ARBITRAGE IN SECURITIES MARKETS WITH SHORT-SALES CONSTRAINTS

In this paper we derive the implications of the absence of arbitrage in securities markets models where traded securities are subject to short-sales constraints and where the borrowing and lending rates differ. We show that a securities price system is arbitrage free if and only if there exists a numeraire and an equivalent probability measure for which the normalized (by the numeraire) price processes of traded securities are supermartingales. Also, the tightest arbitrage bounds that can be inferred on the price of a contingent claim without knowing agents'preferences are equal to its largest and smallest expected normalized payoff with respect to the supermartingale measures. In the case where the underlying security price follows a diffusion process and where short selling is possible but costly, we derive partial differential equations that must be satisfied by the arbitrage bounds on derivative securities prices, and we determine optimal hedging strategies. We compute the arbitrage bounds on common securities numerically for several values of the borrowing and short-selling costs and show that they can be quite sharp.     

MODEL‐INDEPENDENT NO‐ARBITRAGE CONDITIONS ON AMERICAN PUT OPTIONS

We consider the pricing of American put options in a model‐independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market information by supposing that the prices of European options are known. In this setting, we are able to provide conditions on the American put prices which are necessary for the absence of arbitrage. Moreover, if we further assume that there are finitely many European and American options traded, then we are able to show that these conditions are also sufficient. To show sufficiency, we construct a model under which both American and European options are correctly priced at all strikes simultaneously. In particular, we need to carefully consider the optimal stopping strategy in the construction of our process.     

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.     

Arbitrage,cointegration, and the joint dynamics of prices across discrete commodity futures auctions

Underlying the search for arbitrage opportunities across commodity futures markets that differ in market structure is the idea that the futures prices for similar commodities that are traded on different exchanges adjusted for differences in currency, delivery time (if any), location, and market structure are equal. This article examines price linkages in competing discrete commodity futures auction markets. We find no evidence of cointegration of futures prices of similar commodities traded on two contemporaneous discrete auction futures exchanges in Asia. We also find no evidence of arbitrage activities across these two Asian exchanges, though this does not preclude arbitrage activities with North American continuous auction markets. This lack of cointegration may be due to nonstationarities in the trading cost component. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 799–815, 1999     

ON ARBITRAGE AND DUALITY UNDER MODEL UNCERTAINTY AND PORTFOLIO CONSTRAINTS

We consider the fundamental theorem of asset pricing (FTAP) and the hedging prices of options under nondominated model uncertainty and portfolio constraints in discrete time. We first show that no arbitrage holds if and only if there exists some family of probability measures such that any admissible portfolio value process is a local super‐martingale under these measures. We also get the nondominated optional decomposition with constraints. From this decomposition, we obtain the duality of the super‐hedging prices of European options, as well as the sub‐ and super‐hedging prices of American options. Finally, we get the FTAP and the duality of super‐hedging prices in a market where stocks are traded dynamically and options are traded statically.     

Integration and arbitrage in the Spanish financial markets: An empirical approach*

Several authors have introduced different ways to measure integration between financial markets. Most of them are derived from the basic assumptions about asset prices, like the Law of One Price or the absence of arbitrage opportunities. Two perfectly integrated markets must give identical prices to identical final payoffs, and a vector of positive discount factors, common to both markets, must exist. If these properties do not hold, the degree to which they are violated can be defined and considered as a measure of integration. The present paper empirically tests integration measures in the Spanish financial markets. Furthermore, the integration measures are operationalized to analyze the presence of cross‐market arbitrage without previously specifying the exact nature of the arbitrage strategy to be used. When the absence of arbitrage holds, several interesting variables are obtained, for instance, state prices or risk‐neutral probabilities. When this absence fails, explicit cross‐market arbitrage portfolios are provided. The results of the test yield some evidence about market efficiency and integration outside the United States, and they are surprising for several reasons. First of all, arbitrage opportunities do sometimes appear, and the bid–ask spread and transaction costs seem to be unable to prevent arbitrage profits. Furthermore, the criticisms that are usually raised when empirical papers show the existence of arbitrage opportunities do not apply here because we work with perfectly synchronized high frequency data. On the other hand, different integration measures show a similar evolution along the tested period, although these measures give different information about the markets’ efficiency and integration, and they do not necessarily have to be related. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 321–344, 2000     

THE MEANING OF MARKET EFFICIENCY

Fama defined an efficient market as one in which prices always “fully reflect” available information. This paper formalizes this definition and provides various characterizations relating to equilibrium models, profitable trading strategies, and equivalent martingale measures. These various characterizations facilitate new insights and theorems relating to efficient markets. In particular, we overcome a well‐known limitation in tests for market efficiency, i.e., the need to assume a particular equilibrium asset pricing model, called the joint‐hypothesis or bad‐model problem. Indeed, we show that an efficient market is completely characterized by the absence of both arbitrage opportunities and dominated securities, an insight that provides tests for efficiency that are devoid of the bad‐model problem. Other theorems useful for both the testing of market efficiency and the pricing of derivatives are also provided.     

