Ryozo Miura

Decomposition of Japanese Yen Interest Rate Data Through Local Regression

Seven different Japanese Yen interest rates recorded on a daily basis for the period from 1986 to 1992 are simultaneously analyzed. By introducing a new concept of ‘short term trend’, we decompose each interest rate series into three components, ‘long termtrend’, ‘short term trend’ and ‘irregular’. It is obtained by a two step lowess smoothing technique. After that, a multivariate autoregressive model (MAR) is fitted to the vector valued time series obtained by combining those seven irregular components. The decomposition and MAR model fitting were quite satisfactory. It enables us to understand well various aspects of interest rate series from the trends, the MAR (2) coefficients and its residuals. The result is compared with the decomposition through sabl and the advantages of our procedure will be demonstrated in relations to other parametric model fitting like ARCH or GARCH. Based on the decomposition we can have better daily prediction and more stable long term forecasting.

A note on statistical models for individual hedge fund returns

In recent years, a large number of research papers and monographs on the analysis of hedge fund returns have been published. Typically, the authors of these studies implicitly or explicitly treat monthly returns of hedge funds as independent and identically distributed observations. The Hedge Fund Index might be able to serve that role. But the returns of an individual hedge fund are not like that. They behave autoregressively depending on the time periods. This stochastic behavior should be modeled as a combined/regime switching stochastic process of two processes: i.i.d. process and autoregressive process. This paper first depicts the autoregressiveness of hedge fund returns. Then we introduce our statistical model for returns of an individual hedge fund and then, with our retrospective view, we perform several data analyses for individual hedge funds’ return data.

Statistical Methodologies for the Market Risk Measurement

This paper classifies statistical methodologies available for the marketrisk measurement. With the help of the weighted likelihood, a broad class ofnon-normal distributions, which are not generally considered so far, areapplied to possibly hetero-scedastic financial variables. The approach is compared with popular procedures such as GARCH and J. P. Morgans using daily dataof 12 financial variables.

On the asymptotic normality of the R-estimators of the slope parameters of simple linear regression models with associated errors

ABSTRACT The purpose of this paper is to prove, under mild conditions, the asymptotic normality of the rank estimator of the slope parameter of a simple linear regression model with stationary associated errors. This result follows from a uniform linearity property for linear rank statistics that we establish under general conditions on the dependence of the errors. We prove also a tightness criterion for weighted empirical process constructed from associated triangular arrays. This criterion is needed for the proofs which are based on that of Koul [Behavior of robust estimators in the regression model with dependent errors. Ann Stat. 1977;5(4):681–699] and of Louhichi [Louhichi S. Weak convergence for empirical processes of associated sequences. Ann Inst Henri Poincaré Probabilités Statist. 2000;36(5):547–567].

Credit Risk Modeling with Delayed Information

We introduce a notion of market times that are stochastic processes in order to represent information delay in structural credit risk models. The market times are extensions of the time change process introduced by Guo, Jarrow and Zeng in the sense that each component of the market time is not required to be a stopping time. We introduce a class of market times called idempotent market times that contain natural examples including market times driven by Poisson processes. We show that any idempotent market time is hard to be a model of the time change process. We define a filtration modulated by the market time and show that it is an extension of the continuously delayed filtration that is the filtration modulated by the time change process. We show that the conditional expectations given market filtrations have some Markov property in a binomial setting, which is useful for pricing defaultable financial instruments.

The distribution of continuous time rank processes

In this paper, we will give exact calculations of probability disrtributions of continuous rank processes in Brownian case, Brownian motion with drift case, Pinned Brownian motion case. These calculations are based on the results of the joint distributions of Brownian motion and its soujourn time. Also we give new exotic options using rank statistics and calculate the price of rank options.