Incomplete Market Framework Research Articles

Labor supply when productivity keeps growing

We examine the intensive and extensive margins of labor supply in an incomplete-markets framework where productivity keeps growing. What are, in particular, the long-run implications for who will work how much, and how the distribution of economic welfare among households will change? We insist the relative strengths of income and substitution effects to be such as to match historical and cross-country observations. That is, hours will fall toward zero as productivity and income rise, while wages per hour will keep rising and be consistent with stable income shares for labor and capital. Despite this rather drastic path toward zero hours worked, we find that few features of the distribution of outcomes in the population are affected much at all by productivity growth. In particular, the relative distribution of hours worked and of consumption will look very similar to the case without productivity growth.

Pricing weather derivatives in an uncertain environment

Abstract This article deals with the problem of finding a pricing formula for weather derivatives based on temperature dynamics through an uncertain differential equation. Weather-related derivatives are being employed more frequently in alternative risk portfolios with multiple asset classes. We first propose an uncertain process that uses data from the past to describe how the temperature has changed. Despite this, pricing these assets is difficult since it necessitates an incomplete market framework. The volatility is described by a truncated Fourier series, and we provide a novel technique for calculating this constant using Monte Carlo simulations. With this approach, the risk is assumed to have a fixed market price.

Real consequences of open market operations: The role of limited commitment

We study how limited commitment in credit markets affects the implementation of open market operations and characterize when they result in real indeterminacies and when they have real effects. To do so, we consider a frictional and incomplete market framework where agents face stochastic trading opportunities and limited commitment. We find necessary and sufficient conditions for the existence of a unique stationary monetary equilibrium when limited commitment does not restrict agent’s choices. However, real indeterminacies are possible when buyers face a binding no-default constraint. When the endogenous borrowing limit binds and bonds are not priced fundamentally, open market operations generically have real effects. A sale of government bonds can increase or decrease interest rates, depending on the nature of the equilibria. These phenomena are consistent with what is observed in the US. Moreover, when multiple equilibria exists welfare is larger at the steady state with a lower liquidity premium on government debt. Finally, government bond purchases can be used to rule out real indeterminacies, thus finding another rationale for such policy.

Hard vs. soft financial constraints: Implications for the effects of a credit crunch

In the aftermath of the Great Recession, understanding how households’ consumption responds to a credit crunch has been a central goal of macroeconomics. Most of the recent research has explored this question using a “hard constraint” modeling device, where households can borrow at the risk-free rate only up to an exogenous amount. An alternative, and more realistic, way to model financial frictions is to allow households to borrow as much as they want but at an interest rate that depends on the level of debt. I refer to the latter as the “soft constraint” model. In a Standard Incomplete Markets framework with heterogeneous agents, I calibrate two economies differing only in the type of financial constraint that households face and I show that a credit crunch in the hard constraint economy (i.e. decrease in the exogenous borrowing limit) produces a drop in consumption significantly more severe than an equivalent crunch in the soft constraint version (i.e. increase in the borrowing interest rate). I conclude that the quantitative consequences of a credit crunch largely depend on the modeling approach.

Market completion with derivative securities

Let S^{F} be a ℙ-martingale representing the price of a primitive asset in an incomplete market framework. We present easily verifiable conditions on the model coefficients which guarantee the completeness of the market in which in addition to the primitive asset, one may also trade a derivative contract S^{B}. Both S^{F} and S^{B} are defined in terms of the solution X to a two-dimensional stochastic differential equation: S^{F}_{t} = f(X_{t}) and S^{B}_{t}:=mathbb{E}[g(X_{1}) | mathcal{F}_{t}]. From a purely mathematical point of view, we prove that every local martingale under ℙ can be represented as a stochastic integral with respect to the ℙ-martingale S :=(S^{F}, S^{B}). Notably, in contrast to recent results on the endogenous completeness of equilibria markets, our conditions allow the Jacobian matrix of (f,g) to be singular everywhere on mathbb{R}^{2}. Hence they cover as a special case the prominent example of a stochastic volatility model being completed with a European call (or put) option.

Outperformance portfolio optimization via the equivalence of pure and randomized hypothesis testing

We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a general incomplete market framework, this stochastic control problem can be formulated as a composite pure hypothesis testing problem. We analyze the connection between this pure testing problem and its randomized counterpart, and from latter we derive a dual representation for the maximal outperformance probability. Moreover, in a complete market setting, we provide a closed-form solution to the problem of beating a leveraged exchange traded fund. For a general benchmark under an incomplete stochastic factor model, we provide the Hamilton-Jacobi-Bellman PDE characterization for the maximal outperformance probability.

