A Remark on a Singular Perturbation Method for Option Pricing Under a Stochastic Volatility Model

This paper studies the approximation accuracy of a singular perturbation method for option pricing up to the second order under a stochastic volatility model. First, numerical experiments confirm that the first order approximation provides sufficiently accurate option prices in a fast mean-reversion volatility case. On the other hand, it creates relatively large errors in a non-fast mean-reversion volatility environment. Then, the second order approximation formula is derived and the improvement of the approximation is investigated.     

Capital Movements, Intersectoral Resource Shifts, and the Trade Balance with Recursive Preferences

This paper examines interactions between internal resource shifts and the external balance. It sets up a simple infinite-period model with recursive preferences. It shows simple patterns between capital movements and trade balances and clarifies the resource shifts between traded goods and nontraded goods sectors when world interest rate changes and government spending changes are taking place.     

Corporate bankruptcy prediction in Japan

The purpose of this study is to highlight the financial characteristics of failed firms in Japan, and to construct corporate bankruptcy prediction models with greater prediction accuracy. Our principal component analysis indicated that failed firms in Japan could be classified into two groups: a group having negative financial structures and a group having a declining flow of funds. Additionally, they can be classified into two other different categories of groups: one whose financial position during three years before shows a ‘V’ shape and another group that shows a ‘XXX’ shape.Our discriminant analysis indicated that improved prediction accuracy could be obtained by using, as predictor variables, both ratios and absolute amounts based on cash base financial statement data three years before failure. This data was adjusted to properly reflect the exceptions, reservations, and qualifications appearing in the audit reports and those based on accrual base financial statement data.     

The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims

We propose a new methodology for the valuation problem of financial contingent claims when the underlying asset prices follow a general class of continuous Itô processes. Our method can be applied to a wide range of valuation problems including complicated contingent claims associated with the term structure of interest rates. We illustrate our method by giving two examples: the valuation problems of swaptions and average (Asian) options for interest rates. Our method gives some explicit formulas for solutions, which are sufficiently numerically accurate for practical purposes in most cases. The continuous stochastic processes for spot interest rates and forward interest rates are not necessarily Markovian nor diffusion processes in the usual sense; nevertheless our approach can be rigorously justified by the Malliavin–Watanabe Calculus in stochastic analysis.