Dynamic Arbitrage‐Free Asset Pricing with Proportional Transaction Costs

This paper studies multiperiod asset pricing theory in arbitrage‐free financial markets with proportional transaction costs. The mathematical formulation is based on a Euclidean space for weakly arbitrage‐free security markets and strongly arbitrage‐free security markets. We establish the weakly arbitrage‐free pricing theorem and the strongly arbitrage‐free pricing theorem.     

No Arbitrage in Discrete Time Under Portfolio Constraints

In frictionless securities markets, the characterization of the no-arbitrage condition by the existence of equivalent martingale measures in discrete time is known as the fundamental theorem of asset pricing. In the presence of convex constraints on the trading strategies, we extend this theorem under a closedness condition and a nondegeneracy assumption. We then provide connections with the superreplication problem solved in Föllmer and Kramkov (1997).     

Fundamental Theorems of Asset Pricing for Good Deal Bounds

We prove fundamental theorems of asset pricing for good deal bounds in incomplete markets. These theorems relate arbitrage-freedom and uniqueness of prices for over-the-counter derivatives to existence and uniqueness of a pricing kernel that is consistent with market prices and the acceptance set of good deals. They are proved using duality of convex optimization in locally convex linear topological spaces. The concepts investigated are closely related to convex and coherent risk measures, exact functionals, and coherent lower previsions in the theory of imprecise probabilities.     

隐性交易成本与资产定价——基于上证180指数成份股票交易数据的实证研究

文章利用上证180指数成份股票的高频数据计算隐性交易成本,探讨其与资产定价的关系。发现:(1)隐性交易成本与换手率、规模和收益率都存在着明显的线性负相关关系。在股票收益率下降时期,隐性交易成本通过流动性深度成本间接影响股票收益率。(2)较之隐性交易成本,规模因素与换手率因素对收益率的影响有着更好的测度性。很可能是因为这两个因素与流动性深度成本也有着显著相关性。(3)隐性交易成本与规模因素整体上呈线性负相关关系,分段上的关系则很可能是凹函数与凸函数的组合。     

Randomized Stopping Times and American Option Pricing with Transaction Costs

In a general discrete-time market model with proportional transaction costs, we derive new expectation representations of the range of arbitrage-free prices of an arbitrary American option. The upper bound of this range is called the upper hedging price, and is the smallest initial wealth needed to construct a self-financing portfolio whose value dominates the option payoff at all times. A surprising feature of our upper hedging price representation is that it requires the use of randomized stopping times (Baxter and Chacon 1977), just as ordinary stopping times are needed in the absence of transaction costs. We also represent the upper hedging price as the optimum value of a variety of optimization problems. Additionally, we show a two-player game where at Nash equilibrium the value to both players is the upper hedging price, and one of the players must in general choose a mixture of stopping times. We derive similar representations for the lower hedging price as well. Our results make use of strong duality in linear programming.     

An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs

Davis, Panas, and Zariphopoulou (1993) and Hodges and Neuberger (1989) have presented a very appealing model for pricing European options in the presence of rehedging transaction costs. In their papers the 'maximization of utility' leads to a hedging strategy and an option value. The latter is different from the Black–Scholes fair value and is given by the solution of a three–dimensional free boundary problem. This problem is computationally very time–consuming. In this paper we analyze this problem in the realistic case of small transaction costs, applying simple ideas of asymptotic analysis. The problem is then reduced to an inhomogeneous diffusion equation in only two independent variables, the asset price and time. The advantages of this approach are to increase the speed at which the optimal hedging strategy is calculated and to add insight generally. Indeed, we find a very simple analytical expression for the hedging strategy involving the option's gamma.     

