Nonconvex optimization for pricing and hedging in imperfect markets.

The paper deals with imperfect financial markets and provides new methods to overcome many inefficiencies caused by frictions. Transaction costs are quite general and far from linear or convexo The concepts of pseudoarbitrage and efficiency are introduced and deeply analyzed by means of both scalar and vector optimization problems. Their optimality conditions and solutions yield strategies to invest and hedging portfolios, as well as bid-ask spread improvements. They also point out the role of coalitions when dealing with these markets. Several sensitivity results will permit us to show that a significant transaction costs reduction is very often feasible in practice, as well as to measure its effect on the general efficiency of the market. AII these findings may be especially important for many emerging and still illiquid spot or derivative markets (electricity markets, com odity markets, markets related to weather, infiation-linked or insurance-linked derivatives, etc.).Global optimization; Pseudoarbitrage; Spread reduction; Balance point;

Determination of Risk Pricing Measures from Market Prices of Risk

A new insurance provider or a regulatory agency may be interested in determining a risk measure consistent with observed market prices of a collection of risks. Using a relationship between distorted coherent risk measures and spectral risk measures, we provide a method for reconstruction distortion functions from the observed prices of risk. The technique is based on an appropriate application of the method on maximum entropy in the mean.

Data-Driven Smooth Tests for the Martingale Difference Hypothesis

A general method for testing the martingale difference hypothesis is proposed. The new tests are data-driven smooth tests based on the principal components of certain marked empirical processes that are asymptotically distribution-free, with critical values that are already tabulated. The data-driven smooth tests are optimal in a semiparametric sense discussed in the paper, and they are robust to conditional heteroskedasticity of unknown form. A simulation study shows that the smooth tests perform very well for a wide range of realistic alternatives and have more power than the omnibus and other competing tests. Finally, an application to the S&P 500 stock index and some of its components highlights the merits of our approach.

Portfolio choice and optimal hedging with general risk functions: a simplex-like algorithm.

The minimization of general risk functions is becoming more and more important in portfolio choice theory and optimal hedging. There are two major reasons. Firstly, heavy tails and the lack of symmetry in the returns of many assets provokes that the classical optimization of the standard deviation may lead to dominated strategies, from the point of view of the second order stochastic dominance. Secondly, but not less important, many institutional investors must respect legal capital requirements, which may be more easily studied if one deals with a risk measure related to capital losses. This paper proposes a new method to simultaneously minimize several general risk or dispersion measures. The representation theorems of risk functions are applied to transform the general risk minimization problem in a minimax problem, and later in a linear programming problem between infinite-dimensional Banach spaces. Then, new necessary and sufficient optimality conditions are stated and a simplex-like algorithm is developed. The algorithm solves the dual problem and provides both optimal portfolios and their sensitivities. The approach is general enough and does not depend on any particular risk measure, but some of the most important cases are specially analyzed. A final real data numerical example illustrates the practical performance of the proposed methodology.Risk measures; Deviation measure; Portfolio selection; Infinite dimensional linear programming; Simplex like method;

Optimizing Measures of Risk: A Simplex-like Algorithm

The minimization of general risk or dispersion measures is becoming more and more important in Portfolio Choice Theory. There are two major reasons. Firstly, the lack of symmetry in the returns of many assets provokes that the classical optimization of the standard deviation may lead to dominated strategies, from the point of view of the second order stochastic dominance. Secondly, but not less important, many institutional investors must respect legal capital requirements, which may be more easily studied if one deals with a risk measure related to capital losses. This paper proposes a new method to simultaneously minimize several risk or dispersion measures. The representation theorems of risk measures are applied to transform the general risk minimization problem in a minimax problem, and later in a linear programming problem between infinite-dimensional Banach spaces. Then, new necessary and sufficient optimality conditions are stated and a simplex-like algorithm is developed. The algorithm solves the dual (and therefore the primal) problem and provides both optimal portfolios and their sensitivities. The approach is general enough and does not depend on any particular risk measure, but some of the most important cases are specially analyzed.Risk Measure. Deviation Measure. Portfolio Selection. Infinite-Dimensional Linear Programming. Simpl

Nonconvex optimization for pricing and hedging in imperfect markets

The paper deals with imperfect financial markets and provides new methods to overcome many inefficiencies caused by frictions. Transaction costs are quite general and far from linear or convexo The concepts of pseudoarbitrage and efficiency are introduced and deeply analyzed by means of both scalar and vector optimization problems. Their optimality conditions and solutions yield strategies to invest and hedging portfolios, as well as bid-ask spread improvements. They also point out the role of coalitions when dealing with these markets. Several sensitivity results will permit us to show that a significant transaction costs reduction is very often feasible in practice, as well as to measure its effect on the general efficiency of the market. AII these findings may be especially important for many emerging and still illiquid spot or derivative markets (electricity markets, com odity markets, markets related to weather, infiation-linked or insurance-linked derivatives, etc.).Partially funded by "Comunidad Autónoma de Madrid" and Spanish Ministry of Science and Education (ref: BEC2003-09067 -C04-03).Publicad

Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den

We introduce a general binomial model for asset prices based on the concept of random maps. The asymptotic stationary distribution for such model is studied using techniques from dynamical systems. In particular, we present a technique to construct a general binomial model with a predetermined stationary distribution. This technique is independent of the chosen distribution making our model potentially useful in financial applications. We brie y explore the suitability of our construction as an implied binomial tree.

Quote inefficiency in options markets

In an arbitrage-free economy with non-zero bid-ask spreads the existence of payoffs whose price is lower than the price of a dominated payoff cannot be discarded in general. However, when the former price corresponds to trivial portfolios which involve buying or selling one unit of the basis assets, its presence, although not an arbitrage, is a severe market anomaly which we refer to as an inefficient quote. In an empirical study, we report evidence that indicates that in options markets both the frequency and the magnitude of these anomalies are substantial and we document puzzling patterns in their behavior. (C) 2014 Elsevier B.V. All rights reserved

Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory

Here, we consider the following inverse problem: Determination of an increasing continuous function U(x) on an interval [a,b] from the knowledge of the integrals ∫U(x)dFXi(x)=πi where the Xi are random variables taking values on [a,b] and πi are given numbers. This is a linear integral equation with discrete data, which can be transformed into a generalized moment problem when U(x) is supposed to have a positive derivative, and it becomes a classical interpolation problem if the Xi are deterministic. In some cases, e.g., in utility theory in economics, natural growth and convexity constraints are required on the function, which makes the inverse problem more interesting. Not only that, the data may be provided in intervals and/or measured up to an additive error. It is the purpose of this work to show how the standard method of maximum entropy, as well as the method of maximum entropy in the mean, provides an efficient method to deal with these problems.All sources of funding of the study should be disclosed. Please clearly indicate grants that you have received in support of your research work. Clearly state if you received funds for covering the costs to publish in open access

Risk-neutral valuation with infinitely many trading dates

The first Fundamental Theorem of Asset Pricing establishes the equivalence between the absence of arbitrage in financial markets and the existence of Equivalent Martingale Measures, if appropriate conditions hold. Since the theorem may fail when dealing with infinitely many trading dates, this paper draws on the A.A. Lyapunov Theorem in order to retrieve the equivalence for complete markets such that the Sharpe Ratio is adequately bounded.This research was partially supported by "Comunidad Autónoma de Madrid" (Spain), Grants 06/HSE/0150/2004 and s–0505/ittic/000230, and MEyC (Spain), Grant BEC2000–1388–C04–03.Publicad