| dc.description.abstract | Exchange rate movements in the Indian rupee (and many other emerging
market currencies) are characterised by long periods of placidity punctuated
by abrupt and sharp changes. Many, but by no means all, of these sharp
changes are currency depreciations. This paper shows that econometric
models of changing volatility like Generalised AutoRegressive Conditional
Heteroscedasticity (GARCH) with non normal residuals which perform quite
well in other financial markets fail quite miserably in the case of the INRUSD
process because they do not allow for such jumps in the exchange rate.
The empirical results very convincingly demonstrate the need to model the
exchange rate process as a mixed jump-diffusion (or normal mixture) process.
Equally importantly, the empirical results provide strong evidence that the
jump probabilities are not constant over time. From a statistical point of view,
changes in the jump probabilities induce large shifts in the kurtosis of the
process. The failure of GARCH processes arises because they allow for
changes in volatility but not for changes in kurtosis. The time varying mixture
models are able to accommodate regime shifts by allowing both volatility and
kurtosis (not to mention skewness) to change. This also shows that the periods
of calm in the exchange rate are extremely deceptive; in these periods, the
variance of rate changes is quite low, but the kurtosis is so high (in the triple
digit range) that the probability of large rate changes is non trivial. The
empirical results also show that the Black-Scholes-Garman-Kohlhagen model
for valuation of currency options is quite inappropriate for valuing rupeedollar
options and that the Merton jump-diffusion model is the model of
choice for this purpose. | en |
