33] Schönbucher P. J. (2003) Credit derivatives pricing models: models, pricing and implementation. John Wiley & Sons,
[34] SchröTer A., Heider P., “Numerical methods to quantify the model risk of basket default swaps”, Journal of Computational and Applied Mathematics, 251:117-132, 2013.
[35] Shaked M., George Shanthikumar J., “The multivariate hazard construction”, Stochastic Processes and Their Applications, 24 (2):241-258, 1987.
[36] Takada H., Sumita U., “Credit risk model with contagious default dependencies affected by macro-economic condition”, European journal of operational research, 214 (2):365-379, 2011.
[37] Thenmozhi M., Sarath Chand G., “Forecasting stock returns based on information transmission across global markets using support vector machines”, Neural Computing and Applications:1-20, 2015.
[38] Wu P.-C., “Applying a factor copula to value basket credit linked notes with issuer default risk”, Finance Research Letters, 7 (3):178-183, 2010.
[39] Yu F., “Correlated defaults in intensity-based models”, Mathematical Finance, 17 (2):155-173, 2007.
[40] Zangeneh L., Bentley P. J., “Analyzing the credit default swap market using Cartesian genetic programming”, Parallel Problem Solving from Nature, 6238:434-444, 2010.
[41] Zheng H., “Efficient hybrid methods for portfolio credit derivatives”, Quantitative Finance, 6 (4):349-357, 2006.
[42] Zheng H., Jiang L., “Basket CDS pricing with interacting intensities”, Finance and Stochastics, 13 (3):445-469, 2009.