Implicit Bayesian Inference Using Option Prices.

A Bayesian approach to option pricing is presented, in which posterior inference about the underlying returns process is conducted implicitly, via observed option prices. A range of models which allow for conditional leptokurtosis, skewness and time-varying volatility in returns, are considered, with posterior parameter distributions and model probabilities backed out from the option prices. Fit, predictive and hedging densities associated with the different models are produced. Models are ranked according to several criteria, including their ability to fit observed option prices, predict future option prices and minimize hedging errors. In addition to model-specific results, averaged predictive and hedging densities are produced, the weights used in the averaging process being the posterior model probabilities. The method is applied to option price data on the S&P500 stock index. Whilst the results provide some support for the Black-Scholes model, no one model dominates according to all criteria considered.Bayesian Implicit Inference; Option Pricing Errors; Option Price Prediction; Hedging Errors; Nonnormal Returns Models; GARCH; Bayesian Model averaging.

Parametric Pricing of Higher Order Moments in S&P500 Options.

A general parametric framework is developed for pricing S&P500 options. Skewness and leptokurtosis in stock returns as well as time-varying volatility are priced. The parametric pricing model nests the Black-Scholes model and can explain volatility smiles and skews in stock options. The data consist of S&P500 options traded on select days in April, 1995, a total sample of over 500,000 observations. A number of performance criteria are used to evaluate the alternative models. The empirical results show that pricing higher order moments yield improvements in the pricing of options over the Black-Scholes model as well as other models.Option Pricing; Volatility Smiles and Skews; Generalized Student t; Skewness; Kurtosis; Time-Varying Volatility.

Pricing Currency Options in Tranquil Markets: Modelling Volatility Frowns

Volatility smiles arise in currency option markets when empirical exchange rate returns distributions exhibit leptokurtosis. This feature of empirical distributions is symptomatic of turbulent periods when exchange rate movements are in excess of movements based on the assumption of normality. In contrast, during periods of tranquility, movements in exchange rates are relatively small, resulting in unconditional empirical returns distributions with thinner tails than the normal distribution. Pricing currency options during tranquil periods on the assumption of normal returns yields implied volatility frowns, with over-pricing at both deep-in and deep-out-of-the-money contracts and under-pricing for at-the-money contracts. This paper shows how a parametric class of thin-tailed distributions based on the generalized Student t family of distributions can price currency options during periods of tranquility.Option pricing; volatility frowns; thin-tails; generalized Student t.

Coherent Predictions of Low Count Time Series

The application of traditional forecasting methods to discrete count data yields forecasts that are non-coherent. That is, such methods produce non-integer point and interval predictions which violate the restrictions on the sample space of the integer variable. This paper presents a methodology for producing coherent forecasts of low count time series. The forecasts are based on estimates of the p-step ahead predictive mass functions for a family of distributions nested in the integer-valued first-order autoregressive (INAR(1)) class. The predictive mass functions are constructed from convolutions of the unobserved components of the model, with uncertainty associated with both parameter values and model specifcation fully incorporated. The methodology is used to analyse two sets of Canadian wage loss claims data.Forecasting; Discrete Time Series; INAR(1); Bayesian Prediction; Bayesian Model Averaging.

Music in electronic markets: an empirical study

Music plays an important, and sometimes overlooked part in the transformation of communication and distribution channels. With a global market volume exceeding US$40 billion, music is not only one of the primary entertainment goods in its own right. Since music is easily personalized and transmitted, it also permeates many other services across cultural borders, anticipating social and economic trends. This article presents one of the first detailed empirical studies on the impact of internet technologies on a specific industry. Drawing on more than 100 interviews conducted between 1996 and 2000 with multinational and independent music companies in 10 markets, strategies of the major players, current business models, future scenarios and regulatory responses to the online distribution of music files are identified and evaluated. The data suggest that changes in the music industry will indeed be far-reaching, but disintermediation is not the likely outcome

Testing for Dependence in Non-Gaussian Time Series Data

This paper provides a general methodology for testing for dependence in time series data, with particular emphasis given to non-Gaussian data. A dynamic model is postulated for a continuous latent variable and the dynamic structure transferred to the non-Gaussian, possibly discrete, observations. Locally most powerful tests for various forms of dependence are derived, based on an approximate likelihood function. Invariance to the distribution adopted for the data, conditional on the latent process, is shown to hold in certain cases. The tests are applied to various financial data sets, and Monte Carlo experiments used to gauge their finite sample properties.Latent variable model; locally most powerful tests; approximate likelihood; correlation tests; stochastic volatility tests.

A comparison of on-road aerodynamic drag measurements with wind tunnel data from Pininfarina and MIRA

The principal development tool for the vehicle aerodynamicist continues to be the full-scale wind tunnel. It is expected that this will continue for many years in the absence of a reliable alternative. As a true simulation of conditions on the road, the conventional full-scale wind tunnel has limitations. For example, the ground is fixed relative to the vehicle, allowing an unrepresentative boundary layer to develop, and the wheels of the test vehicle do not rotate. These limitations are known to influence measured aerodynamic data. In order to improve the representation of road conditions in the wind tunnel, most of the techniques used have attempted to control the ground plane boundary layer. Only at model scale has the introduction of a moving ground plane and rotating wheels been widely adopted. The Pininfarina full-scale wind tunnel now incorporates the Ground Effect Simulation System which allows testing with a moving belt and rotating wheels. A major feature of this facility is that test vehicles can be easily installed with only minor modifications. This paper compares aerodynamic drag measurements for a large saloon, in various configurations, obtained both in the wind tunnel and on the road. The wind tunnel results are presented for various ground simulations. These are: moving belt with rotating wheels and stationary belt with fixed wheels at Pininfarina, and the conventional fixed ground in the MIRA full-scale wind tunnel. The on-road data is derived from coastdown tests

Reconstruction of superoperators from incomplete measurements

We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via complete tomography of four output states E[rho_j ] that originate from a set of four linearly independent test states j (j = 1, 2, 3, 4) at the input of the channel. We study the situation when less than four linearly independent states are transmitted via the channel and measured at the output. We present strategies how to reconstruct the channel when just one, two or three states are transmitted via the channel. In particular, we show that if just one state is transmitted via the channel then the best reconstruction can be achieved when this state is a total mixture described by the density operator rho = I/2. To improve the reconstruction procedure one has to send via the channel more states. The best strategy is to complement the total mixture with pure states that are mutually orthogonal in the sense of the Bloch-sphere representation. We show that unitary transformations (channels) can be uniquely reconstructed (determined) based on the information of how three properly chosen input states are transformed under the action of the channel.Comment: 13 pages, 6 figure