The Economic Determinants of Interest Rate Option Smiles prachi deuskar

 

of the VAR in this case is 6-month rate, RR, the 5 yr rate - 6 m rate spread, the default spread, the 

ATM vol, and the ATM BA Spread.  A positive shock to the risk reversal for shorter maturities 

(up to 6-year) is followed by a significant increase in the default spread. The results are 

insignificant for higher maturities. The results are consistent with a positive correlation, at short 

maturities, between unexpected shocks to risk reversal and default spread.  An increase in the risk 

reversal occurs during the period when investors are more concerned about falling interest rates 

(leading to enhanced interest in buying out-of-the-money floors), which usually coincides with an 

economic downturn and a consequent increase in default risk.  

Panel C of table 5 presents the decomposition of the forecast error variance of default spread 

computed from the VAR involving risk reversal. Similar to previous cases, own innovations 

contribute the most towards forecast error variance of default spread.  However, it is interesting to 

note that shocks to the risk reversal contribute up to 8% to the variance of the forecast error. This 

is a result consistent with what we find using Granger-causality: risk reversal has information 

about the default spread. 

6. 

Concluding Remarks  

We examine the patterns of implied volatility in the euro interest rate option markets, using data 

on bid and ask prices of interest rate caps and floors across strike rates. We document the pattern 

of implied volatility across strike rates for these options, separately on the bid-side and the ask-

side, and find that the volatility smile curve is clearly evident in this market. 

We further examine the impact of economic variables on the volatility smile curves. We include 

the level of volatility and interest rates to control for the effects arising out of a more elaborate 

model of interest rates. We find that these term structure variables have significant explanatory 

ability for the time-variation in the shape of the smile. During a high-interest-rate regime, the 

smile appears to be steeper and more skewed. When the yield curve is sloping upward more 

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steeply, the smile in the interest rate options is flatter but more skewed.  In addition, when the 

level of volatility in the interest rate markets is high, the smile is flatter, consistent with mean-

reverting stochastic volatility. 

We investigate the behavior of the relationship between the yield curve variables and the shape of 

the smile over time and find that it is not static but dynamic. The yield curve variables have 

information about the future shape of the smile in the interest rate options market. Thus, past 

values of yield curve variables can be used to formulate and implement hedging and risk 

management strategies for the interest rate options. We also find that the shape of the smile has 

information about future default spreads.  Thus, past prices of interest rate options can be useful 

for valuing and hedging credit derivatives. Many of the dealers of interest rate options are also 

likely to have positions in the credit derivatives. This link between interest rate options and 

default spread can be useful for the risk management at the firm level. 

Our results suggest that understanding the dynamic relationship between the economic variables 

and the shape of the smile is important for developing valuation models for interest rate options. 

In future research, these results should be extended to other time periods and currencies. 

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