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thesis by ANTONIO HERRERO GARCIA Abstract In this project we propose the use of some widespread prediction techniques in the last few years for modeling derivatives. In order to do that, we have reviewed the state-of-the-art of the prediction models dealing with stochastic processes. In the oil futures sector, Schwartz suggested a model in which the oil futures price was split in two factors: the long-term equilibrium price and the short-term variations. As a result, we propose a Hull-White discrete-time two-factor interest rate model, whose factors are the short and the long term.
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by Alireza Javaheri and Alain Galli, Abstract In this article we present an introduction to various Filtering algorithms and some of their applications to the world of Quantitative Finance. We shall first mention the fundamental case of Gaussian noises where we obtain the well-known Kalman Filter. Because of common nonlinearities, we will be discussing the Extended Kalman Filter Discuss this paper
Abstract. The paper is an eclectic study of the uses of the Kalman filter in existing econometric literature. An effort is made to introduce the various extensions to the linear filter first developed by Kalman(1960) through examples of their uses in economics. The basic filter is first derived and then some applications are reviewed. Keywords. Kalman filter; Time-varying parameters; Stochastic volatility
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P. J. BOLLAND AND J. T. CONNOR ABSTRACT We present a methodology for modelling real world high frequency financial data. The methodology copes with the erratic arrival of data and is robust to additive outliers in the data set. Arbitrage pricing relationships are formulated into a linear state space representation. Arbitrage opportunities violate these pricing relationships and are analogous to multivariate additive outliers. Robust identification/filtering of arbitrage opportunities in the data is accomplished by Kalman filtering. The state space model used to describe the pricing relationships is general enough to handle both linear and non-linear models. The recursive Kalman equations are adapted to filter tick data, cope with the erratic arrival of observations and produce estimates of all the arbitrage prices on every time step. We demonstrate the methodology with a robust neural network filter applied to foreign exchange triangular arbitrage. Tick data from three markets is used: $/DM, Discuss this paper
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Cristina Sommacampagna Abstract In this paper we develop a new approach to Value-at-Risk estimating the betas of the assets in the portfolio with the Kalman filter. This technique is applied to a portfolio of assets of an insurance company and is compared with the performances of two traditional methodologies: the approach based on the variance-covariance matrix of returns and the approach based on OLS Sharpe betas. The back testing analysis shows that the proposed technique is able to capture the dynamics of financial markets and is flexible enough to match the hedging purposes of a financial institution. Keywords: Value-at-Risk; Kalman filter; Sharpe beta.
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