We take a nonstructural time-series approach to modeling and forecasting daily average temperature in ten U.S. cities, and we inquire systematically as to whether it may prove useful from the vantage point of participants in the weather derivatives market. The answer is, perhaps surprisingly, yes. Time series modeling reveals both strong conditional mean dynamics and conditional variance dynamics in daily average temperature, and it reveals sharp differences between the distribution of temperature and the distribution of temperature surprises. Most importantly, it adapts readily to produce the long-horizon forecasts of relevance in weather derivatives contexts. We produce and evaluate both point and distributional forecasts of average temperature, with some success. We conclude that additional inquiry into nonstructural weather forecasting methods, as relevant for weather derivatives, will likely prove useful. Key Words: Risk management; hedging; insurance; seasonality; average temperature; financial derivatives; density forecasting JEL Codes: G0, C1 Acknowledgments: For financial support we thank the National Science Foundation, the Wharton Financial Institutions Center, and the Wharton Risk Management and Decision Process Center. For helpful comments we thank Marshall Blume, Larry Brown, Jeff Considine, John Dutton, Ren Garcia, Stephen Jewson, Vince Kaminski, Paul Kleindorfer, Howard Kunreuther, Yu Li, Bob Livezey, Cliff Mass, Don McIsaac, Nour Meddahi, David Pozo, Matt Pritsker, S.T. Rao, Claudio Riberio, Til Schuermann and Yihong Xia. We are also grateful for comments by participants at the American Meteorological Society's Policy Forum on Weather, Climate and Energy. None of those thanked, of course, are responsible in any way for the outcome. Address corresponde...

This chapter develops Markov Chain Monte Carlo (MCMC) methods for Bayesian inference in continuous-time asset pricing models. The Bayesian solution to the inference problem is the distribution of parameters and latent variables conditional on observed data, and MCMC methods provide a tool for exploring these high-dimensional, complex distributions. We first provide a description of the foundations and mechanics of MCMC algorithms. This includes a discussion of the Clifford-Hammersley theorem, the Gibbs sampler, the Metropolis-Hastings algorithm, and theoretical convergence properties of MCMC algorithms. We next provide a tutorial on building MCMC algorithms for a range of continuous-time asset pricing models. We include detailed examples for equity price models, option pricing models, term structure models, and regime-switching models. Finally, we discuss the issue of sequential Bayesian inference, both for parameters and state variables.

informs doi 10.1287/mnsc.1060.0520

The growth of the option pricing literature parallels the spectacular developments of deriva-tive securities and the rapid expansion of markets for derivatives in the last three decades. Writing a survey of option pricing models appears therefore like a formidable task. To delimit our focus we will put emphasis on the more recent contributions since there are

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Realized volatility affords the ex-post empirical measurement of the latent notional volatility. However, the time-varying returns autocorrelation induced by microstructure effects represents a challenging problem for standard volatility measures. In this study, a new nonparametric volatility measures based on the Discrete Sine Transform (DST) is proposed. We show that the DST exactly diagonalizes the covariance matrix of MA(1) process. This original result provides us an orthonomal basis decomposition of the return process which permits to optimally disentangle the underlying efficient price signal from the time-varying nuisance component contained in tick-by-tick return series. As a result, two nonparametric volatility estimators which fully exploit all the available information contained in high frequency data are constructed. Moreover the DST orthogonalization allow us to analytically compute the score and the Fischer information matrix of MA(1) processes. In discussing efficient numerical procedures for the likelihood maximizations we also suggest that DST estimator would represent the most valid starting point for the numerical maximization of the likelihood. Monte Carlo simulations based on a realistic model for microstructure effects show the superiority of DST estimators, compared to alternative local volatility proxies for every level of the noise to signal ratio and a large class of noise contaminations. These properties make the DST approach a nonparametric method able to cope with time-varying autocorrelation, in a simple and efficient way, providing robust and accurate volatility estimates under a wide set of realistic conditions. Moreover, its computational efficiency makes it well suitable for real-time analysis of high frequency data.

This note develops general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit the recent asymptotic distributional results in Barndorff-Nielsen and Shephard (2002a), are both easy-to-implement and highly accurate in empirically realistic situations. On properly accounting for the measurement errors in the volatility forecast evaluations reported in Andersen, Bollerslev, Diebold and Labys (2003), the adjustments result in markedly higher estimates for the true degree of return-volatility predictability.

We test for price discontinuities, or jumps, in a panel of high-frequency intraday returns for forty large-cap stocks and an equiweighted index from these same stocks. Jumps are naturally classified into two types: common and idiosyncratic. Common jumps affect all stocks, albeit to varying degrees, while idiosyncratic jumps are stock-specific. Despite the fact that each of the stocks has a β of about unity with respect to the index, common jumps are virtually never detected in the individual stocks. This is truly puzzling, as an index can jump only if one or more of its components jump. To resolve this puzzle, we propose a new test for cojumps. Using this new test we find strong evidence for many modest-sized common jumps that simply pass through the standard jump detection statistic, while they appear highly significant in the cross section based on the new cojump identification scheme. Our results are further corroborated by a striking within-day pattern in the non-diversifiable cojumps.

foreign exchange rates with jumps

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