Calibration of Credit Spread Scenarios for Monte Carlo Simulations

Abstract

The main goal of this paper is to better understand the behavior of credit spreads in the past and the potential risk of unexpected future credit spread changes. One important consideration to note regarding credit spreads is the fact that bond spreads contain a liquidity premium, which compensates for the risk that the bond cannot be sold at fair value due to a lack of liquidity in the market. As the Credit Default Swap (CDS) market demonstrates more liquidity, CDS spreads are a good proxy for credit spreads excluding the liquidity premium. As a result, this paper presents a set of spread shocks derived from both CDS and bond markets in order to capture spread risk excluding or including a liquidity premium in the aforementioned markets. An empirical study demonstrates that an obvious liquidity premium exists between the bond market and the CDS market. Next, an economic study quantifying the appropriate level of spread shocks is examined. Following this, a stochastic model simulated by the Monte Carlo technique including a mean reverting property, a jump process and a predictive model for the volatility is proposed to forecast credit spreads across rating classes. Then, a methodology allowing to transform a non-positive definite correlation matrix into the nearest positive definite correlation matrix is derived. Finally, this paper provides a methodology for computing the marginal spread risk factor contribution applicable to any type of risk factors derived from the Monte Carlo Value-at-Risk method, and offers a practical implementation of Quasi Monte Carlo, a form of low discrepancy sequences offering shorter computational times associated to a higher accuracy than Monte Carlo.

Keywords: credit spreads, liquidity premium, credit default swap, Black-Karasinski, jum process, predictive model for volatility, non-positive definite correlation matrix, marginal spread risk factor contribution, Quasi Monte Carlo sequence

JEL Classification: C10, C13, C15, C20, C22, C30, C32, C40, C50, C51, C52, C53, C60, C61, C63, C68, G21, G22