A saddlepoint approximation to the distribution of the sum of independent non‐identically uniform random variables

Calculating the probability of the corresponding significance point is important for finite sample sizes. However, it is difficult to evaluate this probability when the sample sizes are moderate to large. Under these circumstances, consideration of a more accurate approximation for the distribution function is extremely important. Herein, we performed a saddlepoint approximation in the upper tails for the distribution of the sum of independent non‐identically uniform random variables under finite sample sizes. Saddlepoint approximation results were compared with those for a normal approximation. Additionally, the order of errors of the saddlepoint approximation was derived. © 2014 The Authors. Statistica Neerlandica © 2014 VVS.     

Inverse of the Berge maximum theorem

Summary We consider an inverse of the Berge maximum theorem. We also give an application of our result to fixed point theory.     

ON SURRENDER AND DEFAULT RISKS

This paper examines certain types of saving institutions or insurance companies that are subject to surrender and default risks, in a stochastic interest rate context. In the setting under study, investors are endowed with an option to surrender. The goal of the paper is to study how this option impacts the default risk of the issuing company and the value of the contracts it issues. Surrender risk has been extensively studied in arbitrated markets, using trees or least‐squares Monte Carlo methods for valuations, although practitioners often rely on econometric methods. We deal with surrender risk in a third way, assuming policyholders have sets of information and preferences that differ from those of financial market agents, but without relying on econometric methods. In particular, policyholders are supposed to be only partially rational (at least in the financial sense). This is done by modeling surrender risk through a Cox process correlated to the assets and interest rate dynamics. The paper provides formulas for the dynamics of the assets of the issuing firm (these dynamics drive the default time of the company), and for the valuation of liabilities and equity. A numerical illustration is provided.     

Empirical Study of Nikkei 225 Options with the Markov Switching GARCH Model

This paper investigates the pricing of Nikkei 225 Options using the Markov Switching GARCH (MSGARCH) model, and examines its practical usefulness in option markets. We assume that investors are risk-neutral and then compute option prices by using Monte Carlo simulation. The results reveal that, for call options, the MSGARCH model with Student’s t-distribution gives more accurate pricing results than GARCH models and the Black–Scholes model. However, this model does not have good performance for put options.     

Modeling of Contagious Credit Events and Risk Analysis of Credit Portfolios

We present a new model of the occurence of credit events such as rating changes and defaults for risk analyses of some portfolio credit derivatives. The framework of our model is based on a so-called top-down approach. Specifically, we first consider modeling the point process of each type of credit event in the whole economy using a self-exciting intensity process. Next, we characterize the point processes of credit events in the underlying sub-portfolio using random thinning processes specified by the distribution of credit ratings in the sub-portfolio. One of the main features of our model is that the model can capture credit risk contagion simultaneously among several credit portfolios. We present a credit event simulation algorithm based on our model and illustrate an application of the model to risk analyses of loan portfolios.     

Estimating Cost Functions of Malaysian Commercial Banks: The Differential Effects of Size,Location, and Ownership*

Bank integration and competition policies are a core part of current financial reforms intended to strengthen the financial sector in Malaysia. This paper intends to clarify the production technology employed in Malaysian banks and indicate important policy implications for current bank consolidation policy. While it is essential to conduct a microeconomic analysis of the banking sector to appraise financial reform policy, Katib and Mathews (2000) is the only formal study in this area that uses micro level data on Malaysian banks. Our analysis expands on Katib and Mathews’ study in three aspects. Firstly, while Katib and Mathews employed Data Envelopment Analysis, we use estimation analysis based on a parametric approach. Secondly, we examine technological differences among Malaysian banks according to the size of operations, location of branches and ownership structure. Thirdly, we also explicitly incorporate the existence of hidden bad loans in estimating cost functions. According to our estimation analysis, there is a difference in production technology between large‐sized banks and small or medium‐sized banks. While economies of scale are observed for large‐sized banks, no economies of scope and technological progress are observed for any banks. The results of our analysis suggest that, while the current reform policy is basically appropriate, serious problems remain regarding bank consolidation and the lack of market competition.     

A simple proof of K-K-M-S theorem

Summary We give a simple proof of the K-K-M-S theorem based on the Kakutani fixed point theorem, the separation theorem for convex sets and the Berge maximum theorem.The author is grateful to Gerard Debreu for his advice and to Tatsuro Ichiishi, Michael Todd, Rajiv Vohra, Nicholas Yannelis, Lin Zhou and two anonymous referees for their comments. The original version of this note was written in the fall 1992 while the author was visiting the Department of Economics, University of California at Berkeley.     

Analyses of Mortgage-Backed Securities Based on Unobservable Prepayment Cost Processes

We propose a prepayment model of mortgage based on a structural approach in order to analyze prepayment risk of mortgage-backed securities (MBS). We introduce a continuous process named prepayment cost process. Specifically, each mortgager's prepayment time is defined by the first time when her or his prepayment cost process falls below zero, but prepayment cost processes are supposed to be unobservable in the market. We also introduce a risk unique to each loan pool of mortgages, called a loan pool risk (LPR), and we regard LPR as a systematic risk other than interest rate. Using the model, we discuss the conditional distribution of prepayment times and a risk-neutral valuation of pass-through MBS. It is shown that each mortgager's conditional non-prepayment probability and the posterior distribution of LPR play quite important roles in our study.This research is partially supported by Grant-in-Aid for Young Scientists (B) No. 16710108 from the Ministry of Education, Culture, Sports, Science and Technology.     

Japan 2000

This article describes key determinants shaping Japanese society in the year 2000: population structure, education, social change, resources, the shift to an ‘information society’, Japan's economic and social model, and its relationships with neighbouring countries. A major theme is that Japan has indeed lost its postwar ‘model’.