A Fuzzy Set Approach for Generalized CRR Model: An Empirical Analysis of S&;P 500 Index Options

This paper applies fuzzy set theory to the Cox, Ross and Rubinstein (CRR) model to set up the fuzzy binomial option pricing model (OPM). The model can provide reasonable ranges of option prices, which many investors can use it for arbitrage or hedge. Because of the CRR model can provide only theoretical reference values for a generalized CRR model in this article we use fuzzy volatility and fuzzy riskless interest rate to replace the corresponding crisp values. In the fuzzy binomial OPM, investors can correct their portfolio strategy according to the right and left value of triangular fuzzy number and they can interpret the optimal difference, according to their individual risk preferences. Finally, in this study an empirical analysis of S&P 500 index options is used to find that the fuzzy binomial OPM is much closer to the reality than the generalized CRR model.This project has been supported by NSC 93-2416-H-009-024.JEL Classification:     

Consumption Externality and Equilibrium Underinsurance

Relative consumption has been found to be crucial in many areas, such as asset pricing, the design of taxation, and economic growth. This article extends this line of research to the individual's insurance decision. We first define “keeping up with the Joneses” in the purchase of insurance and find that jealousy does not necessarily give rise to “keeping up with the Joneses.” We also identify several sufficient conditions that cause the optimal coverage in the private market to be less than the social optimum (equilibrium underinsurance). Jealousy is found to be neither a sufficient nor a necessary condition for equilibrium underinsurance. We further show that a social welfare maximizing government could adopt a tax system to correct for the consumption externality and make individuals better off.     

Hidden Overconfidence and Advantageous Selection

Theories of adverse selection and moral hazard predict the occurrence of the risk and the coverage of the insurance should be positively correlated, whereas empirical researches find little support of it. This paper provides a theoretical model of hidden overconfidence and demonstrates that a competitive insurance market may settle on separating equilibrium with advantageous selection predicting a negative relationship between risk and coverage. By assuming heterogeneity in risk perception and hidden action on self-protection, we find that, in equilibrium, the rational type of individual takes precautions to reduce the loss probability, whereas the overconfident type of individual will not make any effort. In the separating equilibrium, the insurer provides a product with high coverage to attract rational type of individual (low risk), and a product with low coverage for overconfident type of individual (high risk). In addition, other types of equilibrium such as adverse selection or linear premium rate are also found.     

Hedging Longevity Risk When Interest Rates are Uncertain

Abstract

This paper proposes an asset liability management strategy to hedge the aggregate risk of annuity providers under the assumption that both the interest rate and mortality rate are stochastic. We assume that annuity providers can invest in longevity bonds, long-term coupon bonds, and shortterm zero-coupon bonds to immunize themselves from the risks of the annuity for the equity holders subject to a required profit. We demonstrate that the optimal allocation strategy can lead to the lowest risk under different yield curves and mortality rate assumptions. The longevity bond can also be regarded as an effective hedging vehicle that significantly reduces the aggregate risk of the annuity providers.     

Who Obtains Greater Discounts on Automobile Insurance Premiums?

Insurance purchasers obtain varied discounts for insurance. This paper examines what drives these differences, specifically whether the loss probability and the wealth of the insured affect the size of the premium discount in automobile insurance. To describe a bargain between a client and an insurer over premiums and coverage, we first develop a sequential insurance bargaining game where the client has an outside option to bargain with another insurer. We find that the equilibrium involves full coverage and, based on the results of comparative statics, we propose hypotheses regarding the effects of the loss probability and the wealth of the insured on the size of the premium discount. We then use a unique data set of 85,806 observations of Taiwanese automobile liability insurance for property damage to empirically test the predictions. After controlling for underwriting and macroeconomic variables, we find that both (1) the insured with a lower claim probability (as a proxy for the insured with a lower loss probability) and (2) the insured with a higher salvage value car (as a proxy for the wealthier insured) receive a greater premium discount. These results support our theoretical results.     

