Introduction Estimating functions provide a general framework for finding estimators and studying their properties in many di#erent kinds of statistical models, including stochastic process models. An estimating function is a function of the data as well as of the parameter to be estimated. An estimator is obtained by equating the estimating function to zero and solving the resulting estimating equation with respect to the parameter. The idea of using estimating equations is an old one and goes back at least to Karl Pearson's introduction of the method of moments. The term estimating function may have been coined by Kimball (1946). The estimating function approach has turned out to be very useful in obtaining, improving and studying estimators for discretely sampled parametric di#usion-type models, where the likelihood function is usually not explicitly known. Estimating functions are often constructed by combining relationships (dependent on the unknown parameter) between an observa

foreign exchange rates with jumps

We study a Markov switching stochastic volatility model with heavy tail innovations in the observable process. Due to the economic interpretation of the hidden volatility regimes, these models have many financial applications like asset allocation, option pricing and risk management. The Markov switching process is able to capture clustering effects and jumps in volatility. Heavy tail innovations account for extreme variations in the observed process. Accurate modelling of the tails is important when estimating quantiles is the major interest like in risk management applications. Moreover we follow a Bayesian approach to filtering and estimation, focusing on recently developed simulation based filtering techniques, called Particle Filters. Simulation based filters are recursive techniques, which are useful when assuming non-linear and non-Gaussian latent variable models and when processing data sequentially. They allow to update parameter estimates and state filtering as new observations become available.

We study a Markov switching stochastic volatility model with heavy tail innovations in the observable process. Due to the economic interpretation of the hidden volatility regimes, these models have many financial applications like asset allocation, option pricing and risk management. The Markov switching process is able to capture clustering effects and jumps in volatility. Heavy tail innovations account for extreme variations in the observed process. Accurate modelling of the tails is important when estimating quantiles is the major interest like in risk management applications. Moreover we follow a Bayesian approach to filtering and estimation, focusing on recently developed simulation based filtering techniques, called Particle Filters. Simulation based filters are recursive techniques, which are useful when assuming non-linear and non-Gaussian latent variable models and when processing data sequentially. They allow to update parameter estimates and state filtering as new observations become available.

The increasing availability of multi-core and multiprocessor architectures provides new opportunities for improving the performance of many computer simulations. Markov Chain Monte Carlo (MCMC) simulations are widely used for approximate counting problems, Bayesian inference and as a means for estimating very highdimensional integrals. As such MCMC has found a wide variety of applications in fields including computational biology and physics, financial econometrics, machine learning and image processing. This paper presents a new method for reducing the runtime of Markov Chain Monte Carlo simulations by using SMP machines to speculatively perform iterations in parallel, reducing the runtime of MCMC programs whilst producing statistically identical results to conventional sequential implementations. We calculate the theoretical reduction in runtime that may be achieved using our technique under perfect conditions, and test and compare the method on a selection of multi-core and multi-processor architectures. Experiments are presented that show reductions in runtime of 35 % using two cores and 55 % using four cores.

This paper analyzes exponentially affine and non-affine stochastic volatility models with jumps in returns and volatility. Markov Chain Monte Carlo (MCMC) technique is applied within a Bayesian inference framework to estimate model parameters and latent variables using daily returns from the S&P 500 stock index. There are two approaches to overcome the problem of misspecification of the square root stochastic volatility model. The first approach proposed by Christoffersen, Jacobs and Mimouni (2008) suggests to investigate some non-affine alternatives of the volatility process. The second approach consists in examining more heavily parameterized models by adding jumps to the return and possibly to the volatility process. The aim of this paper is to combine both model frameworks and to test whether the class of affine models is outperformed by the class of non-affine models if we include jumps into the stochastic processes. We conclude that the non-affine model structure have promising statistical properties and are worth further investigations. Further, we find affine models with jump components that perform similar to the non affine models without jump components. Since non affine models yield economically unrealistic parameter estimates, and research is rather developed for the affine model structures we have a tendency to prefer the affine jump diffusion models.

Abstract—The increasing availability of multi-core and multiprocessor architectures provides new opportunities for improving the performance of many computer simulations. Markov Chain Monte Carlo (MCMC) simulations are widely used for approximate counting problems, Bayesian inference and as a means for estimating very high-dimensional integrals. As such MCMC has had a wide variety of applications in fields including computational biology and physics, financial econometrics, machine learning and image processing. One method for improving the performance of Markov Chain Monte Carlo simulations is to use SMP machines to perform ‘speculative moves’, reducing the runtime whilst producing statistically identical results to conventional sequential implementations. In this paper we examine the circumstances under which the original speculative moves method performs poorly, and consider how some of the situations can be addressed by refining the implementation. We extend the technique to perform Markov Chains speculatively, expanding the range of algorithms that maybe be accelerated by speculative execution to those with non-uniform move processing times. By simulating program runs we can predict the theoretical reduction in runtime that may be achieved by this technique. We compare how efficiently different architectures perform in using this method, and present experiments that demonstrate a runtime reduction of up to 35-42 % where using conventional speculative moves would result in execution as slow, if not slower, than sequential processing. I.

Abstract not found

Lessons from the Eurodollar Markets We estimate affine models using the Eurodollar futures and options data. The rationale for this exercise comes from a combination of recent theoretical and empirical work, which documents a trade-off in models abilities to match the expectations hypothesis and generate conditional volatility, and suggests to break this tight connection by explicitly removing volatility from the term structure dynamics via the unspanned stochastic volatility (USV). However, the USV property is surprising in the light of the interest rate proxies studies, which find strong evidence for stochastic volatility. We believe that these results could be explained in part by estimation methodology typically used, and in part by a limited span of swaps data. We use a more general methodology in this paper, and Recent advances in affine dynamic term structure models show a trade-off between the abilities to match the first moments of the yield curve by means of flexible risk premia and to specify reasonable volatility dynamics (Dai and Singleton, 2002 (DS2 hereafter), Duffee, 2002). 1 These