Semi‐efficient valuations and put‐call parity

We propose an approach to the valuation of payoffs in general semimartingale models of financial markets where prices are nonnegative. Each asset price can hit 0; we only exclude that this ever happens simultaneously for all assets. We start from two simple, economically motivated axioms, namely, absence of arbitrage (in the sense of NUPBR) and absence of relative arbitrage among all buy‐and‐hold strategies (called static efficiency). A valuation process for a payoff is then called semi‐efficient consistent if the financial market enlarged by that process still satisfies this combination of properties. It turns out that this approach lies in the middle between the extremes of valuing by risk‐neutral expectation and valuing by absence of arbitrage alone. We show that this always yields put‐call parity, although put and call values themselves can be nonunique, even for complete markets. We provide general formulas for put and call values in complete markets and show that these are symmetric and that both contain three terms in general. We also show that our approach recovers all the put‐call parity respecting valuation formulas in the classic theory as special cases, and we explain when and how the different terms in the put and call valuation formulas disappear or simplify. Along the way, we also define and characterize completeness for general semimartingale financial markets and connect this to the classic theory.     

Optimal investment,derivative demand,and arbitrage under price impact

This paper studies the optimal investment problem with random endowment in an inventory‐based price impact model with competitive market makers. Our goal is to analyze how price impact affects optimal policies, as well as both pricing rules and demand schedules for contingent claims. For exponential market makers preferences, we establish two effects due to price impact: constrained trading and nonlinear hedging costs. To the former, wealth processes in the impact model are identified with those in a model without impact, but with constrained trading, where the (random) constraint set is generically neither closed nor convex. Regarding hedging, nonlinear hedging costs motivate the study of arbitrage free prices for the claim. We provide three such notions, which coincide in the frictionless case, but which dramatically differ in the presence of price impact. Additionally, we show arbitrage opportunities, should they arise from claim prices, can be exploited only for limited position sizes, and may be ignored if outweighed by hedging considerations. We also show that arbitrage‐inducing prices may arise endogenously in equilibrium, and that equilibrium positions are inversely proportional to the market makers' representative risk aversion. Therefore, large positions endogenously arise in the limit of either market maker risk neutrality, or a large number of market makers.     

Viability and Equilibrium in Securities Markets with Frictions

In this paper we study some foundational issues in the theory of asset pricing with market frictions. We model market frictions by letting the set of marketed contingent claims (the opportunity set) be a convex set, and the pricing rule at which these claims are available be convex. This is the reduced form of multiperiod securities price models incorporating a large class of market frictions. It is said to be viable as a model of economic equilibrium if there exist price-taking maximizing agents who are happy with their initial endowment, given the opportunity set, and hence for whom supply equals demand. This is equivalent to the existence of a positive lineaar pricing rule on the entirespace of contingent claims—an underlying frictionless linear pricing rule—that lies below the convex pricing rule on the set of marketed claims. This is also equivalent to the absence of asymptotic free lunches—a generalization of opportunities of arbitrage. When a market for a nonmarketed contingent claim opens, a bid-ask price pair for this claim is said to be consistent if it is a bid-ask price pair in at least a viable economy with this extended opportunity set. If the set of marketed contingent claims is a convex cone and the pricing rule is convex and sublinear, we show that the set of consistent prices of a claim is a closed interval and is equal (up to its boundary) to the set of its prices for all the underlying frictionless pricing rules. We also show that there exists a unique extended consistent sublinear pricing rule—the supremum of the underlying frictionless linear pricing rules—for which the original equilibrium does not collapse when a new market opens, regardless of preferences and endowments. If the opportunity set is the reduced form of a multiperiod securities market model, we study the closedness of the interval of prices of a contingent claim for the underlying frictionless pricing rules.     

ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS

We develop a theory of robust pricing and hedging of a weighted variance swap given market prices for a finite number of co‐maturing put options. We assume the put option prices do not admit arbitrage and deduce no‐arbitrage bounds on the weighted variance swap along with super‐ and sub‐replicating strategies that enforce them. We find that market quotes for variance swaps are surprisingly close to the model‐free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi‐infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model‐independent and probability‐free setup. In particular, we use and extend Föllmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the “log contract” and similar connections for weighted variance swaps. Our results take the form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk‐neutral expectations of discounted payoffs.     

Lower‐boundary violations and market efficiency: Evidence from the German DAX‐index options market

The informational efficiency of the market for options on the German stock index DAX is examined using intraday transactions data. Problems of previous studies on options‐market efficiency, arising from dividend estimation and the early‐exercise effect, are avoided, because the DAX is a performance index and DAX options are European options. Ex‐post and ex‐ante tests are carried out to simulate trading strategies that exploit irrational lower‐boundary violations of observed option prices. Because the lower‐boundary conditions are solely based on arbitrage considerations, the test results do not depend on the assumption that investors use a particular option‐pricing model. The investigation shows that ex‐post profits are, in general, dramatically reduced when the execution of arbitrage strategies is delayed and/or transaction costs are accounted for. However, arbitrage restrictions, which rely on short selling of the component stocks of the index, tend to be violated more often and with higher persistence. An analysis of consecutive subsamples suggests that, over time, traders have been subjected to a learning process when pricing this relatively new instrument. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20: 405–424, 2000     

ARBITRAGE AND INFORMATION IN A SEQUENTIAL ECONOMY WITH MANY CREDIT AGENCIES

This paper augments the theoretical foundations of organized commodity futures markets and uncovers singular facts about arbitrage and the role of information. Using the term "credit agency" to embrace organized futures markets such as the Chicago Board of Trade as well as independent brokerage houses, we extend the extant theory of temporary equilibrium for an economy with a single credit agency to economies with many credit agencies. In the process, we find that arbitrage with no risk of bankruptcy and with perfect interagency trade information can be incompatible with equilibrium (exact or approximate). On the other hand, the usual regularity assumptions are sufficient for the existence of at least an approximate equilibrium, provided that interagency trade information is imperfect (or risky). However, such imperfect information limits arbitrage so different agencies can have different prices.     

Pricing, price dispersion, and information: The discount brokerage industry

The paper provides an empirical analysis of the pricing behavior of firms within the discount brokerage industry, with emphasis on testing the role of costly information in affecting prices. Several empirical tests are performed that indicate that prices in this industry respond in ways hypothesized by theoretical models of markets operating under conditions of imperfect information. The industry is characterized by a wide degree of price dispersion that does not appear to simply reflect quality differences among firms. In addition, the variance of prices across geographic markets is associated with variables that theoretically should affect the levels of consumer information in those markets.     

PRICE‐ADMISSIBILITY CONDITIONS FOR ARBITRAGE‐FREE LINEAR PRICE FUNCTION MODELS FOR THE TERM STRUCTURE OF INTEREST RATES

To assure price admissibility—that all bond prices, yields, and forward rates remain positive—we show how to control the state variables within the class of arbitrage‐free linear price function models for the evolution of interest rate yield curves over time. Price admissibility is necessary to preclude cash‐and‐carry arbitrage, a market imperfection that can happen even with a risk‐neutral diffusion process and positive bond prices. We assure price admissibility by (i) defining the state variables to be scaled partial sums of weighted coefficients of the exponential terms in the bond pricing function, (ii) identifying a simplex within which these state variables remain price admissible, and (iii) choosing a general functional form for the diffusion that selectively diminishes near the simplex boundary. By assuring that prices, yields, and forward rates remain positive with tractable diffusions for the physical and risk‐neutral measures, an obstacle is removed from the wider acceptance of interest rate methods that are linear in prices.     

OPTIMAL INVESTMENT WITH AN UNBOUNDED RANDOM ENDOWMENT AND UTILITY-BASED PRICING

This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies—those strategies whose wealth process is a super-martingale under all pricing measures with finite relative entropy. We give necessary and sufficient conditions for the absence of utility-based arbitrage, and for the existence of a solution to the primal problem. We consider two utility-based methods which can be used to price contingent claims. Firstly we investigate marginal utility-based price processes (MUBPP's). We show that such processes can be characterized as local martingales under the normalized optimal dual measure for the utility maximizing investor. Finally, we present some new results on utility indifference prices, including continuity properties and volume asymptotics for the case of a general utility function, unbounded endowment and unbounded contingent claims.     

