Satisfying convex risk limits by trading

A random variable, representing the final position of a trading strategy, is deemed acceptable if under each of a variety of probability measures its expectation dominates a floor associated with the measure. The set of random variables representing pre-final positions from which it is possible to trade to final acceptability is characterized. In particular, the set of initial capitals from which one can trade to final acceptability is shown to be a closed half-line . Methods for computing are provided, and the application of these ideas to derivative security pricing is developed.Received: May 2004, Mathematics Subject Classification (2000): 91B30, 60H30, 60G44JEL Classification: G10Steven E. Shreve: Work supported by the National Science Foundation under grants DMS-0103814 and DMS-0139911.Reha Tütüncü: Work supported by National Science Foundation under grants CCR-9875559 and DMS-0139911.     

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.     

Pricing derivatives of American and game type in incomplete markets

In this paper the neutral valuation approach is applied to American and game options in incomplete markets. Neutral prices occur if investors are utility maximizers and if derivative supply and demand are balanced. Game contingent claims are derivative contracts that can be terminated by both counterparties at any time before expiration. They generalize American options where this right is limited to the buyer of the claim. It turns out that as in the complete case, the price process of American and game contingent claims corresponds to a Snell envelope or to the value of a Dynkin game, respectively.On the technical level, an important role is played by -sub- and -supermartingales. We characterize these processes in terms of semimartingale characteristics.Received: June 2003, Mathematics Subject Classification (2000):   91B24, 60G48, 91B16, 91A15, 60G40JEL Classification:   G13, D52, C73The authors want to thank PD Dr. Martin Beibel for the idea leading to the proof of Proposition A.4 and both anonymous referees for many valuable comments. The second author gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft through the Graduiertenkolleg Angewandte Algorithmische Mathematik at Munich University of Technology and by the Fonds zur Förderung der wissenschaftlichen Forschung at Vienna University of Technology.     

No arbitrage and closure results for trading cones with transaction costs

In this paper, we consider trading with proportional transaction costs as in Schachermayer’s paper (Schachermayer in Math. Finance 14:19–48, 2004). We give a necessary and sufficient condition for , the cone of claims attainable from zero endowment, to be closed. Then we show how to define a revised set of trading prices in such a way that, firstly, the corresponding cone of claims attainable for zero endowment, , does obey the fundamental theorem of asset pricing and, secondly, if is arbitrage-free then it is the closure of . We then conclude by showing how to represent claims.      

On irregular functionals of SDEs and the Euler scheme

We prove a sharp upper bound for the error $\mathbb {E}|g(X)-g(\hat{X})|^{p}We prove a sharp upper bound for the error in terms of moments of , where X and are random variables and the function g is a function of bounded variation. We apply the results to the approximation of a solution to a stochastic differential equation at time T by the Euler scheme, and show that the approximation of the payoff of the binary option has asymptotically sharp strong convergence rate 1/2. This has consequences for multilevel Monte Carlo methods. The author was supported by the Finnish Graduate School in Stochastics and Statistics, the Ellen and Artturi Nyyss?nen Foundation, and the Academy of Finland, project #110599.     

Robust utility maximization for complete and incomplete market models

We investigate the problem of maximizing the robust utility functional . We give the dual characterization for its solution for both a complete and an incomplete market model. To this end, we introduce the new notion of reverse f-projections and use techniques developed for f-divergences. This is a suitable tool to reduce the robust problem to the classical problem of utility maximization under a certain measure: the reverse f-projection. Furthermore, we give the dual characterization for a closely related problem, the minimization of expenditures given a minimum level of expected utility in a robust setting and for an incomplete market.Received: September 2004, Mathematics Subject Classification (2000): 62C20, 62O05, 91B16, 91B28JEL Classification: D81, G11I thank Hans Föllmer for his help when writing this paper. Furthermore, I thank Alexander Schied for discussing the topic with me and Michael Kupper and the referees for their helpful remarks.     

On the Validity of the Wiener Process Assumption in Option Pricing Models: Contradictory Evidence from Taiwan

This study tests the validity of the critical assumption underlying the option pricing model that the log form of the stock price movements follows the Wiener process, i.e., stock price movements follow a geometric Brownian motion. Using data compiled from the Taiwan Stock Exchange (TSE), this study's major empirical findings are as follows: first, the null hypothesis that the log of the stock prices is normally distributed is rejected; second, the null hypothesis that the stock price in log form has mean [ln P _s + (µ- ²)_t] and variance t is rejected; third, the null hypothesis that successive non-overlapping increments of the log of the stock price are independent from each other is also rejected. These empirical findings undermine the validity of the Wiener process assumption which is fundamental to many option pricing models.     

Efficient estimation of drift parameters in stochastic volatility models

We study the parametric problem of estimating the drift coefficient in a stochastic volatility model , where Y is a log price process and V the volatility process. Assuming that one can recover the volatility, precisely enough, from the observation of the price process, we construct an efficient estimator for the drift parameter of the diffusion V. As an application we present the efficient estimation based on the discrete sampling with δ _n →0 and n δ _n →∞. We show that our setup is general enough to cover the case of ‘microstructure noise’ for the price process as well.      

