بررسی اعتبار بانک مرکزی در بحران ERM : مقایسه پیش بینی های مبتنی بر بازار گزینه ای و لحظه ای

Financial markets embed expectations of central bank policy into asset prices. This paper compares two approaches that extract a probability density of market beliefs. The first is a simulated moments estimator for option volatilities described in [Mizrach, B., 2002. When Did the Smart Money in Enron Lose Its’ Smirk? Rutgers University Working Paper #2002-24]; the second is a new approach developed by [Haas, M., Mittnik, S., Paolella, M.S., 2004a. Mixed normal conditional heteroskedasticity, J. Financial Econ. 2, 211–250] for fat-tailed conditionally heteroskedastic time series. In an application to the 1992–1993 European Exchange Rate Mechanism crises, we find that both the options and the underlying exchange rates provide useful information for policy makers.

A basic insight of financial economics is that asset prices should reflect views about the future. For this reason, many economists rely on market prices to make predictions. Even when these views are incorrect, policy makers may want to avoid changes that the market is not expecting. In recent years, some novel techniques have been introduced to extract market expectations. This paper explores two of them: extracting implied probability densities from option prices and volatility modeling of the underlying. Both methods have the advantage of producing predictive densities rather than just point forecasts. These tools can, in principal, allow central bankers to examine the full range of risks facing their economies. There are numerous approaches that generalize the Black–Scholes model. Merton (1976) and Bates (1991) allow sudden changes in the level of asset prices. Wiggins, 1987, Hull and White, 1987 and Stein and Stein, 1991 and Heston (1993) allow volatility to change over time. A related literature, with papers by Dumas et al. (1998) and Das and Sundaram (1999), has looked at deterministic variations in volatility with the level of the stock price or with time. To extract market expectations of the exchange rate, we utilize a method first used in Mizrach (2002) that looks directly at the probability distribution. We parameterize the exchange rate process as a mixture of log normals, as in Ritchey (1990) and Melick and Thomas (1997), and fit the model to options prices. In an application to the Enron bankruptcy, Mizrach found that investors were far too optimistic about Enron until days before the stock’s collapse. Our second approach tries to extract information directly from the underlying currencies. We utilize a general mixture of two normal densities to extract information from the spot foreign exchange market. In this model, both the mixing weights as well as the parameters of the component densities, i.e., component means and variances, are time-varying and may depend on past exchange rates as well as further explanatory variables, such as interest rates. The dynamic mixture model we specify is a combination of the logistic autoregressive mixture with exogenous variables, or LMARX, model investigated in Wong and Li (2001) and the mixed normal GARCH process recently proposed by Haas et al. (2004a). The predictive densities generated from the resulting LMARX–GARCH model exhibit an enormous flexibility, and they may be multimodal, for example, in times where a realignment becomes more probable. In this paper, we utilize the two approaches to explore market sentiment prior to the exchange rate crises of September 1992 and July–August 1993. In the first episode, the British Pound (BP) and Italian Lira withdrew from the Exchange Rate Mechanism (ERM) of the European Monetary System (EMS). The Pound had traded in a narrow range against the German Deutsche Mark (DM) for almost two years and the Lira for more than five. The crisis threw the entire plan for European economic and financial integration into turmoil. The French Franc (FF) remained in the mechanism, but speculative pressures against it remained strong. In the second crisis we examine, the Franc, in August 1993, had to abandon its very close link with the DM (the “Franc fort”) and widen it’s fluctuation band. Campa and Chang (1996) have looked at ERM credibility using arbitrage bounds on option prices. They find that option prices reflected the declining credibility of the Lira and Pound in 1992 and the Franc in 1993. Malz (1996) finds an increasing risk of BP devaluation starting in late August 1992. Christoffersen and Mazzotta (2004) find useful predictive information in 10 European countries’ over-the-counter currency options. We first examine the options markets’ implied probability of depreciation in the FF and BP prior to the ERM crises. The model estimates reveal that the market anticipated both events. The devaluation risk with the Franc rises significantly 11 days in advance of the crisis. With