Additional utility of insiders with imperfect dynamical information

In this paper we consider a market driven by a Wiener process where there is an insider and a regular trader. The insider has privileged information which has been deformed by an independent noise vanishing as the revelation time approaches. At this time, the information of every trader is the same. We obtain the semimartingale decomposition of the original Wiener process under dynamical enlargement of the filtration, and we prove that if the rate at which the additional noise in the insiders information vanishes is slow enough then there is no arbitrage and the additional utility of the insider is finite.Received: 1 October 2003, Mathematics Subject Classification: 60G48, 90A09, 60H07, 90A60JEL Classification: D82, G11, G14     

Asymptotic analysis for optimal investment and consumption with transaction costs

We consider an agent who invests in a stock and a money market and consumes in order to maximize the utility of consumption over an infinite planning horizon in the presence of a proportional transaction cost . The utility function is of the form U(c) = c^1-p/(1-p) for p > 0, . We provide a heuristic and a rigorous derivation of the asymptotic expansion of the value function in powers of , and we also obtain asymptotic results on the boundary of the no-trade region.Received: July 2003, Mathematics Subject Classification (1991): 90A09, 60H30, 60G44JEL Classification: G13Work supported by the National Science Foundation under grants DMS-0103814 and DMS-0139911.     

On a Simple Econometric Approach for Utility-Based Asset Pricing Model

The Journal of Finance has published an important paper entitled A Simple Econometric Approach for Utility-Based Asset Pricing Model by Brown and Gibbon (1985). The main purpose of this paper is to extend the research of Brown and Gibbons (1985) and Karson, Cheng and Lee (1995) in estimating the relative risk aversion (RRA) parameter in utility-based asset pricing model. First, we review the distributions of RRA parameter estimate . Then, a new method to the distribution of is derived, and a Bayesian approach for the inference of is proposed. Finally, empirical results are presented by using market rate of return and riskless rate data during the period December 1925 through December 2001.     

Computing a Multivariate Normal Integral for Valuing Compound Real Options

We extend the Geske (1979) model to a multivariate normal integral for the valuation of a compound real option. We compared the computing speeds and errors of three numerical integration methods, namely, Drezner's improved Gauss quadrature method, Monte Carlo method and Lattice method, together with appropriate critical value finding methods. It is found that secant method for finding critical values combined with Lattice method and run by Fortran took merely one second, Monte Carlo method 120 seconds. It is also found that the real option decreases with interest rate, not necessarily positively correlated with volatility , a result different from that anticipated under financial option theory. This is mainly because the underlying of real option is a non-traded asset, which brings dividend-like yield into the formula of compound real options. Dividend-like yield rises with the multiplication of correlation coefficient and . High indicates the poor diversification advantage of the new investment project in relation to the existing market portfolio, and the value of real call option decreases with . Conversely, when is low, the proposed project provides better diversification advantage and the real call option rises with . Irrespective of the value of , when interest rate increases, the value of real call option drops, especially when is high, the value of the project is dominated by interest rate.     

Banks as Interest Rate Managers

Most banks have a two-tier pricing system, offering accounts at market-related interest rates and at posted rates that are changed at discrete intervals. In this paper, I develop a model of bank interest rate management. I consider a bank with two classes of loans and deposits in its balance sheet: One pays a market rate of interest, the other a posted rate. Market rates are exogenous and evolve stochastically over time. Posted rates are altered intermittently by the bank itself. The bank faces imperfect arbitrage by its customers between posted and market rate funds. Under simple assumptions about the stochastic process governing the market rate, I derive optimal decision rules for the adjustment of the posted rate and determine conditions under which these rules are asymmetric. A key prediction of the model is a negative correlation between market loan rates and the gap; this is more consistent with the behavior of British banks than is the contrary prediction of more standard models.     

Liquidity risk and arbitrage pricing theory

Classical theories of financial markets assume an infinitely liquid market and that all traders act as price takers. This theory is a good approximation for highly liquid stocks, although even there it does not apply well for large traders or for modelling transaction costs. We extend the classical approach by formulating a new model that takes into account illiquidities. Our approach hypothesizes a stochastic supply curve for a securitys price as a function of trade size. This leads to a new definition of a self-financing trading strategy, additional restrictions on hedging strategies, and some interesting mathematical issues.Received: 1 November 2003, Mathematics Subject Classification: 60G44, 60H05, 90A09JEL Classification: G11, G12, G13Umut Çetin: This work was performed while Dr. Çetin was at the Center for Applied Mathematics, Cornell UniversityPhilip Protter: Supported in part by NSF grant DMS-0202958 and NSA grant MDA-904-03-1-0092 The authors wish to thank M. Warachka and Kiseop Lee for helpful comments, as well as the anonymous referee and Associate Editor for numerous helpful suggestions, which have made this a much improved paper.     

