Risk Analysis of Equity-Bond Portfolios with Default-Driven Stock Price Jumps

Abstract

In this thesis, we study the risk of a portfolio consisting of stocks and bonds, where bond defaults trigger downward jumps in stock prices. To evaluate the portfolio’s risk exposure, we use Value-at-Risk (VaR) as the primary risk measure. The analysis focuses on a portfolio where the stocks are assumed to be large and homogeneous, and the bond holdings may include any number of defaultable bonds, provided they are exchangeable. The modeling framework is based on the stock-bond setup introduced by Herbertsson (2025b), which explicitly incorporates equity price jumps at bond default events. We extend this framework by analyzing a range of portfolio configurations and testing sensitivity to different asset correlation structures. Default probabilities are estimated using the saddlepoint approximation derived in Herbertsson (2023). To model dependence between bond defaults, we apply both the one-factor Gaussian copula and the Clayton copula, offering flexibility in capturing joint default behavior. Our results show that a stock-bond portfolio with stocks following the model in Herbertsson (2025b) yields substantially higher VaR estimates compared to the case where stocks follow the classical Black and Scholes (1973) model. We also demonstrate that VaR is highly sensitive to the choice of copula parameters, and that increasing the portfolio’s stock allocation generally results in higher risk levels.