Multifrequency jump-diffusions: An equilibrium approach

This paper proposes that equilibrium valuation is a powerful method to generate endogenous jumps in asset prices. We specify an economy with continuous consumption and dividend paths, in which endogenous price jumps originate from the market impact of regime-switches in the drifts and volatilities of fundamentals. We parsimoniously incorporate regimes of heterogeneous durations and verify that the persistence of a shock endogenously increases the magnitude of the induced price jump. As the number of frequencies driving fundamentals goes to infinity, the price process converges to a novel stochastic process, which we call a multifractal jump-diffusion.     

Options and efficiency in spaces of bounded claims

In a seminal contribution, Ross (1976) showed that a static finite state-space market can be completed by supplementing the primitive securities with ordinary call and put options. Galvani (2009) extends this result to norm separable _Lp$L_p$-spaces, with 1≤p<∞$1\le p<\infty$. This study concludes that options maintain the same spanning power in the space of bounded payoffs topologized by the duality with the space of the state price densities. In particular, under mild assumptions on the probability space, options written on a claim that is a.s. equal to an injective function complete the market.     

Estimation of objective and risk-neutral distributions based on moments of integrated volatility

In this paper, we present an estimation procedure which uses both option prices and high-frequency spot price feeds to estimate jointly the objective and risk-neutral parameters of stochastic volatility models. The procedure is based on a method of moments that uses analytical expressions for the moments of the integrated volatility and series expansions of option prices and implied volatilities. This results in an easily implementable and rapid estimation technique. An extensive Monte Carlo study compares various procedures and shows the efficiency of our approach. Empirical applications to the Deutsche mark–US dollar exchange rate futures and the S&P 500 index provide evidence that the method delivers results that are in line with the ones obtained in previous studies where much more involved estimation procedures were used.     

A tale of two yield curves: Modeling the joint term structure of dollar and euro interest rates

Modeling the joint term structure of interest rates in the United States and the European Union, the two largest economies in the world, is extremely important in international finance. In this article, we provide both theoretical and empirical analysis of multi-factor joint affine term structure models (ATSM) for dollar and euro interest rates. In particular, we provide a systematic classification of multi-factor joint ATSM similar to that of Dai and Singleton (2000). A principal component analysis of daily dollar and euro interest rates reveals four factors in the data. We estimate four-factor joint ATSM using the approximate maximum likelihood method of [A?t-Sahalia, 2002] and [A?t-Sahalia, forthcoming] and compare the in-sample and out-of-sample performances of these models using some of the latest nonparametric methods. We find that a new four-factor model with two common and two local factors captures the joint term structure dynamics in the US and the EU reasonably well.     

Equilibrium price dynamics in an overlapping-generations exchange economy

An extension to the Yaari (1965)–Blanchard (1985) continuous time overlapping generations model for an endowment Arrow–Debreu economy with an age-structured population is presented. It is proved that Arrow–Debreu equilibrium prices are represented by a double linear integral equation, and depend on the age-distributions of population and endowments. For an economy with a balanced growth, and logarithmic utility, we prove that bubbles may exist if endowments are distributed earlier than some critical age.     

Can the random walk model be beaten in out-of-sample density forecasts? Evidence from intraday foreign exchange rates

It has been documented that random walk outperforms most economic structural and time series models in out-of-sample forecasts of the conditional mean dynamics of exchange rates. In this paper, we study whether random walk has similar dominance in out-of-sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance. We first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out-of-sample setting and provide simulation evidence on its finite sample performance. Then we conduct a comprehensive empirical analysis on the out-of-sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates—Euro/Dollar and Yen/Dollar. It is found that some sophisticated time series models that capture time-varying higher order conditional moments, such as Markov regime-switching models, have better density forecasts for exchange rates than random walk or modified random walk with GARCH and Student-t innovations. This finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out-of-sample applications involving the probability density.     

Generalized spectral testing for multivariate continuous-time models

We develop an omnibus specification test for multivariate continuous-time models using the conditional characteristic function, which often has a convenient closed-form or can be accurately approximated for many multivariate continuous-time models in finance and economics. The proposed test fully exploits the information in the joint conditional distribution of underlying economic processes and hence is expected to have good power in a multivariate context. A class of easy-to-interpret diagnostic procedures is supplemented to gauge possible sources of model misspecification. Our tests are also applicable to discrete-time distribution models. Simulation studies show that the tests provide reliable inference in finite samples.     

Does home owning smooth the variability of future housing consumption?

We show that the hedging benefit of owning a home reduces the variability of housing consumption after a move. When a current home owner’s house price covaries positively with housing costs in a future city, changes in the future cost of housing are offset by commensurate changes in wealth before the move. Using Census micro-data, we find that the cross-sectional variation in house values subsequent to a move is lower for home owners who moved between more highly covarying cities. Our preferred estimates imply that an increase in covariance of one standard deviation reduces the variance of subsequent housing consumption by about 11%. Households at the top end of the covariance distribution who are likely to have owned large homes before moving get the largest reductions, of up to 40% relative to households at the median.     

The Walras core of an economy and its limit theorem

The Walras core of an economy is the set of allocations that are attainable for the consumers when their trades are constrained to be based on some agreed price system, such that no alternative price system exists for any sub-coalition that allows all members to trade to something better. As compared with the Edgeworth core, both coalitional improvements and being a candidate allocation for the Walras core become harder. The Walras core may even contain allocations that violate the usual Pareto efficiency. Nevertheless, the competitive allocations are the same under the two theories, and the equal-treatment Walras core allocations converge under general conditions to the competitive allocations in the process of replication.     

Multi-scale tests for serial correlation

This paper introduces a new family of portmanteau tests for serial correlation. Using the wavelet transform, we decompose the variance of the underlying process into the variance of its low frequency and of its high frequency components and we design a variance ratio test of no serial correlation in the presence of dependence. Such decomposition can be carried out iteratively, each wavelet filter leading to a rich family of tests whose joint limiting null distribution is a multivariate normal. We illustrate the size and power properties of the proposed tests through Monte Carlo simulations.     

The bull and bear market model of Huang and Day: Some extensions and new results

We develop a financial market model with interacting chartists and fundamentalists that embeds the famous bull and bear market model of Huang and Day as a special case. Their model is given by a one-dimensional continuous piecewise-linear map. Our model, on the other hand, is more flexible and is represented by a one-dimensional discontinuous piecewise-linear map. Nevertheless, we are able to provide a more or less complete analytical treatment of the model dynamics by characterizing its possible outcomes in parameter space. In addition, we show that quite different scenarios can trigger real-world phenomena such as bull and bear market dynamics and excess volatility.