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.
21
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