Forecasting daily exchange rate volatility

: a cointegration analysis

Abstract

Although volatility is at the core of activities in financial markets, the sample path realization of the volatility process is inherently unobservable. Many techniques have been used by both researchers and practitioners to establish volatility proxies. Examples include the traditional close-to-close estimator, the extreme-value estimator (range estimator), etc. Some researchers have found that the range estimator, which equals the difference between the daily highs and lows, is more efficient than some of the more commonly adopted estimators. We have found that the daily highs and daily lows of five exchange rates, U.S dollar vis-à-vis the Australian dollar, Canadian dollar, British pound, Swiss Franc and Japanese yen, are I(1) while the daily range is I(0). Furthermore, it is also found that the daily highs and lows are co-integrated with the ‘range’ series as the error correction term. The inclusion of range estimator in the cointegration framework has provided a fuller picture of the interactive effects of the daily highs, daily lows and the ‘range’. From the practitioners’ viewpoint, it is convenient to model and forecast assets’ volatility by making use of the information embedded in the range estimator. To illustrate the potential benefits of adopting the range estimator, modeling techniques such as naïve model, autoregressive integrated moving-average model and error-correction model are employed. Apart from conventional accuracy measures such as MSE and MAD, we use the Modified Diebold-Mariano (MDM) and the direction of change tests to evaluate their forecasting performance. The implied volatilities extracted from currency options are also compared with the outcome from the models mentioned above. This part of empirical analysis further attests the applicability and appropriateness of incorporating the ‘range’ in the VECM framework.

Date of Award	3 Oct 2006
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Tze-Kin Alan WAN (Supervisor)