The asymptotic expansion of the regular discretization error of Itô integrals

We study an Edgeworth‐type refinement of the central limit theorem for the discretization error of Itô integrals. Toward this end, we introduce a new approach, based on the anticipating Itô formula. This alternative technique allows us to compute explicitly the terms of the corresponding expansion formula. Two applications to finance are given; the asymptotics of discrete hedging error under the Black–Scholes model and the difference between continuously and discretely monitored variance swap payoffs under stochastic volatility models.     

CONVEX RISK MEASURES FOR GOOD DEAL BOUNDS

We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no‐arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized by several equivalent properties and in particular, we see that a convex risk measure is a good deal valuation only if it is given as a risk indifference price. An application to shortfall risk measure is given. In addition, we show that the no‐free‐lunch (NFL) condition is equivalent to the existence of a relevant convex risk measure, which is a good deal valuation. The relevance turns out to be a condition for a good deal valuation to be reasonable. Further, we investigate conditions under which any good deal valuation is relevant.     

Short-time at-the-money skew and rough fractional volatility

The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic expansion of the implied volatility as the time to maturity tends to zero. For this purpose, we introduce a new approach to validate such an expansion, which enables us to treat more general models than in the literature. The local-stochastic volatility model is treated as well under an essentially minimal regularity condition in order to show such a standard model cannot be dynamically consistent to the power law.     

EKC-type transitions and environmental policy under pollutant uncertainty and cost irreversibility

Previous studies have suggested that some pollutant levels first increases due to the economic growth and then start decreasing, the pattern being called the “environmental Kuznets curve” (EKC). We examine EKC-type transitions of pollutant levels not with respect to economic growth but more generally in time. Assuming that each policy maker optimally executes the two switching options of regulation and unregulation for pollution, the switching dynamics of environmental policy can be described by an alternating renewal process. It is shown that the double Laplace transform of transition density of a pollutant level can be obtained by a novel application of renewal theory. The expected level of overall pollutants is then calculated numerically and found to exhibit either a Λ‐shaped or an N-shaped pattern in time. Our results present a simple explanation for the EKC-type transitions of pollutant levels within a real options framework.     

Equilibrium pricing of contingent claims in tradable permit markets

We advance a model of the tradable permit market and derive a pricing formula for contingent claims traded in the market in a general equilibrium framework. It is shown that prices of such contingent claims exhibit significantly different properties from those in the ordinary financial markets. In particular, if the social cost function kinks at some level of abatement, the forward price, as well as the spot price, can be subject to the so‐called price spike. However, this price‐spike phenomenon can be weakened if a system of banking and borrowing is properly introduced. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:559–589, 2010     

Investment and capital structure decisions of foreign subsidiary with international debt shifting and exchange rate uncertainty

This paper examines the impact of international debt shifting and exchange rate uncertainty on investment and capital structure decisions of foreign subsidiary. We find that debt shifting induces earlier investment, earlier default, higher leverage, and larger ex ante firm value of foreign subsidiary. When debt shifting is not so costly, the optimal leverage of foreign subsidiary increases as the tax rate differential increases. Moreover, when the correlation between exchange rate and foreign cash flow uncertainties is positive (negative, respectively), foreign investment advances as exchange rate uncertainty increases (decreases) as well as the correlation increases. These results reveal that the impact of debt shifting and exchange rate uncertainty on investment and capital structure policies cannot be ignored, supporting existing empirical findings.     

On the Hoggard–Whalley–Wilmott Equation for the Pricing of Options with Transaction Costs

The Hoggard–Whalley–Wilmott equation is introduced to model portfolios of European type options incorporating transaction costs. The model gives rise to a nonlinear parabolic partial differential equation (PDE), whose nonlinearity reflects the presence of transaction costs. We show analytically the existence of solutions which are not necessarily convex nor concave. Numerical treatments are also given, which are devised to effectively handle an infinite domain and unbounded solutions.      

Japanese marketing in the post-bubble era

This article analyzes recent changes in marketing practices in Japan against the background of the recession and the high yen rate of the early 1990s. Based on direct observation, press reports, and interviews with experts, the study describes the changing situation in the Japanese market and shows how new opportunities for Western companies are opening up. The longer term implications of the home market changes for Japanese companies' competitiveness abroad are also discussed.     

A dynamic analysis of the differential incidence of capital and labour taxes in a two-class economy

This paper studies a differential incidence model, where a rise in a capital tax is accompanied by a change in a labour tax to hold constant the per capita government revenue, in a two-class growing economy. The major concern is to analyse the conditions necessary for the burden of such a tax substitution to fall solely, partially, or inconsequentially on capitalists or workers. The results obtained indicate that a higher rate of capital tax tends to impose a greater burden on workers.