Weighted V@R and its Properties

The paper deals with the study of a coherent risk measure, which we call Weighted V@R. It is a risk measure of the form where μ is a probability measure on [0,1] and TV@R stands for Tail V@R. After investigating some basic properties of this risk measure, we apply the obtained results to the financial problems of pricing, optimization, and capital allocation. It turns out that, under some regularity conditions on μ, Weighted V@R possesses some nice properties that are not shared by Tail V@R. To put it briefly, Weighted V@R is “smoother” than Tail V@R. This allows one to say that Weighted V@R is one of the most important classes (or maybe the most important class) of coherent risk measures.     

A General Theorem on the Comparative Statics of Changes in Risk

In this paper, the concept of absolutely riskier than is introduced to generalize Gollier's (Journal of Economic Theory, 66, 522–535) necessary and sufficient conditions for the comparative statics of a change in risk for risk averters. The restrictive assumption that the payoff function is monotonic in the risk is relaxed. The policymaker's choice problem, the newsboy problem, and a farmer's example are used to illustrate how easily the monotonicity assumption is violated. Finally, some important properties of the concept of absolutely riskier than, such as its relation with the concept of second-order stochastic dominance, are illustrated using the farmer's example.     

The impact of settlement period on sales price

This study is an empirical investigation of the impact of settlement period on sales price while controlling for marketing period and standard explanatory variables. The hypothesized positive relationship between settlement period and sales price is confirmed by the results of this study. The estimated coefficient on settlement period is 0.0008 meaning that our market, on average, exacts a premium of 0.08 percent per day of settlement period beyond a norm of 60 days. The estimated coefficient on marketing period (a control variable) is –0.0003 meaning that our market, on average, requires a discount of 0.03 percent per day of marketing period. Our findings show the relative importance of settlement period in making real estate pricing decisions.     

Company Tax Structure and Company Tax Incidence

This paper reviews conflicting theories of company tax incidence impliedby the alternative new and traditional views of dividends andexamines their contrasting policy implications. Whereas, under thetraditional view, closer integration of the corporate and personalincome tax systems is suggested, an alternative policy orientationemphasizing the non-distorting features of the classical system is impliedby the new view. Even if the traditional view is accepted, theimplications for design and reform of the company tax vary widely underalternative specifications of domestic and international tax policy objectives. Schedular alternatives to global income taxation are alsoconsidered.     

The Impact of Taxing Unemployment Insurance Benefits on Unemployment Duration and Post-unemployment Earnings

In 1979, unemployment insurance benefits became taxableincome for recipients with income above a specified threshold.Further legislation in 1982 lowered the income threshold. Thispaper uses the Continuous Wage and Benefit History (CWBH) database to evaluate the effects of the 1982 change on the compensatedduration of unemployment and post-unemployment earnings. The1982 episode is a particularly useful natural experimentbecause the treatment group (those newly subject to benefittaxation) is the middle income category and the two controlgroups (those whose benefits were already taxed and those whosebenefits still were not taxed) are the high and low income categories.If the two control groups show similar trends in unemploymentduration (or post-unemployment earnings) and the treatment groupshows a strikingly different pattern, this is compelling evidenceof a tax effect. The empirical results suggest that taxing unemploymentbenefits reduced the affected workers' mean compensated durationby more than a week, but did not have a statistically significanteffect on their post-unemployment earnings.     

Parallel cartoons of fractal models of finance

Summary. Having been crafted to welcome a new scientific journal, this paper looks forward but requires no special prerequisite. The argument builds on a technical wrinkle (used earlier but explained here fully for the first time), namely, the authors grid-bound variant of Brownian motion B(t). While B(t) itself is additive, this variant is a multiplicative recursive process the author calls a cartoon. Reliance on this and related cartoons allows a new perspicuous exposition of the various fractal/multifractal models for the variation of financial prices. These illustrations do not claim to represent reality in its full detail, but suffice to imitate and bring out its principal features, namely, long tailedness, long dependence, and clustering. The goal is to convince the reader that the fractals/multifractals are not an exotic technical nightmare that could be avoided. In fact, the authors models arose successively as proper, natural, and even unavoidable generalization of the Brownian motion model of price variation. Considered within the context of those generalizations, the original Brownian comes out as very special and narrowly constricted, while the fractal/multifractal models come out as nearly as simple and parsimonious as the Brownian. The cartoons are stylized recursive variants of the authors fractal/multifractal models, which are even more versatile and realistic.This revised version was published online in January 2005 with corrections to the Cover date.     

Optimal Consumption Taxes and Social Security Under Tax Measurement Problems and Uncertainty

A representative individual lives for two periods; works when young and depends on savings and a government operated social security system when old—the returns on both sources of income, when old, are random. Due to administrative problems the returns to savings are observed with some measurement error. Two alternative consumption tax systems are considered; the Registered Asset Treatment (RAT) and the Non-Registered Asset Treatment (NRAT). The advantage of the RAT is that it can perform a social insurance role while the disadvantage is that it imposes measurement error risk. Correlation between the random return on saving and its measurement error can provide a risk-hedging role that can be further strengthened by the RAT version. The NRAT version neither provides social insurance nor imposes measurement error risk. Both tax systems hedge against the uncertainties in the social security system. The taxpayer engages in precautionary saving in response to future uncertainty.     

Bank lending ‘manias’ in theory and history

A popular view of banking crises sees them as consequences of prior bank lending manias. Such manias are supposed to be especially likely in legally unrestricted banking systems, where banks can issue notes and are not subject to statutory reserve requirements. Here it is argued that the bank lending mania hypothesis (1) exaggerates the role of subjective factors, including bankers' confidence or optimism, as a stimulus to bank lending, and (2) is not supported by evidence from past, legally unrestricted banking systems.