An unexpected increase in interest rates may trigger expectations of extreme moves in interest
rates in the future, which would cause the butterfly spread to increase. Similarly, we find some
relationship between shocks to the default spread and shocks to the shape of the volatility smile.
In addition, the shocks to the liquidity of at-the-money options appear to be positively related to
the shocks to the butterfly spread, especially for longer maturities. This suggests that when
liquidity dries up, the away-from-the-money options (especially longer maturity) become
disproportionately more expensive, as reflected in the increase in the curvature of the smile.
5.1
The predictors of the volatility smile
In Table 4, we present the pair-wise Granger causality tests between the butterfly spread or risk
reversal and the five economic variables, separately for the bid- and ask-side, for each maturity.
Panel A of the table presents the p-values for rejecting the null hypothesis that variable i Granger-
causes the shape of the smile (butterfly spread or risk reversal), by testing whether the lag
coefficients of variable i are jointly zero when the dependent variable in the VAR is BS or RR.
We find evidence that for most option maturities, the 6-month interest rate and the slope of the
term structure Granger-cause the butterfly spread. Therefore, these yield curve variables have an
impact not only on the contemporaneous BS, as seen from tables 3 and 4, but also on the future
BS. Similarly, we find some evidence that the 6-month interest rate Granger-causes the risk
reversal. Thus, while the slope of the yield curve is related to contemporaneous RR, it is the spot
rate that has predictive information about future values of RR. These results show that past
realizations of the term structure have some information about the shape of the volatility smiles in
this market. We also find some information in past values of the at-the-money volatility and
liquidity costs in predicting the curvature of the volatility smile, but these effects are weaker.
22
We thank Rob Engle for insightful discussions on the econometric procedures used in this section.
17
Next, we present the impulse responses based on the multivariate VAR standardized by Cholesky
decomposition. For the sake of brevity, we only show those cases where we do find Granger
causality. Panel A of figure 3 presents the response of the butterfly spread to a one Cholesky
standard deviation shock to the 6 month rate. The ordering of the VAR for this purpose is the 6-
month rate, the 5 yr rate - 6 m rate differential, the default spread, the ATM BA Spread, BS, and
ATM Vol.
23
On the ask side, except for the 2-year cap, a positive shock to the short term interest
rate results in an increase in the butterfly spread. The effect is significant initially, and remains so
for 5-year and shorter maturities. For longer maturities, the effect becomes insignificant as the
horizon progresses. On the bid-side the results are qualitatively similar.
24
Panel B of figure 3 shows the response of the risk reversal to one Cholesky standard deviation
shock to the 6 month interest rate. The ordering of the VAR in this case is the 6-month rate, the
RR, the 5 yr rate – 6 m rate differential, the default spread, the ATM Vol, and the ATM BA
Spread. On the ask-side, except for the short term maturities like the 2-year, there is a decrease in
the risk-reversal following a positive shock to the short term interest rate. The results are
consistent with the intuition that an increase in the short term interest rate is followed by an
increase in the prices of the out-of-the-money caps, since investors are now more concerned
about hedging the risk of rising interest rates. Hence, the prices of out-the-money caps (LMR<0)
relative to in-the-money caps (LMR>0) increase, thereby decreasing the risk reversal. An
alternate way of thinking about this result is that investors are less concerned about hedging the
risk of decreasing interest rates. Therefore, the prices of out-of-the-money floors (LMR>0)
relative to in-the-money floors (LMR<0) decrease. The results on the bid-side are similar.
23
Usually the Cholesky decomposition is sensitive to the ordering of the VAR. We order the VAR from the
most exogenous variable to the most endogenous variable, based on the results of Granger causality tests.
However, our empirical results are robust to changes in the ordering of these variables in the VAR.
24
We also examined the response of the butterfly spread to the slope of the yield curve computed in the
manner explained above. Although Granger-causality points to the slope of the yield curve having
information about the butterfly spread, the impulse responses do not show a clear pattern.
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Table 5 presents the variance decompositions of the butterfly spread and risk reversal. It shows
how much each of the variables contributes towards the variance of the error in forecasting the
shape of the smile. The bulk of the variance of the forecast error in the butterfly spread or risk
reversal is attributable to the innovations in that variable itself. For butterfly spreads at shorter
maturity, the 6-month interest rate contributes around 2% towards the forecast error variance at
the horizon of one day. This contribution increases to around 6% at the 10-day horizon. The
contributions are smaller for higher maturities. At-the-money volatility is another variable that
contributes towards the forecast error variance of butterfly spread. For the risk reversal as well,
innovations to the 6-month rate are the next contributing factor, after innovations to the risk
reversal itself. Excluding the 2-year maturity, the contribution of innovations to the short rate
starts at around 1% at a 1-day horizon and goes up to 4-5% at the 10-day horizon.
5.2
Information in the volatility smile
Panel B of Table 4 presents p-values for the null hypothesis that the shape of the smile (measured
by the BS or RR) does not Granger-cause any of the other variables of interest. We find that the
shape of the volatility smile plays a role in predicting some of the economic variables. In
particular, the risk reversal Granger-causes the 6-month default spread, implying that the
asymmetry in the volatility smile curves is useful for predicting the default spread in the Euribor
market. This is intuitive since the option prices are forward looking. More importantly, our results
suggest that the asymmetry in the prices of out-the-money options as compared to those for in-
the-money options (which is the cause of the asymmetry in the volatility smile) have information
about the future economic outlook, since the default spread is a reflection of the expectations for
aggregate default risk in the economy.
Panel C of figure 3 presents the response of the default spread to a one Cholesky standard
deviation shock to risk reversal computed in a manner similar to earlier responses. The ordering
19