2,107 research outputs found
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Uncertainty Modelling in Linear Dynamic Systems: A Feedback Point of View
The mathematics of filtering and its applications
This article is a special issue editorial
Linear and nonlinear filtering in mathematical finance: a review
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
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
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Iterative procedures for identification of nonlinear interconnected systems
This work addresses the identification problem of a discrete-time nonlinear system composed by linear and nonlinear subsystems. Systems in this class will be represented by Linear Fractional
Transformations. Iterative identification procedures are examined, that alternate between the estimation of the linear and the nonlinear components. The burden of identification falls naturally on the nonlinear subsystem, as techniques for identification of linear systems have long been established. Two approaches are
examined. A point-wise identification of the nonlinearity, recently proposed in the literature, is applied and its advantages and
drawbacks are outlined. An alternative procedure that employs piecewise affine approximation techniques is proposed. Numerical examples demonstrate the efficiency of the proposed algorithm
Linear State Models for Volatility Estimation and Prediction
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
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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Optimal portfolio control with trading strategies of finite variation
We propose a method for portfolio selection where the trading strategies are constrained to have a finite variation. A simulation example shows a significant reduction in trasaction costs as compared to log-optimal portfolio, for almost same final wealth
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Linear Gaussian Affine Term Structure Models with Unobservable Factors: Calibration and Yield Forecasting
This paper provides a significant numerical evidence for out-of-sample forecasting ability of linear Gaussian interest rate models with unobservable underlying factors. We calibrate one, two and three factor linear Gaussian models using the Kalman filter on two different bond yield data sets and compare their out-of-sample
forecasting performance. One step ahead as well as four step ahead out-of-sample forecasts are analyzed based on the weekly data. When evaluating the one step ahead forecasts, it is shown that a one factor model may be adequate when only the short-dated or only the long-dated yields are considered, but two and three factor
models performs significantly better when the entire yield spectrum is considered. Furthermore, the results demonstrate that the predictive ability of multi-factor models remains intact far
ahead out-of-sample, with accurate predictions available up to one year after the last calibration for one data set and up to three
months after the last calibration for the second, more volatile data set. The experimental data denotes two different periods with different yield volatilities, and the stability of model
parameters after calibration in both the cases is
deemed to be both significant and practically useful. When it comes to four step ahead predictions, the quality of forecasts deteriorates for all models, as can be expected, but the advantage of using a multi-factor model as compared to a one factor model is still significant.
In addition to the empirical study above, we also suggest a nonlinear filter based on linear programming for improving the term structure matching at a given point in time. This method,
when used in place of a Kalman filter update, improves the term structure fit significantly with a minimal added computational overhead. The improvement achieved with the proposed method is
illustrated for out-of-sample data for both the data sets. This method can be used to model a parameterized yield curve consistently with the underlying short rate dynamics
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A new moment matching algorithm for sampling from partially specified symmetric distributions
A new algorithm is proposed for generating scenarios from a partially specified symmetric multivariate distribution. The algorithm generates samples which match the first two moments exactly and match the marginal fourth moments approximately, using a semidefinite programming procedure. The performance of the
algorithm is illustrated by a numerical example
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