Distributions Implied by Exchange Traded Options: A Ghost’s Smile?

Abstract

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 SP 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 European option with the same exercise price and maturity. Further and more importantly, we found that BAW volatilities derived from a pair of put and call CME options with the same exercise price are very close to each other. Indeed, the model independent and arbitrage based put-call parity stipulates that Black-Scholes volatilities implied by European puts and calls with the same exercise price are equal. Therefore, we argue