A GARCH Option Pricing Model with Filtered Historical Simulation

We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model's flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility, and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state-price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.

A GARCH Option Pricing Model with Filtered Historical Simulation

We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics enhancing the model flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.

Securitization of catastrophe mortality risks

Securitization with payments linked to explicit mortality events provides a new investment opportunity to investors and financial institutions. Moreover, mortality-linked securities provide an alternative risk management tool for insurers. As a step toward understanding these securities, we develop an asset pricing model for mortality-based securities in an incomplete market framework with jump processes. Our model nicely explains opposite market outcomes of two existing pure mortality securities.

Modeling Earthquake Risk via Extreme Value Theory and Pricing the Respective Catastrophe Bonds

The aim of the paper is twofold. Firstly, to analyze the historical data of the earthquakes in the boarder area of Greece and then to produce a reliable model for the risk dynamics of the magnitude of the earthquakes, using advanced techniques from the Extreme Value Theory. Secondly, to discuss briefly the relevant theory of incomplete markets and price earthquake catastrophe bonds, combining the model found for the earthquake risk and an appropriate model for the interest rate dynamics in an incomplete market framework. The paper ends by providing some numerical results using Monte Carlo simulation techniques and stochastic iterative equations.

Modeling Earthquake Risk via Extreme Value Theory and Pricing the Respective Catastrophe Bonds

The aim of the paper is twofold. Firstly, to analyze the historical data of the earthquakes in the boarder area of Greece and then to produce a reliable model for the risk dynamics of the magnitude of the earthquakes, using advanced techniques from the Extreme Value Theory. Secondly, to discuss briefly the relevant theory of incomplete markets and price earthquake catastrophe bonds, combining the model found for the earthquake risk and an appropriate model for the interest rate dynamics in an incomplete market framework. The paper ends by providing some numerical results using Monte Carlo simulation techniques and stochastic iterative equations.

ON THE TIMING OPTION IN A FUTURES CONTRACT

The timing option embedded in a futures contract allows the short position to decide when to deliver the underlying asset during the last month of the contract period. In this paper we derive, within a very general incomplete market framework, an explicit model independent formula for the futures price process in the presence of a timing option. We also provide a characterization of the optimal delivery strategy, and we analyze some concrete examples.

Equilibrium Pricing in Incomplete Markets

AbstractGiven the exogenous price process of some assets, we constrain the price process of other assets that are characterized by their final payoffs. We deal with an incomplete market framework in a discrete-time model and assume the existence of the equilibrium. In this setup, we derive restrictions on the state-price deflators. These restrictions do not depend on a particular choice of utility function. We investigate numerically a stochastic volatility model as an example. Our approach leads to an interval of admissible prices that is more robust than the arbitrage pricing interval.

Efficient Derivative Pricing by Extended Method of Moments

In this paper we consider an incomplete market framework and explainhow to use jointlyobserv ed prices of the underlying asset and of some derivativeswritten on this asset for an efficient pricing of other derivatives. Thisquestion involves two types of moment restrictions, which can be writteneither for a given value of the conditioning variable or can be uniform withrespect to this conditioning variable. This distinction between local and uniformconditional moment restrictions leads to an extension of the GeneralizedMethod of Moments (GMM), a method in which all restrictions are assumeduniform. The Extended Method of Moments (XMM) provides estimators ofthe parameters with different rates of convergence: the rate is the standardparametric one for the parameters which are identifiable from the uniformrestrictions, whereas the rate can be nonparametric for the risk premiumparameters. We derive the (kernel) nonparametric efficiencyb ounds for estimatinga conditional moment of interest and prove the asymptotic efficiencyof XMM. To avoid misleading arbitrage opportunities in estimated derivativeprices, an XMM estimator based on an information criterion is introduced.The general results are applied in a stochastic volatilitymo del to get efficientderivatice prices, to measure the uncertaintyof estimated prices and toestimate the risk premium parameters.

Equilibrium Pricing in Incomplete Markets

Given exogenously the price process of some asets, we constrain the price process of other assets, which are characterised by their final pay-offs. We deal with an incomplete market framework in a discrete time model and assume the existence of the equilibrium. In this setup, we derive restrictions on the state-price deflators and these restrictions do not depend on a particular choice of utility function. A stochastic volatility model is numerically investigated as an example. Our approach leads to an interval of admissible prices much better than the arbitrage pricing interval.

