Seisho Sato

Stationary and Non-stationary Simultaneous Switching Autoregressive Models with an Application to Financial Time Series

A common observation among economists on many economic time-series, including major financial time-series, is the asymmetrical movement between the downward phase and the upward phase of their sample paths. Since this feature of time irreversibility cannot be described by the Gaussian ARMA, ARIMA or ARCH time-series models, we propose stationary and non-stationary simultaneous switching autoregressive (SSAR) models, which are nonlinear switching time-series models. We discuss some properties of these time-series models and the estimation method for their unknown parameters. The asymmetrical conditional heteroscedasticity can be easily incorporated into the SSAR models. We also report a simple empirical result on Nikkei 225 Spot and Futures indices by using a non-stationary SSAR model. JEL Classification Numbers: C22, C32.

The SIML estimation of realized volatility of the Nikkei-225 Futures and hedging coefficient with micro-market noise

For the estimation problem of the realized volatility and hedging coefficient by using high-frequency data with possibly micro-market noise, we use the Separating Information Maximum Likelihood (SIML) method, which was recently developed by Kunitomo and Sato [11-13]. By analyzing the Nikkei-225 Futures data, we found that the estimates of realized volatility and the hedging coefficients have significant bias by using the traditional historical method which should be corrected. The SIML method can handle the bias problem in the estimation by removing the possible micro-market noise in multivariate high-frequency data. We show that the SIML method has the asymptotic robustness under non-Gaussian cases even when the market noises are autocorrelated and endogenous with the efficient market price or the signal term.

An FBSDE Approach to American Option Pricing with an Interacting Particle Method

In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise premium can be cast into the form of a decoupled non-linear FBSDE. We numerically solve the FBSDE by applying an interacting particle method recently proposed by Fujii and Takahashi (2012c), which allows one to perform a Monte Carlo simulation in a fully forward-looking manner. We perform the fourth-order analysis for the Black–Scholes (BS) model and the third-order analysis for the Heston model. The comparison to those obtained from existing tree algorithms shows the effectiveness of the particle method.

Style analysis with particle filtering and generalized simulated annealing

This paper proposes a new approach to style analysis of mutual funds in a general state space framework with particle filtering and generalized simulated annealing (GSA). Specifically, we regard the exposure of each style index as a latent state variable in a state space model and employ a Monte Carlo filter as a particle filtering method, where GSA is effectively applied to estimating unknown parameters.An empirical analysis using data of three Japanese equity mutual funds with six standard style indexes confirms the validity of our method. Moreover, we create fund-specific style indexes to further improve estimation in the analysis.

Dynamic Instrument Rules Based on Time Varying Coefficients Vector Autoregressive Modeling and Forecast-Based Monetary Policy

This paper proposes a method to construct monetary instrument rules whose coefficients are time varying. We refer the instrument rules as the dynamic instrument rules. Our approach is a statistical and practical tool for the central bank to achieve some specified targets. The dynamic instrument rules consist of two elements: (1) time varying coefficients vector autoregressive modeling (time varying VAR) with the vector of control variables and (2) linear quadratic dynamic programming. The coefficients of time varying VAR are assumed to change gradually (this assumption is widely known as smoothness priors of the Bayesian procedure), and they are estimated by the Kalman filer. Based on the estimated time varying VAR and linear quadratic dynamic programming, the dynamic instrument rules are derived in each period for achieving the targets. Our approach is convenient and effective for the practitioners in the central bank when they are unaware of the true model of the economy. However, it is not based on the theory of the economic agents who have rational expectations. In our empirical analyses, we show the effectiveness of our approach by applying it to the inflation targeting of the United Kingdom and the nominal growth rate targeting of Japan. Furthermore, we emphasize that the optimal monetary policy must be forecast-based because there exist lags of monetary policy. Our method realizes a forecast-based policy. Additionally, we find that the coefficients of time varying VAR change in response to the changes of monetary policy.

An Application to Nikkei-225 Futures and Some Simulation

We present an application of the SIML estimation. We used the high-frequency financial data of the Nikkei-225 Futures, which are the major financial products that are traded actively in Japan. We also give the simulation results of SIML estimation in the basic case and consider the hedging problem, which was the original motivation of developing the SIML method.

Extensions and Robust Estimation (1)

We investigate the asymptotic properties of the SIML estimator and the micro-market price-adjustment mechanisms in the process of forming the observed transaction prices. We also investigate the problem of volatility estimation in the round-off error model, which is a nonlinear transformation model of hidden stochastic process.

Local SIML Estimation of Brownian Functionals

We introduce the local SIML (LSIML) method for estimating some Brownian functionals including the asymptotic variance of the SIML estimator. It is an extension of the basic SIML method and we show the usefulness of the LSIML method through simulations.

The SIML Estimation of Volatility and Covariance with Micro-market Noise

We introduce the SIML method for estimating the integrated volatility and co-volatility (or covariance) parameters from a set of discrete observations. We first define the SIML estimator in the basic case and then give the asymptotic properties of the SIML estimator in more general cases.

Continuous-Time Models and Discrete Observations for Financial Data

We introduce continuous-time financial models and the stochastic processes of diffusions and jumps. This chapter reviews recent developments in mathematical finance and financial econometrics and then summarizes the basic financial problems that motivate the SIML estimation in this book.