2,106 research outputs found

    The mathematics of filtering and its applications

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    This article is a special issue editorial

    Linear and nonlinear filtering in mathematical finance: a review

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    Copyright @ The Authors 2010This paper presents a review of time series filtering and its applications in mathematical finance. A summary of results of recent empirical studies with market data are presented for yield curve modelling and stochastic volatility modelling. The paper also outlines different approaches to filtering of nonlinear time series

    Regime switching volatility calibration by the Baum-Welch method

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    Regime switching volatility models provide a tractable method of modelling stochastic volatility. Currently the most popular method of regime switching calibration is the Hamilton filter. We propose using the Baum-Welch algorithm, an established technique from Engineering, to calibrate regime switching models instead. We demonstrate the Baum-Welch algorithm and discuss the significant advantages that it provides compared to the Hamilton filter. We provide computational results of calibrating and comparing the performance of the Baum-Welch and the Hamilton filter to S&P 500 and Nikkei 225 data, examining their performance in and out of sample

    Linear State Models for Volatility Estimation and Prediction

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    This report covers the important topic of stochastic volatility modelling with an emphasis on linear state models. The approach taken focuses on comparing models based on their ability to fit the data and their forecasting performance. To this end several parsimonious stochastic volatility models are estimated using realised volatility, a volatility proxy from high frequency stock price data. The results indicate that a hidden state space model performs the best among the realised volatility-based models under consideration. For the state space model different sampling intervals are compared based on in-sample prediction performance. The comparisons are partly based on the multi-period prediction results that are derived in this report

    Measuring the risk of a nonlinear portfolio with fat tailed risk factors through probability conserving transformation

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    This paper presents a new heuristic for fast approximation of VaR (Value-at-Risk) and CVaR (conditional Value-at-Risk) for financial portfolios, where the net worth of a portfolio is a non-linear function of possibly non-Gaussian risk factors. The proposed method is based on mapping non-normal marginal distributions into normal distributions via a probability conserving transformation and then using a quadratic, i.e. Delta–Gamma, approximation for the portfolio value. The method is very general and can deal with a wide range of marginal distributions of risk factors, including non-parametric distributions. Its computational load is comparable with the Delta–Gamma–Normal method based on Fourier inversion. However, unlike the Delta–Gamma–Normal method, the proposed heuristic preserves the tail behaviour of the individual risk factors, which may be seen as a significant advantage. We demonstrate the utility of the new method with comprehensive numerical experiments on simulated as well as real financial data
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