| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 97 === Collateralized debt obligation (CDO) develops very fast in recent year; the price of this product is an important issue. The major research of past literatures investigated that how to price the synthetic CDO. One factor Gaussian copula model becomes the standard pricing model because of its simplicity, but this model exists some problems. First, the Gaussian distribution doesn’t have fat-tailed; this phenomenon doesn’t coincide with the market state. Second, pairwise correlations, default intensities and recovery rates will not equal and constant for all assets in the reference portfolio and different market situations. Third, the impact of fast default event will cause the default probabilities of survivors become higher. Hence, we use fat-tailed distribution – Student t and Normal Inverse Gaussian distribution – to solve first problem. Then, we consider random recovery to release the assumption of recovery rate is constant, and using external default model to solve last problem. Final, we will utilize our model to price DJ iTraxx EUR and DJ CDX.IG. We find that using fat-tailed distirbutions the pricing results will more precise than Gaussian distribution, and considering random recovery has little adjusted effect. The performances of external default model are different according to market sutiautions. When the market is in bad time, the external default model has better behavior. On the other hand, we find that the calibrated parameters are close to market situations. Therefore, when taking account of fat-tailed distributions、random recovery and external default model will improve our pricing result.
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