The Economic Determinants of Interest Rate Option Smiles prachi deuskar

 

option dealers.  It could affect the prices of away-from-the-money options more than the prices of 

ATM options, thus affecting the shape of the smile.  

We also include a measure of the at-the-money relative bid-ask spreads of these options. The 

objective of including this variable is to directly control for the explicit liquidity of these options, 

while examining the relationship of the other economic variables to the volatility smile. The 

relative bid-ask spreads of ATM options capture the general level of liquidity in the market. 

The results from this regression analysis are presented in Table 2. The curvature of the smile is 

positively and significantly related to the 6-month interest rate, with the effect being insignificant 

for long maturity options. When interest rates are high, the away-from-the-money options, 

especially the ones with shorter maturities, are priced relatively higher than during times when 

interest rates are low. On the other hand, the curvature of the smile is negatively related to the 

slope of the term structure; interestingly, this effect is significant only for the longer maturity 

options. It appears that the volatility smiles in this market have more curvature when the term 

structure is relatively flat. These results are consistent for the bid- as well as the ask-side 

quotations. 

The results also show that the degree of curvature is negatively related to the volatility of at-the-

money options, although this effect is significant mostly for short/medium maturity options. 

Therefore, highly volatile periods tend to be associated with a lower curvature of the smile, which 

is consistent with the evidence in the equity options literature (Pena, Rubio, and Serna (1999)). 

These results suggest a stochastic volatility framework with the volatility itself exhibiting mean 

reversion. In such a model, high volatility periods are likely to be followed by lower volatility 

periods, which would result in a shallow smile when volatility is high. We also find weak 

evidence of the curvature of the smile being positively related to the liquidity costs in the market, 

but this effect is significant only for long maturity options on the ask-side. This is understandable, 

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since higher liquidity costs i.e. higher costs of continuously hedging the options positions would 

of more concern in case of away from the money options and longer maturities. Therefore, 

especially for longer maturity options, it may be important to account for liquidity effects while 

modeling the volatility smile. 

The slope of the volatility smile (RR) exhibits somewhat different relationships to the 

contemporaneous determinants examined in this section. When the short-term interest rate is 

high, the RR appears to be more negative, especially for longer maturity options. Since the RR is 

the difference between ScaledIVs at +0.25 LMR and -0.25 LMR, it is important to understand the 

effects separately for caps and floors. A negative (positive) LMR refers to out-of-the-money caps 

(floors). A negative relationship between 6-month rate and RR implies that when interest rates 

increase (decrease), out-of-the-money caps (floors) become disproportionately expensive. These 

results are quite intuitive. It is possible that the demand for out-of-the-money caps (floors) is 

higher when interest rates go up (down). Then, consistent with the findings of Bollen and Whaley 

(2004) and Garleanu, Pedersen and Poteshman (2006), demand pressure may affect the prices of 

interest rate options at some strikes, thereby affecting the shape of the volatility smile. Similarly, 

when the term structure becomes more steeply upward sloping, the smile becomes more negative. 

An upward-sloping yield curve is a signal that interest rates will increase in the future, thereby 

leading to higher demand for out-of-the-money caps, which would make the volatility smile more 

negative. An alternate way of thinking about this effect is that the slope of the yield curve 

captures the skew of the distribution of future interest rates, thus affecting the slope of the smile. 

Finally, we find some evidence that the slope of the smile curve is related to the default spread. 

However, this relationship is not consistent across all maturities. Perhaps there is a relation 

between RR and the leads or lags of the default spread. The nature of such dynamic relationships 

between the economic variables and the volatility smile is what we explore in the next section.  

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5. 

Multivariate Vector Autoregression 

In the previous section, we show that economic variables are significantly related to the shape of 

the  contemporaneous  smile. In this section, we examine the relationship between the lagged 

values of economic variables and the shape of the smile, and vice-versa. We estimate a six-

equation, multivariate, vector autoregression separately for the butterfly spread and the risk 

reversal, each of which includes the five economic and liquidity variables (ATM volatility, 6-

month rate, the slope of the term structure, the default spread, and the ATM bid-ask spreads).

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This framework can provide useful information on the linkages between the economic variables 

and the volatility smile in a dynamic, predictive sense. We choose the appropriate number of lags 

for the multivariate VAR estimation in each case, using the Akaike information criterion (AIC). 

For most option maturities, this estimation results in two or three lags, with the maximum number 

of lags in any system being five. We estimate 36 VAR models (9 option maturities each, for the 

bid and ask sides, separately for BS and RR) that provide a comprehensive description of the 

time-series movements in the shape of the smile and the economic and liquidity variables.  

We first examine the cross-correlations of the innovations obtained from the VAR system. 

Unexpected shocks to any of the economic variables may be related to the unexpected 

fluctuations in the shape of the volatility smile. These correlations are presented in Table 3. The 

most striking relationship noticed from the table is the negative correlation between the shocks to 

the slope of the term structure and the shocks to the curvature and slope of the volatility smile, 

which is consistent with our results in the previous section. It appears that unexpected twists in 

the term structure, which may be proxies for unexpected changes in the higher moments of the 

risk neutral distribution of interest rates, are related to unexpected changes in the shape of the 

volatility smile curve. To a lesser degree, we find that the shocks to the 6-month interest rate are 

positively correlated with the shocks to the shape of the smile, especially to the butterfly spread. 

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