The Economic Determinants of Interest Rate Option Smiles prachi deuskar

 

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.  

                                                                                                                                                                             

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 We thank Rob Engle for insightful discussions on the econometric procedures used in this section. 

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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.

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  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.

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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. 

                                                           

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 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. 

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 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 

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