A Fundamental Theorem of Asset Pricing for Large Financial Markets

We formulate the notion of “asymptotic free lunch” which is closely related to the condition “free lunch” of Kreps (1981) and allows us to state and prove a fairly general version of the fundamental theorem of asset pricing in the context of a large financial market as introduced by Kabanov and Kramkov (1994). In a large financial market one considers a sequence (Sⁿ)_n=1^∞ of stochastic stock price processes based on a sequence (Ωⁿ, Fⁿ, (F_tⁿ)_t∈In, Pⁿ)_n=1^∞ of filtered probability spaces. Under the assumption that for all n∈ N there exists an equivalent sigma‐martingale measure for Sⁿ, we prove that there exists a bicontiguous sequence of equivalent sigma‐martingale measures if and only if there is no asymptotic free lunch (Theorem 1.1). Moreover we present an example showing that it is not possible to improve Theorem 1.1 by replacing “no asymptotic free lunch” by some weaker condition such as “no asymptotic free lunch with bounded” or “vanishing risk.”     

Cash Stream Valuation In the Face of Transaction Costs and Taxes

The usual notion of every future cash stream having a net present value determined from a single term structure breaks down when transaction costs are taken into account, especially the sizable costs associated with short-borrowing. the difficulties are compounded by taxes, which can lead to paradoxes of disequilibrium if elementary NPV is assumed to be a rational basis for decision making. This paper systematically develops a theory of valuation which overcomes these shortcomings by accepting the multiplicity of no-arbitrage term structures that may be present for each tax class of investors, and uses the entire set of them to impute both a "long price" and a "short price" for every cash stream, regardless of the sign of the future payments. the valuation operators giving these prices are nonlinear but readily calculated from linear programming formulas.     

NO‐ARBITRAGE PRICING FOR DIVIDEND‐PAYING SECURITIES IN DISCRETE‐TIME MARKETS WITH TRANSACTION COSTS

We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete‐time markets with dividend‐paying securities. Specifically, we show that the no‐arbitrage condition under the efficient friction assumption is equivalent to the existence of a risk‐neutral measure. We derive dual representations for the superhedging ask and subhedging bid price processes of a contingent claim contract. Our results are illustrated with a vanilla credit default swap contract.     

Bounds on Derivative Prices in an Intertemporal Setting with Proportional Transaction Costs and Multiple Securities

The observed discrepancies of derivative prices from their theoretical, arbitrage-free values are examined in the presence of transaction costs. Analytic upper and lower bounds on the reservation write and purchase prices, respectively, are obtained when an investor's preferences exhibit constant relative risk aversion between zero and one. The economy consists of multiple primary securities with stationary returns, a constant rate of interest, and any number of American or European derivatives with, possibly, path-dependent arbitrary payoffs.     

Robust martingale selection problem and its connections to the no‐arbitrage theory

We analyze the martingale selection problem of Rokhlin in a pointwise (robust) setting. We derive conditions for solvability of this problem and show how it is related to the classical no‐arbitrage deliberations. We obtain versions of the Fundamental Theorem of Asset Pricing in models spanning frictionless markets, models with proportional transaction costs, and models for illiquid markets. In all these models, we also incorporate trading constraints.     

Hedging under Transaction Costs in Currency Markets: a Continuous‐Time Model

We consider a general semimartingale model of a currency market with transaction costs. Assuming that the price process is continuous and the solvency cone is proper we prove a hedging theorem describing the set of initial endowments that allows the investor to hedge a contingent claim in various currencies by a self‐financing portfolio.     

家族涉入、网络结构与家族企业的网络交易成本

文章利用浙江和重庆两地制造业家族企业的调查数据,实证检验了家族涉入对家族企业降低网络交易成本的影响及网络结构的中介效应,研究结果表明：（1）家族所有权、家族承诺对家族企业降低网络交易成本有显著的正向影响,领导企业的家族代数对家族企业降低网络交易成本有显著的负向影响;（2）网络中心度和密度在家族承诺与降低网络交易成本之间起部分中介作用。本文的研究结论对于提高我国家族企业网络组织效率具有一定的现实意义。