Conduit Entities: Implications of Indirect Tax-Efficient Financing Structures for Real Investment

As well known, companies shift income from high to low tax jurisdictions. Typically, profit shifting is achieved by direct financing structures whereby companies use debt finance in the high tax entity and equity finance in the low tax entity. However, certain tax policies can lead to indirect financing structures whereby a conduit entity provides an opportunity to achieve at least two deductions for interest expenses for an investment made in the host country. The effect of direct and indirect financing structures on real investment is compared.     

The Pitfalls of International Integration: A Comment on the Bush Proposal and its Aftermath

In January 2003, the Bush Administration proposed a new system for taxing corporate dividends, under which domestic shareholders in U.S. corporations would not be taxed on dividends they received, provided the corporation distributed these dividends out of after-tax earnings (the Bush Proposal). The Bush Proposal was introduced in Congress on February 27, 2003. Ultimately, however, Congress balked at enacting full-fledged dividend exemption. Instead, in the Jobs and Growth Tax Relief Reconciliation Act of 2003 (JGTRRA) as enacted on May 28, 2003, a lower rate of 15% was adopted for dividends paid by domestic and certain foreign corporations,¹ and the capital gains rate was likewise reduced to 15%. Significantly and in stark contrast to the original Bush proposal, under JGTRRA the lower rate for dividends and capital gains does not depend on any tax being paid at the corporate level.This comment will focus primarily on the international aspects of both the Bush Proposal and JGTRRA. I will not lay out the proposal or the law in any detail. Instead, I will ask whether either the Bush Proposal or JGTRRA make sense from an economic efficiency perspective when the international implications are taken into account. I will leave to others the question of whether either the Bush Proposal or JGTRRA are sensible ways to stimulate the economy (for discussion of the effect of the 2001 tax cuts see Shapiro and Slemrod, 2001, 2002). I will also omit any discussion of the distributive effects of either the Bush Proposal or JGTRRA, which have been extensively discussed elsewhere (e.g., Tax Policy Center, 2003; Burman, Gale and Orszag, 2003).     

What is the Truth About the Scale of Japanese Banks' Bad Debts? Is the Situation Manageable?

In January 1998, the Japanese Ministry of Finance (MoF, 1998) released figures which suggested that the Japanese banking industry';s bad debts might be as high as ¥77 trillion (since revised upward to ¥87.5 trillion, if cooperative-type institutions are included; Financial Supervisory Agency (FSA), 1998). This compared with the previous official estimate of ¥28 trillion. The revelation was designed to do three things: (1) to convince investors, at home and abroad, who had long suspected that the true level of bad debts was much higher than the authorities (and the banks) were willing to admit to, that the authorities were sincere in their quest to enhance disclosure by local financial intermediaries; (2) to stifle opposition to the government's plans to use up to ¥30 trillion (since increased to ¥60 trillion) of public funds to stabilize the financial system¹ by underlining the gravity of the situation facing the Japanese economy; and (3) to pave the way for the introduction of more transparent reporting by the banks in April 1998 when a regime of prompt corrective action (PCA)² was scheduled to commence. This article explains the evolution of bad debt disclosure by the Japanese banking industry and assesses the significance of the latest figures. In particular, it highlights the extent to which accounting forbearance has been, and continues to be, used to mask the true level of the banks' bad debts and refutes the claim that the industry's bad debt burden peaked in 1995. The banking industry's ability to handle the continuing bad debt problem, in the face of a significant impairment of economic capital and the market's relentless drive for full disclosure and transparency, also is assessed.     

Diversified Portfolios in Continuous Time

We study a financial market containing an infinite number of assets, where each asset price is driven by an idiosyncratic random source as well as by a systematic noise term. Introducing asymptotic assets which correspond to certain infinitely well diversified portfolios we study absence of (asymptotic) arbitrage, and in this context we obtain continuous time extensions of atemporal APT results. We also study completeness and derivative pricing, showing that the possibility of forming infinitely well diversified portfolios has the property of completing the market. It also turns out that models where the all risk is of diffusion type are qualitatively quite different from models where one risk is of diffusion type and the other is of Poisson type. We also present a simple martingale based theory for absence of asymptotic arbitrage.