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Table 1 

 

Functional forms for implied volatility smiles 

 

This table presents regression results when the scaled implied flat volatility for euro interest rate caps and 

floors, for various maturities, is regressed on a quadratic function of the Log Moneyness Ratio (LMR), as 

follows: 

2

*

3

*

2

1

 

LMR

c

LMR

c

c

IV

Scaled

+

+

=

 

The statistics are presented for the period, Jan 99 - May 01, for various maturities, based on data obtained from 

WestLB Global Derivatives and Fixed Income Group. The coefficient and regression statistics are presented 

for caps and floors pooled together, separately for bid and ask prices, for all maturities. An asterisk implies 

significance at the 5% level. 

 

 

Maturity 

 

 

c1 

 

c2 

 

c3 

 

Adj R

2

 

Ask

 

 

 

 

 

2-year 1.09* -0.62* 3.60*  0.64 

3-year 1.09* -0.15* 1.84*  0.58 

4-year 1.08* -0.06* 1.38*  0.62 

5-year 1.11* 0.02 0.92* 0.57 

6-year 1.11* 0.10* 0.50*

 

0.42 

7-year 1.13* 0.19* 0.36*  0.25 

8-year 1.08* 0.19* 0.11*  0.47 

9-year 1.07* 0.18* 0.11*  0.51 

10-year 1.13* 0.26* 0.07*

 

0.59 

Bid

 

 

 

 

2-year 0.95* -0.72* 2.40*  0.53 

3-year 0.98* -0.30* 0.87*  0.30 

4-year 0.98* -0.17* 0.69*  0.33 

5-year 0.99* -0.12* 0.55*  0.40 

6-year 0.99* -0.01 0.36*  0.39 

7-year 1.02* 0.11* 0.24*  0.52 

8-year 0.98* 0.15* 0.07*  0.54 

9-year 0.97* 0.14* 0.09*  0.59 

10-year 1.03* 0.20* 0.06*  0.64 

 

 

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