Research
Working Papers
Quasi Monte Carlo Kalman Filter for Nonlinear and Non-Gaussian State Space Models, Job Market Paper, July 2020
In this study, we present a new filtering approach for nonlinear and non-Gaussian state space models. This approach builds on the well-established Kalman filter, featuring a state-dependent least-square linearization of the nonlinear function and a Gaussian-mixture approximation to the error distribution, and it applies the quasi Monte Carlo method for numerical integration during the computation. We compare our approach with other existing methods using simulated data, and we find that the proposed approach can outperform these methods in terms of speed and accuracy. This study also provides analysis on the stability of this new filtering approach. In addition, we propose two methods to estimate the unknown parameters, and establish the consistency of the proposed quasi-maximum likelihood estimator under general conditions. To illustrate the proposed approach, we discuss several numerical examples. We also consider two empirical applications. The first is a stochastic volatility model for foreign exchange data between Sterling and Dollar. The second is a jump model for the 3-month T-bill rate data, where we show that the jump size has a Gaussian mixture representation. We estimate the jump probability and investigate the jump sources based on macroeconomic events.
Hermite Polynomial Based Valuation of American Options with General Jump-Diffusion Processes, (with Li Chen), July 2020
We present a new approximation scheme for the price and exercise policy of American options. The scheme is based on Hermite polynomial expansions of the transition density of the underlying asset dynamics and the early exercise premium representation of the American option price. The advantage of the proposed approach is threefold. First, our approach does not require the transition density and characteristic functions of the underlying asset dynamics to be attainable in closed form. Second, our approach is fast and accurate, while the prices and exercise policy can be jointly produced. Third, our approach has a wide range of applications. We show that the proposed approximations of the price and optimal exercise boundary converge to the true ones. We also provide a numerical method based on a step function to implement our proposed approach. Applications to nonlinear mean-reverting models, double mean-reverting models, Merton and Kou’s jump-diffusion models are presented and discussed.
Publications
- Pairs Trading with General State Space Models, forthcoming, Quantitative Finance, February 2021. Online Appendix
- Constructing Employment and Compensation Matrices and Measuring Labour Input in China (with Harry X. Wu, and Ximing Yue), RIETI Discussion Papers, 2015, 15-E-005