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.     

On Level Curves of Value Functions in Optimization Models of Expected Utility

We study the level sets of value functions in expected utility stochastic optimization models. We consider optimal portfolio management models in complete markets with lognormally distributed prices as well as asset prices modeled as diffusion processes with nonlinear dynamics. Besides the complete market cases, we analyze models in markets with frictions like correlated nontraded assets and diffusion stochastic volatilities. We derive, for all the above models, equations that their level curves solve and we relate their evolution to power transformations of derivative prices. We also study models with proportional transaction costs in a finite horizon setting and we derive their level curve equation; the latter turns out to be a Variational Inequality with mixed gradient and obstacle constraints.     

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.     

Flight-to-liquidity: Evidence from China's stock market

In an order-driven and strictly regulated stock market, illiquidity risks' effects on asset pricing should be highlighted, particularly in such extreme market conditions as those in China. This paper utilizes panel data from China's stock market in an attempt to answer whether the illiquidity risk in various dimensions—including price impacts, the transaction speed, trading volume, transaction costs, and asymmetric information—can explain stock returns. We find that almost all dimensions of stock illiquidity are positively associated with excess stock returns. More importantly, smaller, less-liquid stocks suffer more liquidity costs, providing a strong evidence for “flight-to-liquidity.” Additionally, the transaction costs and asymmetric information, denoted by bid-ask spreads, robustly account for these illiquidity effects on stock pricing and differ from the findings in the U.S. market. We also find that the “flight-to-liquidity” can partially explain the idiosyncratic volatility puzzle, investors' gambling, and herding psychologies. This study provides substantial policy implications in regulation and portfolio management for emerging markets.     

Toward A Convergence Theory For Continuous Stochastic Securities Market Models1

This article reviews some recently developed approximation schemes for financial markets with continuous trading. Two methods for approximating continuous-time stochastic securities market models whose exogenously given prices have continuous sample paths are described and compared One method approximates both the paths and the information structure; the other is an approximation in distribution with a Markovian structure. In both cases, the approximating models have a finite state space, discrete time, and possess the same “structural” properties (e.g., “no arbitrage” and “completeness”) as the continuous model. the latter characteristic is an important criterion for judging the merits of the approximations. Taking advantage of the “structure-preserving” characteristic, one can formulate a convergence theory for frictionless markets with continuous trading. the theory provides convergence results for objects such as contingent claim prices, replicating portfolio strategies (hedging policies), optimal consumption policies, and cumulative financial gains (i.e., stochastic integrals), which are constructed along the approximation. the convergence theory enables one to combine the intuitive appeal of discrete models and the analytic tractability of continuous models to provide new insight into the theory of modern financial markets. We survey the current state of such a convergence theory and illustrate the results with some examples of well-known continuous securities market models.     

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.     

Illiquidity transmission from spot to futures markets

We develop a model of illiquidity transmission from spot to futures markets that formalizes the derivative hedge theory of Cho and Engle (1999). The model shows that spot market illiquidity does not translate one to one to the futures market but, rather, interacts with price risk, liquidity risk, and the risk aversion of the market maker. The model's predictions are tested empirically with data from the stock market and markets for single-stock futures and index futures. The results support our model and show that the derivative hedge theory provides an explanation for the liquidity link between spot and futures markets.     

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).     

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.     

UTILITY MAXIMIZATION IN AN INSIDER INFLUENCED MARKET

We study a controlled stochastic system whose state is described by a stochastic differential equation with anticipating coefficients. This setting is used to model markets where insiders have some influence on the dynamics of prices. We give a characterization theorem for the optimal logarithmic portfolio of an investor with a different information flow from that of the insider. We provide explicit results in the partial information case that we extend in order to incorporate the enlargement of filtration techniques for markets with insiders. Finally, we consider a market with an insider who influences the drift of the underlying price asset process. This example gives a situation where it makes a difference for a small agent to acknowledge the existence of an insider in the market.     

Consumption and Portfolio Policies With Incomplete Markets and Short-Sale Constraints: the Finite-Dimensional Case1

We use a martingale approach to study optimal intertemporal consumption and portfolio policies in a general discrete-time, discrete-state-space securities market with dynamically incomplete markets and short-sale constraints. We characterize the set of feasible consumption bundles as the budget-feasible set defined by constraints formed using the extreme points of the closure of the set of Arrow-Debreu state prices consistent with no arbitrage, and then establish a relationship between the original problem and a dual minimization problem.     