Long-run purchasing power parity with asymmetric adjustment: Further evidence from nine transition countries

In this study, we applied a threshold cointegration test to investigate the properties of asymmetric adjustment on long-run purchasing power parity (PPP) in nine transition countries between January 1995 and December 2008. Although there was strong evidence of long-run PPP for these nine transition countries (i.e., Bulgaria, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, and Russia), the adjustment mechanism was asymmetric. These results have important policy implications for the nine transition countries included in the study.     

Mining the R&D innovation performance processes for high-tech firms based on rough set theory

The research and development (R&D) innovation of firms continues to be viewed as an important source of competitive advantage to academics and practitioners. To explore and extract the R&D innovation decision rules, it is important to understand how the R&D innovation rule-base works. However, many studies have not yet adequately induced and extracted the decision rule of R&D innovation and performance based on the characteristics and components of the original data rather than on post-determination models. The analysis of this study is grounded in the taxonomy of induction-related activities using a rough set theory approach or rule-based decision-making technique to infer R&D innovation decision rules and models linking R&D innovation to sales growth. The rules developed using rough set theory can be directly translated into a path-dependent flow network to infer decision paths and parameters. The flow network graph and cause-and-effect relationship of decision rules are heavily exploited in R&D innovation characteristics. In addition, an empirical case of R&D innovation performance will be illustrated to show that the rough sets model and the flow network graph are useful and efficient tools for building R&D innovation decision rules and providing predictions. We will then illustrate that integrating the flow network graph with rough set theory can fully reflect the characteristics of R&D innovation, and, through the established model, we can obtain a more reasonable result than with artificial influence.     

Inconsistencies Across Three Contextual Meanings of Reliability

The purpose of this article is to assess the nature of reliability and its inconsistent definitions across three contextual (conceptual, measurement and statistical) levels under the traditional true score theory. Due to such inconsistencies, two existing quantitative approaches (using r and covariance) are not uniformly understood in Psychology and other disciplines; consequently, their applications to measurements and testings are limited to ambiguous interpretations at the conceptual and measurement levels. To examine the extent of this problem, a questionnaire including various contextual definitions and interpretations of reliability in the literature was distributed in a nationwide survey. Results from six groups of experts representing editors, professors and advanced graduate students in both quantitative and clinical areas indicate that all subject groups generally agreed that a reliable instrument possesses the characteristics of the repeatability of responses of all test-takers at the conceptual level, and the reproducibility of the instrument with little or no variations from the underlying true scores at the measurement level. However, between the editors and noneditors, the endorsements of the common definition at the measurement level show obvious discrepancies. Further, at the statistical level, significant differences were found not only between but also within subject-groups in their interpretations of product-moment correlations and Alpha coefficients for the assessment of reliability at the conceptual and measurement levels. The causes of such inconsistencies were discussed in terms of the inherent limitations of the two statistical approaches used and their insufficiencies for indexing the conceptual and measurement meanings of reliability. Finally, this paper called for developing new statistical indices that are coherent with conceptual and measurement definitions. Before such development, the capacities of existing reliability indices shall be redefined and their application qualifications shall be proportionally re-established for educational, research and clinical purposes.     

Empirical Evidence for Advantageous Selection in the Commercial Fire Insurance Market

De Meza and Webb (2001) indicated that individuals with a higher degree of risk aversion would demand more insurance and invest in self-protection to reduce risk probability when both the preference type and investment in self-protection are hidden from insurers. They referred to the negative correlation between market insurance and risk type as advantageous selection. However, the relationship between risk type and the degree of risk aversion is debatable in both theoretical and empirical research. This paper therefore proposes that advantageous selection could be supported from another angle by directly examining the relationships that exist among market insurance, self-protection, and risk probability. By focusing on the commercial fire insurance market, information on the purchase of market insurance, investment in self-protection, and fire accident records is hand-collected by means of a unique survey. It is found that firms purchasing market insurance have a greater tendency to channel efforts into self-protection. It is also found that firms expending effort on self-protection are less likely to suffer a fire accident. Furthermore, it is found that firms with commercial fire insurance have less chance of suffering a fire accident than those without such insurance. Each of the above three findings jointly supports the view that advantageous selection could play a critical role in the commercial fire insurance market.