Mathematical and physical analysis of pricing models for structured financial securities.

摘要

In this thesis, we present an extension of the one-factor Gaussian copula model for pricing collateralized debt obligations (CDOs): Instead of using flat default correlation and rate parameters across the whole portfolio, we use individual correlation coefficients between each reference entity and the market (S&P 500 index) based on 5-year daily stock prices, and we use specific rate parameter for each entity by curve-fitting the default probability term structure. Spreads from this improved model are compared to those obtained from the one-factor Gaussian copula model with flat correlation. Results show that uniform correlation and rate parameters fail to capture that a few or even one single asset can substantially impact the credit quality of the whole portfolio. Heterogeneity of correlations and rate parameters of different reference entities is indispensable for constructing reliable and realistic models for pricing synthetic CDOs.;We also introduce analytical solutions to the pricing of both homogeneous and heterogeneous CDOs. We compare these analytical solutions with results obtained from simulation models. Results show very good consistency.;At the end, we introduce the analysis of another financial derivative - Securitized Life Settlements (SLSs) and present an analytical solution to the pricing of homogeneous SLSs.