Saddlepoint Approximation Method in Credit Risk

• Main Authors: Shin-Wen Liang, 梁馨文
• Other Authors: Yi-Ping Chang
• Format: Others
• Language: en_US
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/kzhyeq

碩士 === 東吳大學 === 商用數學系 === 96 === (I) A comparison of saddlepoint approximation in the Vasicek portfolio credit risk model Bank of International Settlement announced The New Basel Capital Accord (Basel II 2004) in which encouraged financial institution to build its internal credit rating model. Because the distribution of portfolio loss is unknown and complicated, it is critical in studying how to select an effective model to describe loss model and calculate its corresponding Value-at-Risk (VaR). In this paper, we select the KMV/Vasicek model as a default model and propose an algorithm in which we apply the saddlepoint approximation to the conditional moment generating function instead of the usual unconditional one. We also calculate the VaR (with confidence level suggested by Basel II) for method of law of large numbers and Monte Carlo simulation. Benchmarking on the 95% interval of Monte Carlo simulation, we compare the results obtained from the conditional and unconditional approaches and conclude that the proposed saddlepoint approximation under conditional calculation outperformed method of law of large numbers and saddlepoint approximation under unconditional calculation. (II)Saddlepoint approximations in the Vasicek portfolio credit risk with random recovery rate models Bank of International Settlement announced The New Basel Capital Accord (Basel II 2004) in which encouraged financial institution to build its internal credit rating model. Because the distribution of portfolio credit loss is unknown and complicated, it is critical in studying how to select an effective model to describe loss model and calculate its corresponding to Value-at-Risk (VaR). In this paper, we assume that macroeconomic systematic factor has influence on both probabilities of default and recovery rates of obligors. We apply saddlepoint approximation to calculate credit portfolio loss distribution of its corresponding tail probability and credit VaR. We also calculate credit VaR for Monte Carlo simulation which is benchmark. Then, we have sensitivity analysis about model of recovery rate.