We decompose real appreciation in tradables derived from producer price indexes in three Central European countries between the pricing-to-market component (disparity) and the local relative price component (the substitution ratio). Appreciation is only partially explained by local relative prices. The rest is absorbed by disparity, depending on the size of the no-arbitrage band. The observed disparity fluctuates in a wider band for differentiated products than for commodity like goods.JEL classifications: F12, F15.

A new and easily applicable method for estimating risk-neutral distributions (RND) implied by American futures options is proposed. It amounts to inverting the Barone-Adesi and Whaley method (BAW method) to get the BAW implied volatility smile. Extensive empirical tests show that the BAW smile is equivalent to the volatility smile implied by corresponding European options. Therefore, the procedure leads to a legitimate RND estimation method. Further, the investigation of the currency options traded on the Chicago Mercantile Exchange and OTC markets in parallel provides us with insights on the structure and interaction of the two markets. Unequally distributed liquidity in the OTC market seems to lead to price distortions and an ensuing interesting "ghost-like" shape of the RND density implied by CME options. Finally, using the empirical results, we propose a parsimonious generalization of the existing I would like to acknowledge the support of the Czech Grant Agency under Grant 402/00/0814. The article is based on research pursued during an Academic Project for the Centre for Central Banking Studies (CCBS) at the Bank of England. I would like to thank everybody in the CCBS for their strong support and all of their kind help. I would also like to thank Ron Anderson, Aris Bikos, Neil Cooper, Joe Ganley, Gordon Gemmill, Toni Gravelle, Allan Malz, Richhild Moessner, Jose Noguera, Nikolaos Panigirtzoglou, Peter Sinclair, and the journal referee for their valuable suggestions and worthwhile discussions. All errors and omissions are mine alone. For correspondence, Czech National Bank, Na Prikope 28, 115 03, Prague 1, Czech Republic; e-mail: martin.cincibuch@cnb.cz It is a well established result that the price of a derivative asset that depends only on prices of traded securities may be expressed as its expected payoff discounted by the risk-free rate, where the expectation is taken over by the risk-neutral distribution. However, in general, true and risk-neutral distributions may be quite distinct; the only necessary restriction is that the distributions share a common support. Grundy (1991) examines the relationship between option prices and the true distribution of the underlying asset, and finds that imposing simple restrictions on the true distribution leads to useful bounds of its noncentral moments. Rubinstein (1994) shows that for standard utility functions the true distribution tends to be slightly shifted with respect to the risk-neutral one, but its shape remains very similar. methods for estimating volatility smiles from OTC options. A single free parameter significantly improves the fit. Received April 2002; Accepted March 2003 I Martin Cincibuch is a PhD candidate and is at the Czech National Bank and Center for Economic Research and Graduate Education in Prague, Czech Republic.

Risk neutral distributions summarise much of the available information associated with market prices and therefore they are attractive for market, academic and central bank economists. As Bliss and Panigirtzoglou (2000) note, RNDs estimated from liquid assets may be used by market participants for pricing exotic derivatives. Further, from the point of view of the central bank, option markets provide information in addition to that provided by spot and futures markets, and implied risk neutral distributions represent a convenient tool for interpreting this additional information. Clews, Panigirtzoglou and Proudman (2000) describe the methods used at the Bank of England for estimating distributions implied by interest rate futures, which enter as a regular input at its Monetary Policy Committee briefings. At other central banks, RNDs are estimated from currency options and used for monitoring the foreign exchange market, for example, at the Bank of Canada or the Czech National Bank.Next, due to the forward-looking nature of option prices, accurate estimates of implied distributions might arguably enhance VaR modelling. There is an increasing amount of literature pointing to the shortcomings of risk modelling based on the assumption that market price data follow a stochastic process which only depends on past observations. (e.g. Danielsson (2000), Ahn et. al. (1999), Artzner et. al. (2000). On the other hand, empirical evidence suggests that option-based measures of uncertainty are a better predictor of future volatility of the underlying asset than statistical time-series models. Christensen and Prabhala (1998) offer such evidence for S&P index options; Jorion (1995) for currency options for major currency pairs; and Bouc and Cincibuch (2001) for Czech koruna options. The question whether options also carry useful information about the fat-tailedness of the distribution of future assets' returns and about other deviations from lognormality is an important one from the risk management point of view. And indeed, the first step to answering such a question is to have a reliable estimate of the risk neutral distribution implied by the option prices.The results presented in this article are threefold. First, we discuss a new method for estimating risk neutral distributions (RND) implied by American futures options. In contrast to other methods that utilise lower and upper bounds for the prices of American options, this method amounts to inverting the Barone-Adesi and Whaley method (1987) (BAW method) to get the BAW implied volatility from the option prices and then approximating the BAW volatility smile with the weighted smoothing spline. Using the full history of yen futures options traded on the Chicago Mercantile Exchange (CME) and comparing them with relevant option prices from the interbank over-the-counter (OTC) market, we found good support for the hypothesis that the BAW volatility implied by a American futures option does not differ significantly from the Black-Scholes volatility implied by the price of the Eu...