The author proposes a new method for estimating the volatility parameters of security prices, which is an improvement of the estimation method by M. Parkinson (1980). The author assumes that the security prices follow the geometric Brownian motion. However, contrary to the setting of Parkinson,...

We will generalize the Black-Scholes option pricing formula by incorporating stochastic interest rates. Although the existing literature has obtained some formulae for stock options under stochastic interest rates, the closed-form solutions have been known only under the Gaussian (Merton type)...

There have been large fluctuations observed in major macro-economic variables in Japan. When the official seasonal adjustment such as U.S. Census X-12-ARIMA is used, it has been important to make the change point analysis carefully. We illustrate the related problems by using recent official...

We propose a new parameter estimation procedure for the Levy processes and the class of infinitely divisible distribution. We shall show that the empirical likelihood method gives an easy way to estimate the key parameters of the infinitely divisible distributions including the class of stable...

In the recent X-12-ARIMA program developed by the United States Census Bureau for seasonal adjustments, the RegARIMA modeling has been extensively utilized. We shall discuss some problems in the RegARIMA modeling when the time series are realizations of non-stationary integrated stochastic...

Recently the various types of the equity-linked insurance have been introduced and actively traded in Japanese insurance markets. We investigate the basic problems of the actuarial risk management methods for those products based on the Markovian regime-switching time series model, which was...

We re-examine some statistical aspects of the task force report by Canadian Institute of Actuaries on the segregated fund investment guarantees. We argue that there can be non-trivial statistical problems involved for the equity-linked life insurances and investigate the statsitical properties...

This paper provides a general valuation method for the European options whose payoff is restricted by curved boundaries contractually set on the underlying asset price process when it follows the geometric Brownian motion. Our result is based on the generalization of the Levy formula on the...

Kunitomo and Takahashi (1995), and Takahashi (1997) have proposed a new methodology, called Small Disturbance Asymptotics, for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Ito processes. It can be applicable to a wide...