The Accuracy of Density Forecasts from Foreign Exchange Options

Abstract

Financial decision makers often consider the information in currency option valuations when making assessments about future exchange rates. The purpose of this paper is to systematically assess the quality of option based volatility and density forecasts. We use a unique dataset consisting of over 10 years of daily data on over-the-counter currency option prices. We find that the OTC implied volatilities provide largely unbiased and fairly accurate forecasts of 1-month and 3-month ahead realized volatility. Furthermore, we find that the 1-month option implied density forecasts are well calibrated for the centre of the distribution but we find evidence of misspecification in the tail density forecasts. * Corresponding author: peter.christoffersen@mcgill.ca. We would like to thank the Editors (Rene Garcia and Ruey Tsay) and two anonymous referees for very helpful comments. We have benefited from several visits to the External Division of the European Central Bank whose hospitality is gratefully acknowledged. Very useful comments were also provided by Torben Andersen, Lorenzo Cappiello, Olli Castren, Bruce Lehmann, Filippo di Mauro, Stelios Makrydakis, Nour Meddahi and Neil Shephard. The OTC volatilities used in this paper were provided by Citibank N.A. The usual disclaimer applies.

Predictable dynamics in implied volatility surfaces from OTC currency options

“…This should translate to less noisy IVS's and more precision in the identification of factors affecting their dynamics. Similar OTC currency options data have been used in previous studies by Campa and Chang (1995), (1998), Carr and Wu (2007a), (2007b) and Christoffersen and Mazzotta (2005); the latter study actually concludes that OTC currency options data are of superior quality for volatility forecasting purposes.…”

Cross-Dynamics of Volatility Term Structures Implied by Foreign Exchange Options

“…8 For instance, Corrado and Miller (1996) show that for short maturity at-themoney options the implied volatilities derived from the Black-Scholes model are virtually identical to the volatilities based on stochastic volatility models. Finally, as recently documented by Christoffersen and Mazzotta (2005), OTC currency option data appears to be of superior quality for volatility forecasting purposes. 7 It is becoming a standard practice in the OTC currency options market to quote implied volatilities with respect to deltas rather than strike prices.…”

A Proposed Solution for the Chicken-Egg Dilemma in Pricing Currency Options

“…Further, Kazantzis and Tessaromatis (2001) find that IV is generally better than historic volatility forecasts for horizons ranging from one day to three months. Using the OTC currency options price, Christoffersen and Mazzotta (2005) suggest that IV provides largely unbiased and fairly accurate forecasts of the actual volatility one month and three months ahead. Before the launching of WCO in PHLX, the options traded only had a maturity of three months.…”

“…Jorion's results suggest that IV outperforms statistical time-series models in terms of information content and predictive power. Christoffersen and Mazzotta (2005) used OTC currency options and found that IV provides a largely unbiased and fairly accurate forecast of the actual volatility one month and three months ahead. Chang and Tabak (2007) presented evidence that the IV, in the case of OPs, contains information that is not present in past returns for the Brazilian real exchange rate against the US dollar.…”