The Economic Determinants of Interest Rate Option Smiles prachi deuskar

 

It is important to note that we estimate the risk reversal and the butterfly spread by only going 

away-from-the-money by 0.25 LMR on either side of the at-the-money strike rate. To understand 

the moneyness levels in terms of actual contract strikes, consider a cap with an at-the-money 

strike rate of 4%. In this case, a cap with an LMR of 0.25 would have a strike rate of about 3.1%, 

while a cap with an LMR of -0.25 would have a strike rate of about 5.1%. These strike rates are 

well within the range of actively traded caps in terms of moneyness.  

4. 

The Determinants of the Volatility Smile 

One of the objectives of this paper is to examine the determinants of the volatility smiles in 

interest rate option markets. A clear understanding of the determinants of these smile patterns can 

help in developing models that eventually explain the entire smile. To this end, we explore the 

contemporaneous relationship between the slope and curvature of the daily smiles and several 

economic and liquidity variables. The economic determinants include the level of volatility of at-

the-money interest rate options (ATMVol), the spot 6-month Euribor (6Mrate), the slope of the 

term structure captured by the difference between the 5-year rate and the 6-month rate 

(5yr6Mslope), the default spread defined as the 6-month Treasury-Euribor spread (DefSpread), 

and the scaled ATM bid-ask spread (atmBAS) as a proxy of liquidity costs in the market. These 

are time-series regressions of curvature and asymmetry measures calculated using data across all 

the strikes each day. The regression specifications are as follows:

18,19

 

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

+

+

+

+

+

=

+

+

+

+

+

=

(3) 

 

                                                           

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 This time series regression is estimated by including AR(2) error terms to correct for serial correlation. 

We find no serial correlation in the residuals after this correction. In addition, for all maturities, the Durbin-

Watson statistic is insignificantly different from 2. Therefore, the inclusion of the AR(2) error terms, 

indeed, takes care of any serial correlation in the regression model. 

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 We also estimate this equation using the slope and curvature of the smile obtained from unscaled 

(absolute) implied volatilities, as well as using volatility and maturity adjusted moneyness (in the spirit of 

Li and Pearson (2004)). The results, which are similar, are not reported in the paper to save space, but are 

available upon request from the authors. 

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The intuition for examining these independent variables is as follows. First, the at-the-money 

volatility variable is added to examine whether the patterns of the smile vary significantly with 

the level of uncertainty in the market. During more uncertain times, reflected by higher volatility, 

market makers may charge higher than normal asking prices for away-from-the-money options, 

since they may be more averse to taking short position at these strike rates. This would lead to a 

steeper smile, especially on the ask side of the smile curve. Also, during times of greater 

uncertainty, a risk-averse market maker may demand higher compensation for providing liquidity 

to the market, which would affect the shape of the smile. Since we have already divided the 

volatility of each option by the volatility of the corresponding ATM cap to obtain the scaled IV, 

we use the ATM swaption volatility (of comparable maturity), a general measure of the future 

interest rate volatility, as an explanatory variable here, in order to avoid having the same variable 

on both sides of the regression equation.

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Second, we include the spot 6-month Euribor and the slope of the yield curve as indicators of 

general economic conditions, as well as the direction of interest rate changes in the future - for 

example, if interest rates are mean-reverting, very low interest rates are likely to be followed by 

rate increases. Similarly, an upward sloping yield curve is also indicative of future rate increases. 

This would manifest itself in a higher demand for out-of-the-money caps in the market, thus 

affecting the prices of these options, and possibly the shape of the implied volatility smile itself.

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Our next variable, the default spread, is often used as a measure of aggregate liquidity as well as 

the default risk of the constituent banks in the Euribor fixing. A wider spread indicates a higher 

default risk for the constituent banks, and possibly also higher risk of default of interest rate 

                                                           

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 Although swaption implied volatilities are not exactly the same as the cap/floor implied volatility, they 

both tend to move together. Hence, swaption implied volatilities are a valid proxy for the perceived 

uncertainty in the future interest rates. The data on the ATM swaption volatility in the Euro market was 

obtained from DataStream. 

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 The ATM volatility and the term structure variables act as approximate controls for a model of interest 

rates that displays skewness and excess kurtosis. Typically, in such models the future distribution of 

interest rates depends on today’s volatility and the level of interest rates.   

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