the Pound, the risk is subdued until only five days before it devalued on “Black Wednesday” September 16, 1992. Vlaar and Palm (1993) were the first to use the normal mixture density to model EMS exchange rates against the DM, noting that, in contrast to freely floating currencies, these often show pronounced skewness, due to jumps which occur in case of realignments, but also, for example, as a result of expected policy changes or speculative attacks. Although Vlaar and Palm (1993) noted that making the jump probability a function of explanatory variables, such as inflation and interest rates, may be a promising task, they did not undertake such analysis. Neely (1994) surveys research on forecasting realignments in the EMS and reports evidence for realignments to be predictable to some extent from information such as interest rates and the position of the exchange rate within the band. Building both on the results surveyed in Neely (1994) and the work of Vlaar and Palm (1993) and Palm and Vlaar (1997), the studies of Bekaert and Gray, 1998 and Neely, 1999 and Klaster and Knot (2002) use more general dynamic mixture models of exchange rates in target zones. Thus, the model employed below has some similarities with those developed in these studies, as will be discussed below. The dynamic mixture model provides, as in the options-based approach, estimates of the probability of a depreciation. For the FF, the model indicates a considerable increase of this probability one week in advance of the crisis, and a further increase immediately before the de facto devaluation of the FF, when the bands of the target zone were widened to ±15%±15%. For the BP, we can, in contrast to the options-based approach, not develop a promising dynamic mixture model, because the BP joined the ERM only in October 1990 and withdrew in September 1992. During this period there were no realignments or large jumps within the band, so that the sample does not provide information that is necessary to fit a target zone mixture model. Consequently, the mixed normal GARCH model detects a rise in the devaluation probability only after the Pound was withdrawn from the ERM. Both models provide a complete predictive density for the exchange rate, and the last part of the paper examines the fit of the entire density. We utilize the approach of Berkowitz (2001) to formally compare the model’s density-forecasting performance. In the options market, the predictive density becomes indistinguishable from the post crisis density on July 21 for the FF, 11 days before the crisis. For the BP, there are some early warning signals in mid-August and the beginning of September. In the FF spot market, the predictive density is consistent with the post-crisis data from the outset. For the BP, the result is similar to the options. There are some brief early signals, but the densities statistically differ from the post-devalation period until September 10th. The paper continues with some discussion of the ERM. Section 3 describes the theory of implied density extraction from options. It also proposes a mixture of log normals specification which nests the Black–Scholes model. We also develop a GARCH mixture model for the spot exchange rate. Section 4 contains some stylized features of the currency options, and some detailed issues in estimation for both models. From the two sets of parameter estimates, we compute implied devaluation probabilities. Section 5 compares the entire predictive density statistically. Section 6 concludes with directions for future research.

Analyzed with some recently developed modeling techniques, asset prices can provide insights into the entire probability distribution of future events. This paper has utilized the mixture of log normals in two separate contexts: with options and with the underlying currencies. The crisis of the European Exchange Rate Mechanism case was certainly an epochal event for the markets, where central bankers became aware – perhaps for the first time – that the markets might be an irresistible force. Policy makers may find these tools and inference worthwhile in a variety of contexts. Their subjective weights between types I and II errors should not only be tested ex-post but incorporated directly in the estimation. Both Skouras (2001) and Christoffersen and Jacobs (2001) have made progress along these lines. Loss aversion on the part of investors and traders may give them similar preferences. Whether or not the accuracy of density predictions can be improved by combining options and spot-market information is the subject of future research. One possible strategy in this direction, employed in Claessen and Mittnik (2002), is to use implied volatility as an explanatory variable in the GARCH equation. Alternatively, the predicted density could be formed by a mixture of options- and the spot market-based density predictions.