Table 2
Effects of economic variables on volatility smiles
This table presents regression results for the impact of economic and liquidity variables on the curvature of the
volatility smile (as proxied by the butterfly spread, BS) and asymmetry in the volatility smile (as proxied by
risk reversal, RR):
atmBAS
d
DefSpread
d
Mslope
yr
d
Mrate
d
ATMVol
d
d
RR
atmBAS
c
DefSpread
c
Mslope
yr
c
Mrate
c
ATMVol
c
c
BS
*
6
*
5
6
5
*
4
6
*
3
*
2
1
*
6
*
5
6
5
*
4
6
*
3
*
2
1
+
+
+
+
+
=
+
+
+
+
+
=
The statistics are presented for the period, Jan 99 - May 01, based on data obtained from WestLB Global
Derivatives and Fixed Income Group and DataStream. The coefficients and regression statistics are presented
for the pooled sample of caps and floors, separately for bid and ask prices. Lagged error terms are included in
the regression equation to correct for serial correlation. ** and * indicate statistical significance at the 5% and
10% level respectively. The results are presented for three representative maturities - 2-year, 5-year, and 10-
year.
Panel A: BS
Maturity
c1 c2 c3 c4 c5 c6 Adj
R
2
Ask
2-year 0.44** -1.99**
8.23** -1.61 -1.38** -0.01
0.92
5-year -0.01 -0.14 2.76** 0.19 0.02 0.14 0.97
10-year 0.02 -0.12 0.78* -1.05* 0.04 0.04** 0.95
Bid
2-year 0.46** -1.90**
3.45** -1.83 -1.87** 0.21*
0.86
5-year 0.10** -0.61**
0.76** -0.49 -0.46** 0.09
0.58
10-year 0.09** -0.51** -0.03 -1.03** 0.01 -0.09** 0.79
Panel B: RR
Maturity d1
d2 d3 d4 d5 d6 Adj
R
2
Ask
2-year -2.42** 2.42**
41.57* -11.32 2.05* -0.25
0.86
5-year 0.69** -0.33
-12.62**
-14.91**
0.58** 0.02
0.73
10-year 0.41* -0.07
-5.53**
-9.53** -0.37 -0.13 0.89
Bid
2-year -0.75 2.87**
-5.90
-10.60
3.64** 0.01 0.94
5-year 0.44** -0.20
-10.89**
-5.30** 0.30 0.12
0.90
10-year 0.17* 0.24 -3.01**
-2.88*
-0.52**
0.66** 0.89
26
Table 3
Correlations in VAR innovations
This table presents the correlations between innovations from the multivariate vector autoregression for six
variables - the level of volatility of at-the-money interest rate options (ATM Vol), the spot 6-month Euribor (6
m rate), the slope of the term structure (5 yr rate - 6 m rate), the 6-month Treasury-Euribor spread (Default
Spread), the scaled ATM bid-ask spreads (ATM BA spread) and butterfly spread (BS) or risk reversal (RR)
separately for ask and bid sides for the period Jan 99 - May 01, based on data obtained from WestLB Global
Derivatives and Fixed Income Group and DataStream. The correlations between innovations of the smile
variables (BS / RR) and innovations and other variables are presented below. ** and * represent p-values less
than or equal to 5% and 10% respectively. The results are presented for three representative maturities - 2-year,
5-year, and 10-year.
Ask
Bid
ATM
Vol.
6 m
Rate
5 yr rate
– 6 m
Rate
Default
Spread
ATM
BA
Spread
ATM
Vol.
6 m
Rate
5 yr rate
– 6 m
Rate
Default
Spread
ATM
BA
Spread
BS
2-year
-0.06 -0.15**
0.03 -0.13**
0.00
-0.01 -0.29**
0.02
-0.22**
0.06
5-year
-0.06 0.15**
-0.01
0.04 0.16**
-0.07
-0.04
0.10** -0.10**
0.02
10-year -0.05
0.14**
-0.14** 0.08* 0.13**
-
0.10**
0.12**
-0.08
0.07
-0.15**
RR
2-year
0.08 0.26** -0.18** 0.19**
-0.06
0.02
0.08
-0.16** 0.24**
0.00
5-year
-0.02
-0.04 -0.46** 0.13**
0.06
0.00 -0.09** -0.21**
0.05
0.04
10-year
0.04 -0.13** -0.14** -0.09*
-0.07
0.08*
-0.07
-0.03
-0.16** 0.15**
27