SPARSE CALIBRATIONS OF CONTINGENT CLAIMS

The two problems of determining the existence of arbitrage among a finite set of options and of calculating the supremum price of an option consistent with other options prices have been reduced to finding an appropriate model of bounded size in many special cases. We generalize this result to a class of arbitrage-free  m -period markets with    d  + 1   basic securities and with no prior measure. We show there are no dominating trading strategies for a given set of  l  contingent claims if and only if their bid-ask prices are asymptotically consistent with models supported by at most   ( l  +  d  + 1)( d  + 1) ^{m −1}   points, if    m  ≥ 1  . An example showing the tightness of our bound is given.     

Pricing efficiency of the S&P 500 index market: Evidence from the Standard & Poor's Depositary Receipts

Standard & Poor's Depositary Receipts (SPDRs) are exchange traded securities representing a portfolio of S&P 500 stocks. They allow investors to track the spot portfolio and better engage in index arbitrage. We tested the impact of the introduction of SPDRs on the efficiency of the S&P 500 index market. Ex‐post pricing efficiency and ex‐ante arbitrage profit between SPDRs and futures were also examined. We found an improved efficiency in the S&P 500 index market after the start of SPDRs trading. Specifically, the frequency and length of lower boundary violations have declined since SPDRs began trading. This result is consistent with the hypothesis that SPDRs facilitate short arbitrage by simplifying the process of shorting the cash index against futures. Tests of pricing efficiency comparing SPDRs and futures suggested that index arbitrage using SPDRs as a substitute for program trading in general results in losses. Although short arbitrages earn a small profit on average, gains are statistically insignificant. A trade‐by‐trade investigation showed that prices are instantaneously corrected after the presence of mispricing signals, introducing substantial risk in arbitraging. Evidence in general supported pricing efficiency between SPDRs and the S&P 500 index futures—both ex‐post and ex‐ante. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:877–900, 2002     

Optimal No‐Arbitrage Bounds on S&P 500 Index Options and the Volatility Smile

This article shows that the volatility smile is not necessarily inconsistent with the Black–Scholes analysis. Specifically, when transaction costs are present, the absence of arbitrage opportunities does not dictate that there exists a unique price for an option. Rather, there exists a range of prices within which the option's price may fall and still be consistent with the Black–Scholes arbitrage pricing argument. This article uses a linear program (LP) cast in a binomial framework to determine the smallest possible range of prices for Standard & Poor's 500 Index options that are consistent with no arbitrage in the presence of transaction costs. The LP method employs dynamic trading in the underlying and risk‐free assets as well as fixed positions in other options that trade on the same underlying security. One‐way transaction‐cost levels on the index, inclusive of the bid–ask spread, would have to be below six basis points for deviations from Black–Scholes pricing to present an arbitrage opportunity. Monte Carlo simulations are employed to assess the hedging error induced with a 12‐period binomial model to approximate a continuous‐time geometric Brownian motion. Once the risk caused by the hedging error is accounted for, transaction costs have to be well below three basis points for the arbitrage opportunity to be profitable two times out of five. This analysis indicates that market prices that deviate from those given by a constant‐volatility option model, such as the Black–Scholes model, can be consistent with the absence of arbitrage in the presence of transaction costs. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:1151–1179, 2001     

Export prices,selection into exporting and market size: Evidence from China and India

This paper empirically analyses the export pricing behaviour of Chinese and Indian exporters when there is selection into exporting. Previous exchange rate pass-through estimates that did not take selection into account could be biased if selection into exporting is correlated with pricing strategy. We use 6-digit product-level data across high- and low-income export destinations over the period 1994–2007 and assess a number of determinants of the degree of pass-through of exchange rates to export prices, such as the level of external demand, exporter’s wage cost, degree of competition in export markets, currency volatility and the direction of currency movements. We find systematic differences in the pricing strategies of Chinese and Indian exporters while uncovering a selection bias in exports to high-income markets, although the pricing of exports to low-income markets is independent of the decision to export. Export prices do not increase systematically with the destination market per capita income, and tend to be less sensitive in shipments to advanced nations. Export prices of India are sensitive to the volatility of the trade-weighted nominal effective exchange rate (NEER), indicating heterogeneity in prices to maintain competitiveness, but not in China as volatility is insignificant given a fixed currency system. It is also revealed that a country with a relatively flexible currency regime and arms-length trade such as India is more likely to exhibit incomplete pass-through, whereas a country with an inflexible currency system and involved in outward processing trade is more likely to have full pass-through as shown in the case of China.