The Economic Determinants of Interest Rate Option Smiles prachi deuskar

 

equity options markets using liquidity effects or market frictions, with some success.

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  However, 

very little research has been conducted on directly examining the economic determinants of the 

volatility smile patterns in the options markets. An exception is the paper by Pena, Rubio, and 

Serna (1999), who examine the determinants of the implied volatility function in the Spanish 

equity index options market.   

In contrast to the literature on equity options, research on the smile in the interest rate options 

market has been quite sparse.  The sole exception is a paper by Jarrow, Li and Zhao (2006) who 

examine the smile in US dollar caps and floors, and find that even models augmented with 

stochastic volatility and jumps do not fully capture the smile.  

The conclusions from equity options markets cannot be readily extended to interest rate option 

markets, since these markets differ significantly from each other for several reasons. First, in 

contrast to equity option markets, interest rate option markets are almost entirely institutional, 

with hardly any retail presence. Most interest rate options, particularly the long-dated ones such 

as caps, floors and swaptions, are sold over-the-counter (OTC) by large market makers, typically 

international banks. The customers are usually on one side of the market (the ask-side), and the 

size of individual trades is relatively large. Second, many popular interest rate option products, 

such as caps, floors and collars are portfolios of options, from relatively short-dated to extremely 

long-dated ones. These features lead to significant issues relating to supply/demand and 

asymmetric information that are different from those for exchange traded equity options. Third, 

since interest rate options are traded in an OTC market, there are also important credit risk issues 

that may influence the pricing of these options, especially during periods of crisis. Therefore, 

inferences drawn from studies in the equity option markets are not directly relevant for interest 

rate option markets, although there may be some broad similarities.  

                                                           

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 See Ederington and Guan (2002), Mayhew (2002), Pena, Rubio and Serna (1999, 2001), Bollen and 

Whaley (2004), and Garleanu, Pedersen and Poteshman (2006), for example. 

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Given the limited success of attempts to model the distribution of the underlying to explain the 

smile, we adopt a different approach. We seek to directly examine the economic determinants of 

the smile.  To give an analogy, our approach is similar to finding empirical risk factors as 

opposed to calibrating utility-based models in order to explain the cross-section of stock returns, 

in the asset pricing literature.  In this paper, we contribute to the literature in three distinct ways. 

First, we present an extensive documentation of the volatility smile patterns in the interest rate 

options markets for different maturities, separately for the bid and the ask sides of the market. 

Second, we explore the determinants of volatility smiles in these markets, in terms of macro-

economic and liquidity variables. Third, we examine the bidirectional Granger-causality between 

volatility smiles and the macro-economic and liquidity variables to understand the dynamic 

nature of these relationships. 

We find that there are clearly perceptible volatility smiles in caps and floors, across all maturities. 

Short-term caps and floors exhibit smiles that are significantly steeper than those for longer-term 

caps and floors. Long-term options display more of a “smirk” than a smile. Measures of the shape 

of the volatility smile (slope and curvature) are significantly related to term structure variables. In 

particular, the curvature of the smile is positively related to the 6-month interest rate for shorter 

maturity options and negatively related to the slope of the term structure for longer maturity 

options. This suggests that away-from-the-money options, especially of shorter maturity, are 

significantly more expensive (compared to at-the-money options), during higher interest rate 

regimes. On the other hand, the away-from-the-money options are comparatively less expensive 

when the term structure is relatively flat. Our results for the slope of the volatility smile show that 

out-of-the money caps (floors) become disproportionately more expensive when interest rates go 

up (down). This may be a result of the existence of price pressure in this market induced by 

hedging demand from customers, consistent with some of the results reported in Bollen and 

Whaley (2004) and Garleanu, Pedersen and Poteshman (2006). Alternatively, the slope of the 

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yield curve may capture the skew of the distribution of future interest rate, and thus affect the 

slope of the smile. These relationships between the term structure variables and the smile 

variables also hold for their innovations.  

In addition, we find that high-volatility periods are associated with flatter volatility smiles, 

suggesting a stochastic volatility framework with mean reversion in volatility. We also find 

evidence that the curvature of the smile for longer maturity options is positively related to the 

liquidity costs in this market, as proxied by the bid-ask spreads. We conjecture that, perhaps, 

liquidity effects could account for a part of the smile, especially for longer maturity options.  

We use multivariate Granger-causality tests to examine if lagged values of any of the explanatory 

variables can predict the curvature and asymmetry of the volatility smile and vice-versa. We find 

that the 6-month interest rate Granger-causes the slope and the curvature of the volatility smile, 

while the slope of the term structure Granger-causes the curvature of the smile curve. We also 

find that slope of the volatility smile curve can predict the aggregate default spread, even after 

controlling for the persistence in the default spread, and in the lagged values of yield curve 

variables.  The impulse response function shows that a positive shock to the slope of the smile of 

shorter maturity options is followed by an increase in the default spread.  This is intuitive because 

a higher slope of the smile implies higher relative prices of out-of-the-money floors that hedge 

the risk of falling interest rates, which are associated with an economic downturn and higher 

default risk, and thus, an increase in the default spread.   

The results of our paper have important implications for the modeling and risk management of 

interest rate derivatives, especially options. We find that even after controlling for the persistence 

in the shape of the smile, lags of the 6-month interest rate and the slope of the yield curve have 

information about future shapes of the smile. Usually, while calibrating the interest rate option 

models, only the contemporaneous yield curve is used. Our results suggest that using lagged 

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