The fundamental theorem of asset pricing, the hedging problem and maximal claims in financial markets with short sales prohibitions

This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuous-time financial models where asset prices are driven by nonnegative, locally bounded semimartingales. A key step in this proof is an extension of a well-known result of Ansel and Stricker. In the second part we study the hedging problem in these models and connect it to a properly defined property of "maximality" of contingent claims.Comment: Published in at http://dx.doi.org/10.1214/12-AAP914 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A non-arbitrage liquidity model with observable parameters for derivatives

We develop a parameterised model for liquidity effects arising from the trading in an asset. Liquidity is defined via a combination of a trader's individual transaction cost and a price slippage impact, which is felt by all market participants. The chosen definition allows liquidity to be observable in a centralised order-book of an asset as is usually provided in most non-specialist exchanges. The discrete-time version of the model is based on the CRR binomial tree and in the appropriate continuous-time limits we derive various nonlinear partial differential equations. Both versions can be directly applied to the pricing and hedging of options; the nonlinear nature of liquidity leads to natural bid-ask spreads that are based on the liquidity of the market for the underlying and the existence of (super-)replication strategies. We test and calibrate our model set-up empirically with high-frequency data of German blue chips and discuss further extensions to the model, including stochastic liquidity

Superhedging in illiquid markets

We study contingent claims in a discrete-time market model where trading costs are given by convex functions and portfolios are constrained by convex sets. In addition to classical frictionless markets and markets with transaction costs or bid-ask spreads, our framework covers markets with nonlinear illiquidity effects for large instantaneous trades. We derive dual characterizations of superhedging conditions for contingent claim processes in a market without a cash account. The characterizations are given in terms of stochastic discount factors that correspond to martingale densities in a market with a cash account. The dual representations are valid under a topological condition and a weak consistency condition reminiscent of the ``law of one price'', both of which are implied by the no arbitrage condition in the case of classical perfectly liquid market models. We give alternative sufficient conditions that apply to market models with nonlinear cost functions and portfolio constraints

Can Cross-Border Financial Markets Create Endogenously Good Collateral in a Crisis?

In this paper, we explore whether markets can create endogenously good collateral in a crisis by analyzing a simple exchange economy where a country-specific catastrophic shock is shared between two countries. To see this possibility, we examine whether the equilibrium achieved by the time-0 complete markets with solvency constraints can be recovered in the dynamically complete markets with collateral constraints. This paper demonstrates that it is possible to recover the time-0 equilibrium outcome in a sequential manner when pricing errors occur randomly in evaluating Lucas trees at a catastrophic event. Such stochastic components may be interpreted as a policy initiative to create good collateral and yield constrained efficient outcomes at crisis periods.Solvency Constraints, Collateral Constraints, Dynamic Optimal Contract, Catastrophic Shocks

Valuations and dynamic convex risk measures

This paper approaches the definition and properties of dynamic convex risk measures through the notion of a family of concave valuation operators satisfying certain simple and credible axioms. Exploring these in the simplest context of a finite time set and finite sample space, we find natural risk-transfer and time-consistency properties for a firm seeking to spread its risk across a group of subsidiaries.Comment: 26 page

Distribution Risk and Equity Returns

In this paper we entertain the hypothesis that observed variations in income shares are the result of changes in the balance of power between workers and capital owners in labor relations. We show that this view implies that income share variations represent a risk factor of ¯rst-order importance for the owners of capital and, consequently, are a crucial determinant of the return to equity. When both risks are calibrated to observations, this distribution risk dominates in importance the usual systematic risk for the pricing of assets. We also show that distribution risks may originate in non-traded idiosyncratic income shocks.income shares; distribution risk; equity premium; limited market participation