Paresh Date

An algorithm for identification in the /spl nu/-gap metric

This paper suggests a method for identification in the /spl nu/-gap metric. For a finite number of frequency response samples, a problem for identification in the /spl nu/-gap metric is formulated and an approximate solution is described. It uses an iterative technique for obtaining an /spl Lscr//sub 2/-gap approximation. Each stage of the iteration involves solving an LMI optimisation. Given a known stabilising controller and the /spl Lscr/2-gap approximation, it is shown how to derive a /spl nu/-gap approximation.

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 non-linear 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.

A new algorithm for latent state estimation in non-linear time series models

We consider the problem of optimal state estimation for a wide class of non-linear time series models. A modified sigma point filter is proposed, which uses a new procedure for generating sigma points. Unlike the existing sigma point generation methodologies in engineering, where negative probability weights may occur, we develop an algorithm capable of generating sample points that always form a valid probability distribution while still allowing the user to sample using a random number generator. The effectiveness of the new filtering procedure is assessed through simulation examples.

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.

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.

A fast calibrating volatility model for option pricing

In this paper, we propose a new random volatility model, where the volatility has a deterministic term structure modified by a scalar random variable. Closed-form approximation is derived for European option price using higher order Greeks with respect to volatility. We show that the calibration of our model is often more than two orders of magnitude faster than the calibration of commonly used stochastic volatility models, such as the Heston model or Bates model. On 15 different index option data sets, we show that our model achieves accuracy comparable with the aforementioned models, at a much lower computational cost for calibration. Further, our model yields prices for certain exotic options in the same range as these two models. Lastly, the model yields delta and gamma values for options in the same range as the other commonly used models, over most of the data sets considered. Our model has a significant potential for use in high frequency derivative trading.

Identification of Piecewise Affine LFR Models of Interconnected Systems

Identification of interconnected systems is a challenging problem in which it is crucial to exploit the available knowledge about the interconnection structure. This paper addresses the identification of discrete-time dynamical models in linear fractional representation form, composed by the interconnection of a linear time-invariant block and a static nonlinearity. An iterative identification approach is adopted, which alternates the estimation of the linear and the nonlinear components. Standard identification techniques are applied to the linear part, whereas recently developed piecewise affine identification techniques are employed for modeling the static nonlinearity. The proposed method takes advantage of the interconnection structure to identify models which are more accurate and often much simpler than those obtained when applying black-box piecewise affine identification techniques to the overall system. This is demonstrated through the application of the adopted identification algorithm to the silverbox problem, a popular real-life benchmark in nonlinear system identification.

Electricity futures price models: Calibration and forecasting

A new one factor model with a random volatility parameter is presented in this paper for pricing of electricity futures contracts. It is shown that the model is more tractable than multi-factor jump diffusion models and yields an approximate closed-form pricing formula for the electricity futures prices. On real market data, it is shown that the performance of the new model compares favourably with two existing models in the literature, viz. a two factor jump diffusion model and its jump free version, i.e., a two factor linear Gaussian model, in terms of ability to predict one day ahead futures prices. Further, a multi-stage procedure is suggested and implemented for calibration of the two factor jump diffusion model, which alleviates the difficulty in calibration due to a large number of parameters and pricing formulae which involve numerical evaluation of integrals. We demonstrate the utility of our new model, as well as the utility of the calibration procedure for the existing two factor jump diffusion model, by model calibration and price forecasting experiments on three different futures price data sets from Nord pool electricity data. For the jump diffusion model, we also investigate empirically whether it performs better in terms of futures price prediction than a corresponding, jump-free linear Gaussian model. Finally, we investigate whether an explicit calibration of jump risk premium in the jump diffusion model adds value to the quality of futures price prediction. Our experiments do not yield any evidence that modelling jumps leads to a better price prediction in electricity markets.

Pricing and risk management of interest rate swaps

This paper reformulates the valuation of interest rate swaps, swap leg payments and swap risk measures, all under stochastic interest rates, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations which solves this system is developed and allows for fast and accurate computation. The proposed method provides a computationally efficient alternative to Monte Carlo based valuations and risk measurement of swaps. This is demonstrated by conducting numerical experiments and so our method provides a potentially important real-time application for analysis and calculation in markets.

Higher order sigma point filter: A new heuristic for nonlinear time series filtering

In this paper we present some new results related to the higher order sigma point filter (HOSPoF), introduced in [1] for filtering nonlinear multivariate time series. This paper makes two distinct contributions. Firstly, we propose a new algorithm to generate a discrete statistical distribution to match exactly a specified mean vector, a specified covariance matrix, the average of specified marginal skewness and the average of specified marginal kurtosis. Both the sigma points and the probability weights are given in closed-form and no numerical optimization is required. Combined with HOSPoF, this random sigma point generation algorithm provides a new method for generating proposal density which propagates the information about higher order moments. A numerical example on nonlinear, multivariate time series involving real financial market data demonstrates the utility of this new algorithm. Secondly, we show that HOSPoF achieves a higher order estimation accuracy as compared to UKF for smooth scalar nonlinearities. We believe that this new filter provides a new and powerful alternative heuristic to existing filtering algorithms and is useful especially in econometrics and in engineering applications.