Bank interest rates impact the economy of a country
and also its trade and development in the global
context. While in most of the developed countries
the apex banks work on a suggestive role, in developing
and underdeveloped countries apex banks work on
a regulatory role. Of course in the last decade
or so, even in these economies some flexibility
within the regime is being afforded. It has been
a time-tested practice to work out interest rates
based on the term, estimated elasticity and volatility
and probability accuracy desired over a specific
term. Single factor and multi factor models developed
across the globe have been adopted with varying
degrees of success in given situations. Researchers
and probability experts indulge in continuous
appraisal of the models in vogue and recommend
adaptation of parameters in changing scenarios.
In the case of one bank, although freedom to adopt
a given model /mix does exist, a judicious compilation
of the economic environment, government policy,
term over which the rate is sought to be determined
and competition is the essence of input for a
final decision on methodology and rate fixation.
Interest rates and CKLS- an appraisal
Widespread debate on estimation in models of
the instantaneous spot rate of interest has emanated
since the popular contribution of CKLS. The sustained
interest in this topic is due to the great deal
of activity, both amongst academics and practitioners.
Gneralised Method of Moments (GMM) is the fountainhead
for all empirical studies to estimate the parameters
of a one-factor model of the instantaneous spot
rate of interest that is mean-reverting in the
drift term and has a diffusion term that is of
constant elasticity in the spot rate. Their estimate
for US data of about 1.5 for the elasticity in
the diffusion term provoked much discussion as
it was much higher than the value of 0.5 for the
popular Cox, Ingersoll and Ross (1985) model.
Subsequent contributions either extended the
basic CKLS formulation and/or considered
alternative estimation procedures.Longstaff and
Schwartz (1992), Brenner et al. (1996), Andersen
and Lund (1997) and Koedijk et al. (1997) in various
ways added volatility fluctuations to the model
for interest rate dynamics. Sun (2003) considers
a quite general specification allowing for a non-linear
drift as well as ARCH-type stochastic volatility.
However Nowman (1997, 1998) applied the Gaussian
estimation techniques developed by Bergstrom (1990)
for continuous time stochastic differential equations
In contrast to GMM, the Gaussian estimation methodology
has the advantage of producing the exact maximum
likelihood estimator. Episcopos (2000) subsequently
applied this methodology to estimate the parameters
of the CKLS specification for the short-term interest
rate for a number of countries.
Irrespective of the estimation methodology one
employs, another significant issue relates
to what data is used to estimate the instantaneous
spot rate of interest. Proxy variables that have
been used include US one-month Treasury bill rates
(CKLS) and one-month interbank rates (Episcopos).
Errors and biases due to proxy variables choice
have been effectively countered in the framework
of Heath-Jarrow-Morton (1992) and to model the
dynamics of interest rate market.
Most large financial institutions use term structure
models to price and hedge interest rate derivative
securities.
On a theoretical basis, although a one-factor
model might suffice for the pricing
of caps, it is likely to be inappropriate for
the pricing of swaptions, because swaption prices
directly depend on the correlation between interest
rates of different maturities. In one-factor models
these (instantaneous) correlations are equal to
one, contradicting empirical observations because
it is not always the case (correlation 1).
Single factor Vs multifactor consideration
In countries like India, Australia and Canada
both univariate (CKLS, ARIMA and ARCH/GARCH) and
multivariate models (VAR, VECM and Bayesian VAR)
have been extensively applied to forecast short
and long-term rates, viz., call money rate, 15-91
days Treasury Bill rates and interest rates on
Government securities with (residual) maturities
of one year, five years and ten years.
Multivariate models consider factors such as liquidity,
Bank Rate, repo rate, yield spread, inflation,
credit, foreign interest rates and forward premium.
Studies find that multivariate models generally
outperform univariate ones over longer forecast
horizons. Overall, the studies conclude that the
forecasting performance of Bayesian VAR models
is satisfactory for most interest rates and their
superiority in performance is marked at
longer forecast horizons.
In the US too, several articles have empirically
examined such term structure models. A large part
of this literature has focused on the performance
of these models in terms of the pricing of bonds,
for example, Babbs and Nowman (1999), Dai and
Singleton (1999), and Pearson and Sun (1994).
In general, the conclusion is that models that
have one factor that drives interest rates of
all maturities are rejected in favor of two- or
three-factor models. However, there exists little
empirical evidence of how multi-factor
models perform in terms of the pricing and hedging
of interest rate derivatives. Parameter stability
and model-based trading strategies finally determine
pricing options.
Factors /Variables for interest rate determination
In the final analysis whether it is for Call Money,
Treasury Bills or Securities of short term or
long term, the mix of key variables that have
to be factored in to a model are inflation rate
(preferably year-on- year), yield spread, liquidity,
foreign interest rate (6 months LIBOR) and forward
premium (6 months).
Conclusion
In the given task, a Bank is interested in the
main in using a single factor model (CKLS) of
the short-term interest rate. Nevertheless a multi-factor
interest rate could be applied if it is proved
to be more suitable. In the aforesaid paragraphs,
the variables, the single and multi-factor models
and their applications to given situations have
been discussed.
For each interest rate, a search for the “best”
forecasting model is conducted. The “best
model” is defined as one that produces the
most accurate forecasts such that the predicted
levels are close to the actual realized values.
Furthermore, the predicted variables should move
in the same direction as the actual series. In
other words, if a series is rising or (falling),
the forecasts should reflect the same direction
of change. If a series is changing direction,
the forecasts should also identify this. If the
bank is looking at only short term and single
factor model EPISCOPOS is evidenced to be a better
alternative to CKLS.However if single factor model
is not a stipulation and the bank has an open
mind, multi-factor models are a better bet. ARMA-GARCH
model is more suited for very short-term forecasting
while a BVAR model can be used for longer-term
forecasting.
To add, in the end, one needs to not only evaluate
the economics and accuracy of a given model in
relation to profitability objectives and macro
economic environment, but also the ground realities
of stability of policy, extent of competition
and regime undercurrents in the given country.