Models for Bundle Trading in Financial Markets

Bundle trading is a new trend in financial markets that allows traders to submit consolidated orders to sell and buy packages of assets. We propose a new formulation for portfolio bundle trading that extends the previous models of the literature through a more detailed representation of portfolios and the formulation of new bidding requirements. We also present post-optimality tie-breaking procedures intended to discriminate equivalent orders on the basis of their submission times. Numerical results evaluate the "bundle" effect as well as the bidding flexibility and the computational complexity of our formulation. Une nouvelle tendance dans les marchés financiers consiste à transiger des valeurs financières sous forme d'ordres composites d'achat et de vente. Nous proposons une nouvelle formulation basée sur les ordres composites du problème d'allocation de valeurs financières. Notre modèle, comparativement à ceux de la littérature, permet une représentation plus détaillée des portefeuilles financiers et la formulation de nouvelles contraintes transactionnelles. Nous présentons en outre une procédure de discrimination d'ordres équivalents sur la base de leur temps de soumission. Les résultats numériques de notre étude permettent d'évaluer empiriquement l'effet « ordres composites », ainsi que la flexibilité et la complexité numérique de notre formulation.Auction Design, Financial Markets, Bundle Trading, Discrimination Procedures, Mécanisme d'enchères, marchés financiers, ordres composites, procédures de discrimination

Decomposing Intraday Dependence in Currency Markets: Evidence from the AUD/USD Spot Market

The local Hurst exponent, a measure employed to detect the presence of dependence in a time series, may also be used to investigate the source of intraday variation observed in the returns in foreign exchange markets. Given that changes in the local Hurst exponent may be due to either a time-varying range, or standard deviation, or both of these simultaneously, values for the range, standard deviation and local Hurst exponent are recorded and analyzed separately. To illustrate this approach, a high-frequency data set of the spot Australian dollar/U.S. dollar provides evidence of the returns distribution across the 24-hour trading day with time-varying dependence and volatility clearly aligning with the opening and closing of markets. This variation is attributed to the effects of liquidity and the price-discovery actions of dealers.Comment: 3 Figures, 3 Tables, 28 page

Models of self-financing hedging strategies in illiquid markets: symmetry reductions and exact solutions

We study the general model of self-financing trading strategies in illiquid markets introduced by Schoenbucher and Wilmott, 2000. A hedging strategy in the framework of this model satisfies a nonlinear partial differential equation (PDE) which contains some function g(alpha). This function is deep connected to an utility function. We describe the Lie symmetry algebra of this PDE and provide a complete set of reductions of the PDE to ordinary differential equations (ODEs). In addition we are able to describe all types of functions g(alpha) for which the PDE admits an extended Lie group. Two of three special type functions lead to models introduced before by different authors, one is new. We clarify the connection between these three special models and the general model for trading strategies in illiquid markets. We study with the Lie group analysis the new special case of the PDE describing the self-financing strategies. In both, the general model and the new special model, we provide the optimal systems of subalgebras and study the complete set of reductions of the PDEs to different ODEs. In all cases we are able to provide explicit solutions to the new special model. In one of the cases the solutions describe power derivative products.Comment: 17 pages, 3 figure

Endogenous debt constraints in collateralized economies with default penalties

In infinite horizon financial markets economies, competitive equilibria fail to exist if one does not impose restrictions on agents' trades that rule out Ponzi schemes. When there is limited commitment and collateral repossession is the unique default punishment, Araujo, Páscoa and Torres-Martínez (2002) proved that Ponzi schemes are ruled out without imposing any exogenous/endogenous debt constraints on agents' trades. Recently Páscoa and Seghir (2009) have shown that this positive result is not robust to the presence of additional default punishments. They provide several examples showing that, in the absence of debt constraints, harsh default penalties may induce agents to run Ponzi schemes that jeopardize equilibrium existence.The objective of this paper is to close a theoretical gap in the literature by identifying endogenous borrowing constraints that rule out Ponzi schemes and ensure existence of equilibria in a model with limitedcommitment and (possible) default. We appropriately modify the definition of finitely effective debt constraints, introduced by Levine and Zame (1996) (see also Levine and Zame (2002)), to encompass models with limited commitment, default penalties and collateral. Along this line, we introduce in the setting of Araujo, Páscoa and Torres-Martínez (2002), Kubler and Schmedders (2003) and Páscoa and Seghir (2009) the concept of actions with finite equivalent payoffs. We show that, independently of the level of default penalties, restricting plans to have finite equivalent payoffs rules out Ponzi schemes and guarantees the existence of an equilibrium that is compatible with the minimal ability to borrow and lend that we expect in our model.An interesting feature of our debt constraints is that they give rise to budget sets that coincide with the standard budget sets of economies having a collateral structure but no penalties (as defined in Araujo,Páscoa and Torres-Martínez (2002)). This illustrates the hidden relation between finitely effective debt constraints and collateral requirements.

Experimental evidence for the interplay between individual wealth and transaction network

We conduct a market experiment with human agents in order to explore the structure of transaction networks and to study the dynamics of wealth accumulation. The experiment is carried out on our platform for 97 days with 2,095 effective participants and 16,936 times of transactions. From these data, the hybrid distribution (log-normal bulk and power-law tail) in the wealth is observed and we demonstrate that the transaction networks in our market are always scale-free and disassortative even for those with the size of the order of few hundred. We further discover that the individual wealth is correlated with its degree by a power-law function which allows us to relate the exponent of the transaction network degree distribution to the Pareto index in wealth distribution.Comment: 6 pages, 7 figure

Can You hear the Shape of a Market? Geometric Arbitrage and Spectral Theory

Geometric Arbitrage Theory reformulates a generic asset model possibly allowing for arbitrage by packaging all assets and their forwards dynamics into a stochastic principal fibre bundle, with a connection whose parallel transport encodes discounting and portfolio rebalancing, and whose curvature measures, in this geometric language, the 'instantaneous arbitrage capability' generated by the market itself. The cashflow bundle is the vector bundle associated to this stochastic principal fibre bundle for the natural choice of the vector space fibre. The cashflow bundle carries a stochastic covariant differentiation induced by the connection on the principal fibre bundle. The link between arbitrage theory and spectral theory of the connection Laplacian on the vector bundle is given by the zero eigenspace resulting in a parametrization of all risk neutral measures equivalent to the statistical one. This indicates that a market satisfies the (NFLVR) condition if and only if $0$ is in the discrete spectrum of the connection Laplacian on the cash flow bundle or of the Dirac Laplacian of the twisted cash flow bundle with the exterior algebra bundle. We apply this result by extending Jarrow-Protter-Shimbo theory of asset bubbles for complete arbitrage free markets to markets not satisfying the (NFLVR). Moreover, by means of the Atiyah-Singer index theorem, we prove that the Euler characteristic of the asset nominal space is a topological obstruction to the the (NFLVR) condition, and, by means of the Bochner-Weitzenb\"ock formula, the non vanishing of the homology group of the cash flow bundle is revealed to be a topological obstruction to (NFLVR), too. Asset bubbles are defined, classified and decomposed for markets allowing arbitrage.Comment: arXiv admin note: substantial text overlap with arXiv:1406.6805, arXiv:0910.167