Regression Results

The correlation results discussed in the previous section have already shown the existence of comovement of IV and CDS level for the underlying firms. In this sec- tion, we control for standard expected variables and explain each of the following tables presented for the regressions. It is important to note that we have a pooled panel data set with essentially two dimensions of cross-sectional variables: firms, and various options written on the same firm.

In the following subsections we continue the findings by testing for different hy- potheses, sub-groups, stratifications, robustness (endogeneity), as well as options liquidity and financial leverage impact. We also explain the effect of firm-level variables included.

In order to be making comparative and consistent analysis we need to catego- rize the options into buckets of similar moneyness and maturity. As such we create three groups for maturity: “long”, “medium”, and “short”; and three groups for moneyness: deep in the money, deep out of the money, and, near or at the money. The result is nine groups on which we perform the regressions to record the special differences or similarities. Tables 3, 4, and 5 show results for “short maturity”. In Table 3 we present four different regression models for “short maturity, ITM”

put options. We start with excluding the default risk variables in model (1) and increment by adding CDS spread and CDS liquidity proxy in model (2). Then we augment by including lagged CDS in model (3). Finally, model (4) includes lagged IV, CDS, and CDS liquidity proxy. We shall refer to model (4) as the baseline model which will be tested across various buckets of maturity and moneyness as shown in hypothesis specification (3.5).

Table 3 shows that CDS is consistently a significant variable in explaining implied volatility. We also find the CDS liquidity proxy (measured through stan- dardization of the number of contributors), is consistently significant with negative sign. This shows that more liquid CDS contracts signal smaller implied volatility while IV increases with as illiquidity risk increases. Intuitively, investors need to be compensated for the liquidity risk and hence a higher IV is expected when the option is less liquid, consistent with the findings presented.

Table 4 repeats the previous setup of four key regressions on “short maturity” and deep OTM put options. The interesting finding is that the explanatory power of CDS disappears when we move to deep OTM put options. Not CDS nor CDS liquidity can explain the IV variation based on Table 4 findings, while the aggre- gate variables and firm level variables gain more power in the IV regression for short deep OTM options.

Tables 5 to 7 perform the baseline regression (explained in equation 3.5) for short, medium, and long maturity groups. In each regression table we split data into the three moneyness groups and show the findings.

Table 5 shows that for short maturity, CDS is only significant for ITM options and loses significance for ATM and OTM groups. This finding is reversed for medium and long maturity groups where CDS is more significant for ATM and OTM groups. By looking at all the tables and focusing on the various bins tested, we find that for deep in the money and deep out of the money options the default risk as measured by CDS level is more economically significant.22 This is in-line with our hypothesis that higher default risk is more significant for deep out of the money (subject to higher default risk) and deep in the money (more liquid) equity put options.

3.7.2.1 Default Risk and IV-Skew

We define option implied skewness besides the implied volatility measure. For each point in time we also compute an implied volatility skewness measure, which is the difference between the implied volatility of all out-of-the-money put option, and the implied volatility of an at-the-money put option with a strike-to-spot ratio closest to 1, for all contracts issued by the same firm. The implied volatility skew is closely related to the skewness of the risk-neutral equity return distribution and we expect it to be positively related to the CDS spread. In simple words, for our sample of put options:

Skewi,t =AV ERAGEOT M(IVi,t)−AV ERAGEAT M(IVi,t) (3.4)

Tables 8 to 10 show the results of applying the baseline regression to the IV- Skew. The results vary based on the option bins focused on which is expected given

the definition of IV-Skew explained above. Among the 9 bins, skewness is best explained for by CDS in medium and long maturity groups and most prominent for OTM options. The signs and significance vary as well, resulting in no consistent finding across all 9 bins. As a result, the CDS level cannot conclusively explain the variation of skewness across all groups of moneyness and maturity; For all put options the findings vary bin by bin, with most statistically and economically significant values belonging to higher maturity and smaller moneyness.

3.7.2.2 Effect of Firm-level Variables

Reviewing the findings so far (for example, Table 3) we find that the firm size is proved to be a significant variable with negative coefficients which implies the size effect on the option implied volatility of the firm. As expected smaller firms have higher risk of default and higher implied volatility which is consistent with the theoretical understanding. Moreover, small firms also exhibit more volatility than large firms so the significance of this coefficient may also reflect this stylized fact. Leverage is also a negative significant factor in the model for short-maturity options. However, the significance drops as the maturity increases and the results are not conclusive for medium and long maturity groups. Once the model includes lagged variable the significance of leverage is again dropped. To further uncover the impact of leverage we will run additional tests in Table 14.

Market to Book ratio is consistently significant with similar level and power as size impact which is consistent and expected. Firm’s stock return is positive and significant in explaining IV changes in some of the bins and insignificant in the rest. This is also consistent with the options pricing theory as higher values of IV

expect higher return on the underlying stocks (which can be due to compensation for the cost of higher default risk.)

3.7.2.3 Macroeconomic and Market Variables

We control for all standard macroeconomic variables and additionally include a complete model for default risk.

In the regression tables we control for VIX, return on S&P500, Yield curve slope, Treasury rate, Aggregate default Spread, and TED spread 23. Once all included, market return becomes insignificant in explaining the IV. However, the CDS remains a prominent significant factor even after controlling for all macroe- conomic and market variables as shown in Tables 3 and 4.

We later use the macroeconomic and market variables to test for endogeneity. Together with firm variables, they are the common set of explanatory variables that explain both CDS and implied volatility and hence potential for endogeneity existence.