The Economic Determinants of Interest Rate Option Smiles prachi deuskar

 

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 

---