A CDO Pricing Model with Bivariate Tree Approach: Considering the Correlation between Stochastic Interest Rate and Stock Price
Date Issued
2012
Date
2012
Author(s)
Tseng, Hsin-Ying
Abstract
A defaultable bivariate tree approach is introduced to simulate the value of CDX and compare with real market price.
The stochastic processes of both stock prices and interest rates are considered in my bivariate model. The model also took the dividends and the correlation between two stochastic variables into account. I also adopted Dai’s mean tracking algorithm to improve the stability of probabilities and improved the default intensity formula by Nelson, Siegel’s (1987) parsimonious yield curve model.
I used the corresponding data of iTaxx index and applied Monte Carlo simulation to simulate the spread of the iTraxx tranches. On the first stage, the model is calibrated to the current CDS market. Then I output the cumulated probability and compare with default probability. The default event is identified and the route on the bivariate tree is decided during the process. One the second stage, the tranche structure is created and the spread value is evaluated. I adopted the backward induction during the process for calculating the present discounted value. The above procedures were repeated twice under two assumptions: (1) The stochastic processes of interest rates and stock prices are independent. (2) The stochastic processes of interest rates and stock prices are dependent by considering the correlation coefficients between interest rates and each company. Finally, I compared the absolute errors between independent case and dependent case. The result shows that the independent case was slightly closer to the dependent case.
Subjects
CRR tree model
Hull-White model
mean-tracking algorithm
Cholesky Decomposition
Stochastic process of Interest rate
Default Intensity
iTraxx index
CDO Tranche
Type
thesis
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