Long‐term information,short‐lived securities

The authors explore strategic trade in short‐lived securities by agents who have private information that is potentially long‐term, but do not know how long their information will remain private. Trading short‐lived securities is profitable only if enough of the private information becomes public prior to contract expiration; otherwise the security will worthlessly expire. How this results in trading behavior fundamentally different from that observed in standard models of informed trading in equity is highlighted. Specifically, it is shown that informed speculators are more reluctant to trade shorter‐term securities too far in advance of when their information will necessarily be made public, and that existing positions in a shorter‐term security make future purchases more attractive. Because informed speculators prefer longer‐term securities, this can make trading shorter‐term contracts more attractive for liquidity traders. The conditions are characterized under which liquidity traders choose to incur extra costs to roll over short‐term positions rather than trade in distant contracts, providing an explanation for why most longer‐term derivative security markets have little liquidity and large bid‐ask spreads. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:465–502, 2006     

Non‐Tradable Share Reform,Liquidity, and Stock Returns in China

This article studies the influence of the non‐tradable share reform in the cross‐section of stock returns in China. Prior research has generally neglected this important development in the Chinese stock market. We find that the firm‐specific illiquidity measures that reflect direct transaction costs, price impact and difficulties in trading immediacy, exhibit a positive and significant relationship with stock returns. These effects are particularly pronounced after the non‐tradable share reform. Furthermore, in the post‐reform era, portfolios with high illiquidity (i.e. high relative bid–ask spread, high Amihud illiquidity, low Amivest liquidity ratio) significantly outperform portfolios with low illiquidity, controlling for size, and book‐to‐market effects.     

Analyst forecasts and price discovery in futures markets: The case of natural gas storage

We investigate analyst forecasts in a unique setting, the natural gas storage market, and study the contribution of analysts in facilitating price discovery in futures markets. Using a high‐frequency database of analyst storage forecasts, we show that the market appears to condition expectations regarding a weekly storage release on the analyst forecasts and beyond that of various statistical‐based models. Further, we find that the market looks through the reported consensus analyst forecast and places differential emphasis on the individual forecasts of analysts according to their prior accuracy. Also, the market appears to place greater emphasis on analysts' long‐term accuracy than on their recent accuracy. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:451–477, 2009     

Is there an illiquidity premium in frontier markets?

We perform a comprehensive examination of the role of stock-level liquidity in the cross-section of frontier market stock returns. Using several popular liquidity measures and a battery of asset pricing tests, we investigate the illiquidity premium in 22 countries for the years 1991–2019. Contrary to typical relationships in developed and emerging markets, we find no evidence of illiquidity premium in frontier equities. Our findings support the hypothesis that for countries not fully integrated with the global economy, the diversification benefits offset the illiquidity, which, in turn, proves less important.     

PRICING AND HEDGING OF DERIVATIVES BASED ON NONTRADABLE UNDERLYINGS

This paper is concerned with the study of insurance related derivatives on financial markets that are based on nontradable underlyings, but are correlated with tradable assets. We calculate exponential utility‐based indifference prices, and corresponding derivative hedges. We use the fact that they can be represented in terms of solutions of forward‐backward stochastic differential equations (FBSDE) with quadratic growth generators. We derive the Markov property of such FBSDE and generalize results on the differentiability relative to the initial value of their forward components. In this case the optimal hedge can be represented by the price gradient multiplied with the correlation coefficient. This way we obtain a generalization of the classical “delta hedge” in complete markets.     

Ergodicity, State Prices, and Long Bond Returns

We present an analysis of price systems in securities markets with infinitely many time periods and infinitely many uncertain states of the world. A key result is that a Markov price system (MPS) has a unique representation in terms of the returns on a known set of bonds. The result implies that securities prices are the discounted value of dividends, where discount factors are the reciprocal of the returns on a long-horizon discount bond.     

金融市场中的机构投资者行为研究

机构投资者作为金融市场中的主要参与者 ,是推进证券市场市场化的核心。成熟的资本市场经验表明 :资产管理机构化趋势越来越强 ,机构投资者的重要性不断增长。对于我国证券市场来说 ,超常规、创造性地培育和发展机构投资者是我国证券市场不断完善和深化、最终同国际化接轨的重要推动力量     

APPROXIMATE HEDGING PROBLEM WITH TRANSACTION COSTS IN STOCHASTIC VOLATILITY MARKETS

This paper studies the problem of option replication in general stochastic volatility markets with transaction costs, using a new specification for the volatility adjustment in Leland's algorithm. We prove several limit theorems for the normalized replication error of Leland's strategy, as well as that of the strategy suggested by Lépinette. The asymptotic results obtained not only generalize the existing results, but also enable us to fix the underhedging property pointed out by Kabanov and Safarian. We also discuss possible methods to improve the convergence rate and to reduce the option price inclusive of transaction costs.