Labour Relations and Asset Returns

This paper proposes a dynamic GE model with standard business cycle properties that also achieves a satisfactory replication of the major financial stylized facts. We ride on two major ideas. First, we show that operating leverage, originating in the priority status of wage claims given the observed business cycle characteristics of the latter, magnifies the risk properties of the residual payments to firm owners and justifies a substantial risk premium. Further we build on the observation that the low frequency variations in income shares constitute a significant source of risk, one that is unlikely to be insurable. When we price this risk in an incomplete market framework, we obtain a GE model with return volatilities close to observations and a sizable equity premium. This is accomplished in a world of low risk aversion and standard utility function but with agent heterogeneity. Workers with restricted access to financial markets are insured by firms and the consumption and preferences of firm owners solely determine the pricing kernel.

Dynamic programming and mean-variance hedging

We consider the mean-variance hedging problem when asset prices follow Ito processes in an incomplete market framework. The hedging numeraire and the variance-optimal martingale measure appear to be a key tool for characterizing the optimal hedging strategy (see Gourieroux et al. 1996; Rheinlander and Schweizer 1996). In this paper, we study the hedging numeraire \(\tilde a\) and the variance-optimal martingale measure \(\tilde P\) using dynamic programming methods. We obtain new explicit characterizations of \(\tilde a\) and \(\tilde P\) in terms of the value function of a suitable stochastic control problem. We provide several examples illustrating our results. In particular, for stochastic volatility models, we derive an explicit form of this value function and then of the hedging numeraire and the variance-optimal martingale measure. This provides then explicit computations of optimal hedging strategies for the mean-variance hedging problem in usual stochastic volatility models.

Contingent Claims and Market Completeness in a Stochastic Volatility Model

In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in contingent claims is allowed. We extend recent results by Bajeux and Rochet (1996) in a stochastic volatility model to the case where the asset price and its volatility variations are correlated. We also relate the ability of a given contingent claim to complete the market to the convexity of its price function in the current asset price. This allows us to state our results for general contingent claims by examining the convexity of their “admissible arbitrage prices.”

The Role of Fiscal Policy in an Incomplete Markets Framework

A general-equilibrium model is developed to highlight the link between neo-Keynesian models of unemployment and recent results on the constrained sub-optimality of competitive economies with incomplete asset markets. Although the model deviates from the Arrow-Debreu paradigm only by the absence of some contingent claims, the competitive equilibrium exhibits under-employment and balanced-budget fiscal policies have Keynesian effects which are Pareto improving. Will a market economy, left to itself, fully employ its resources? In The General Theory, Keynes exploited several mechanisms through which real economies differ from the classical paradigm where unemployment is either voluntary or non-existent. A common characteristic of these mechanisms is the difficulty of coordinating production and consumption plans in a decentralized economy. In recent years neo-Keynesians have sought to develop general-equilibrium models from micro foundations where this coordination problem can be analyzed. These efforts are of interest for two reasons. First, as an intellectual exercise it is of interest to explore which deviations from the classical paradigm are necessary and/ or sufficient to generate Keynesian effects. Second, from a policy perspective, it is important to start from micro-foundations to verify the welfare implications of policy. The neo-Keynesian literature has gone in several directions. We will not review them here.' At this point it is sufficient to note that the argument developed below is based on incomplete financial markets and thus is related to the asymmetric information models of Greenwald and Stiglitz.2 The main contribution of this paper is the development of a model where we can make the following three points: 1) The Keynesian coordination problem can arise naturally in a competitive system with perfectly flexible prices and rational expectations. 2) The mechanism underlying the coordination problem is related to recent work on the constrained sub-optimality of competitive equilibria with incomplete markets. As such, the coordination problem is generic to this and other models with incomplete financial markets. 3) Familiar, and feasible, policies can be welfare improving even though they do not directly address the fundamental microeconomic causes of the coordination failure. We study in detail the welfare effects of two fiscal policies and discuss briefly how other policies can be studied within this model.

The Role of Fiscal Policy in an Incomplete Markets Framework

A general-equilibrium model is developed to highlight the link between neo-Keynesian models of unemployment and recent results on the constrained suboptimality of competitive economies with incomplete asset markets. Although the model deviates from the Arrow-Debreu paradigm only by the absence of some contingent claims, the competitive equilibrium exhibits under-employment and balanced-budget fiscal policies have Keynesian effects which are Pareto improving.