Stochastic bequest games

In this paper, we prove the existence of a stationary Markov perfect equilibrium for a stochastic version of the bequest game. A novel feature in our approach is the fact that the transition probability need not be non-atomic and therefore, the deterministic production function is not excluded from consideration. Moreover, in addition to the common expected utility we also deal with a utility that takes into account an attitude of the generation towards risk.     

Stochastic optimal growth with risky labor supply

Production takes time, and labor supply and profit maximization decisions that relate to current production are typically made before all shocks affecting that production have been realized. In this paper we re-examine the problem of stochastic optimal growth with aggregate risk where the timing of the model conforms to this information structure. We provide a set of conditions under which the economy has a unique, nontrivial and stable stationary distribution. In addition, we verify key optimality properties in the presence of unbounded shocks and rewards, and provide the sample path laws necessary for consistent estimation and simulation.     

SHADOW PRICES FOR CONTINUOUS PROCESSES

In a financial market with a continuous price process and proportional transaction costs, we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e., a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredients are the continuity of the price process and the hypothesis of “no unbounded profit with bounded risk.” A counterexample reveals that these hypotheses cannot be relaxed.     

Subgame-perfect equilibria in stochastic timing games

We develop a notion of subgames and the related notion of subgame-perfect equilibrium – possibly in mixed strategies – for stochastic timing games. To capture all situations that can arise in continuous-time models, it is necessary to consider stopping times as the starting dates of subgames. We generalize Fudenberg and Tirole’s (Rev. Econom. Stud. 52, 383–401, 1985) mixed-strategy extensions to make them applicable to stochastic timing games and thereby provide a sound basis for subgame-perfect equilibria of preemption games. Sufficient conditions for equilibrium existence are presented, and examples illustrate their application as well as the fact that intuitive arguments can break down in the presence of stochastic processes with jumps.     

Volatility swaps and volatility options on discretely sampled realized variance

Volatility swaps and volatility options are financial products written on discretely sampled realized variance. Actively traded in over-the-counter markets, these products are often priced by continuously sampled approximations to simplify the computations. This paper presents an analytical approach to efficiently and accurately price discretely sampled volatility derivatives, under a general stochastic volatility model. We first obtain an accurate approximation for the characteristic function of the discretely sampled realized variance. This characteristic function is then applied to price discrete volatility derivatives through either semi-analytical pricing formulae (up to an inverse Fourier transform) or an efficient Fourier-cosine series method. Numerical experiments show that our approximation is more accurate in comparison to the approximations in the literature. We remark that although discretely sampled variance swaps and options are usually more expensive than their continuously sampled counterparts, discretely sampled volatility swaps are more prone to be cheaper than the continuously sampled counterparts. An analysis is then provided to explain why this is the case in general for realistic contract specifications and reasonable model parameters.     

Corporate credit risk prediction under stochastic volatility and jumps

This paper examines the impact of allowing for stochastic volatility and jumps (SVJ) in a structural model on corporate credit risk prediction. The results from a simulation study verify the better performance of the SVJ model compared with the commonly used Merton model, and three sources are provided to explain the superiority. The empirical analysis on two real samples further ascertains the importance of recognizing the stochastic volatility and jumps by showing that the SVJ model decreases bias in spread prediction from the Merton model, and better explains the time variation in actual CDS spreads. The improvements are found particularly apparent in small firms or when the market is turbulent such as the recent financial crisis.     

Alternative to beta coefficients in the context of diffusions

We develop an alternative to the beta coefficient of the CAPM theory. We show the link between this notion and the Wiener chaos expansion of the underlying processes. In the setting of Markov diffusions, we define the drift-neutral beta, which is the quantity of benchmark such that the resulting portfolio is immune to an infinitesimal change of drift on the Brownian motion driving the benchmark. Our approach yields a coefficient which in many practical cases depends on the initial values of both the portfolio and its benchmark. It can also be used to take into account extreme risks and not only the variance. We study several classical diffusion processes and give a full analysis in the case of Jacobi processes. Examples with credit indices show the efficiency of the method in hedging a portfolio.     

Demand clustering in freight logistics networks

Demand clustering in freight logistics networks is an important strategic decision for carriers. It is used to incorporate new business to their networks, detecting potential economies, optimizing their operation, and developing revenue management strategies. A specific example of demand clustering is truckload combinatorial auctions where carriers bundle lanes of demand and price them taking advantage of economies of scope. This research presents a novel approach to cluster lanes of demand. Community detection is used to cluster the emergent network finding profitable collections of demand. Numerical results show the advantages of this method.     

Gradient-based simulated maximum likelihood estimation for stochastic volatility models using characteristic functions

Parameter estimation and statistical inference are challenging problems for stochastic volatility (SV) models, especially those driven by pure jump Lévy processes. Maximum likelihood estimation (MLE) is usually preferred when a parametric statistical model is correctly specified, but traditional MLE implementation for SV models is computationally infeasible due to high dimensionality of the integral involved. To overcome this difficulty, we propose a gradient-based simulated MLE method under the hidden Markov structure for SV models, which covers those driven by pure jump Lévy processes. Gradient estimation using characteristic functions and sequential Monte Carlo in the simulation of the hidden states are implemented. Numerical experiments illustrate the efficiency of the proposed method.     

US airport ownership,efficiency, and heterogeneity

All US commercial airports are in the public sector yet not all have the same ownership type. For medium and large hub US airports we use stochastic frontier analysis to analyze the efficiency differences for alternative airport ownership types. We find that while form of ownership may matter for cost efficiency, in general its effect is relatively small. Yet type of public sector ownership does have cost efficiency implications in certain environments. Further, when heterogeneity is not controlled, the results change substantially so that type of ownership matters much more which demonstrates the importance of controlling for cross section heterogeneity.