The modified adaptation of the Nelson–Siegel (1987) model, as suggested by

Diebold and Li (

2006), is used in the study. The empirical model of the analysis takes the following form:

where

$CD{S}_{i,t}$ is sector-wise CDS spread;

$\mathsf{\Delta}{L}_{t}$,

$\mathsf{\Delta}{S}_{t}$ and

$\mathsf{\Delta}{C}_{t}$ are the unanticipated movements in the level, slope and curvature factor of the yield curve; while

${\beta}_{0,t}$,

${\beta}_{L,t}$,

${\beta}_{S,t}$ and

${\beta}_{C,t}$ are the parameters that measure the sensitivity of CDS spreads to changes in the long-, medium- and short-term yield rates

3.

Diebold and Li (

2006) used variations in the exponential component of the Nelson–Siegel model to obtain the factor structure of the yield curve, i.e., level, slope and curvature.

Chen and Tzang (

1988),

Devaney (

2001),

Swanson et al. (

2002) and

Stevenson et al. (

2007) used an array of interest rates jointly and established that regardless of the time structure, there exists a negative relationship between yield rates and CDS spreads.

Zhu (

2006) found that CDS spreads and bond yields may hold equivalence in the long run, but there is a substantial deviation in the short term. In addition,

Shahzad et al. (

2017) and (Malhotra) found that the equity prices and the volatility index serve as less significant but positive determinants of the industry-level CDS spreads.

Wegener et al. (

2017) suggested that positive oil price shocks lead to lower sovereign CDS. Thus, in the framework of the analysis, two potentially influential macroeconomic and financial variables are used, namely sector-wise returns and the OVX volatility index. Thus, the final proposed model can be specified as follows:

where

$\mathsf{\Delta}{R}_{S,t}$ and

$\mathsf{\Delta}OV{X}_{t}$ denote the changes in the sector-wise returns and volatility index.

The OLS regression model estimates the mean of the explained variable for specific values of the explanatory variables, i.e., it focuses on the central tendency of the variable and does not take into account the extreme values. In the case of non-normal errors, OLS regression fails to give robust results.

Koenker and Bassett (

1982) came up with the standard quantile regression (QR), which is an expansion of the classical linear regression model. It allows for the impact of an explanatory variable to vary across the quantiles of the explained variable. An additional attribute of this technique is that it aids in analysing the effect of independent variables not only in the middle of the distribution but also at the tails. In this way, it treats the outliers and non-normality issues. Therefore, it could be used to see how the relationships between variables are impacted in varying market states. Additionally, it acknowledges the implicit heterogeneity in the data by relaxing the assumption of independently and identically distributed error terms. Thus, in the case of non-normal errors, when the OLS regression fails to give robust results, the QR model proves to be efficient. Further, it is rational to assume that the impact of the yield curve factors on the sector-wise CDS premia may be disproportionate under specific market states (bearish/bullish). With this contextual intent, the quantile regression (QR) model is used to examine the sector-wise CDS spread sensitivities to changes in the yield curve factors. Eventually, in the QR framework, the multifactor model in Equation (2) can be rewritten as follows:

where

${Q}_{\theta}$ denotes the conditional quantile of the CDS spreads for the sector-wise portfolios, 0 <

θ < 1. The quantiles can be inferred to be signifying various market conditions. For instance, the upper quantiles are linked with an upbeat state of the market, while the lower quantiles are associated with a bearish state of the market. Conditional on the quantile, different weights are assigned to the positive and negative residuals, which are then minimized. The positive error terms carry a weight of

θ, and the negative error terms are (1 −

θ) in the objective function. For instance, at the 0.90 quantile, the positive error terms have a weight of 90, and the negative error terms have a weight of 10. At the 0.50 quantile, the weights are equal for the positive and negative error terms. The QR model allows for the parameters to vary over quantiles by amplifying

θ from 0 to 1. In this way, a distribution of the explained variable contingent on the explanatory variables is obtained.

Buchinsky (

1995) advocated for the application of the bootstrap method to obtain the error terms of the QR coefficients, due to its improved results for smaller datasets.