Self exciting threshold interest rates models.

In this paper, we study a new class of tractable diffusions suitable for model's primitives of interest rates. We consider scalar diffusions with scale s'(x) and speed m(x) densities discontinuous at the level x*. We call that family of processes Self Exciting Threshold (SET) diffusions. Following Gorovoi and Linetsky (2004), we obtain semianalytical expressions for the transition density of SET (killed) diffusions. We propose several applications to interest rates modeling. We show that SET short rate processes do not generate arbitrage possibilities and we adapt the HJM procedure to forward rates with discontinuous scale density. We also extend the CEV and the shiftedlognormal Libor market models. Finally, the models are calibrated to the U.S. market. SET diffusions can also be used to model stock price, stochastic volatility, credit spread, etc.Eigenfunction expansions; Interest rates; Market models; SETAR; Skew Brownian motion; State-price density;

Risk aversion and herd behavior in financial markets

We show that differences in investors risk aversion can generate herd behavior in stock markets where assets are traded sequentially. This in turn prevents markets from being efficient in the sense that financial market prices do not converge to the asset's fundamental value. The informational efficiency of the market depends on the distribution of the risky asset across risk averse agents. These results are obtained without introducing multidimensional uncertainty.herd behavior; stock markets; efficiency

Market informational inefficiency, risk aversion and quantity grid

In this paper we show that long run market informational inefficiency is perfectly compatible with standard rational sequential trade models. Our inefficiency result is obtained taking into account two features of actual financial markets: tradable quantities belong to a quantity grid and traders and market makers do not have the same degree of risk aversion. The implementation of our model for reasonable values of the parameters suggests that the long term deviations between asset prices and fundamental value are important. We explain the ambiguous role of the quantity grid in exacerbating or mitigating market inefficiency. We show that stock splits can improve the information content of the order flow and consequently increase price volatility.informational efficiency; quantity grid; stock splits

Transition probabilities for diffusion equations by means of path integrals.

In this paper, we investigate the transition probabilities for diffusion processes. In a first part, we show how transition probabilities for rather general diffusion processes can always be expressed by means of a path integral. For several classical models, an exact calculation is possible, leading to analytical expressions for the transition probabilities and for the maximum probability paths. A second part consists of the derivation of an analytical approximation for the transition probability, which is useful in case the path integral is too complex to be calculated. The approximation we present is based on a convex combination of a new analytical upper and lower bound for the transition probabilities. The fact that the approximation is analytical has some important advantages, e.g. for the investigation of Asian options. Finally, we demonstrate the accuracy of the approximation by means of a few graphical illustrationsAdvantages; Comonotonicity; Diffusion processes; Models; Option; Path integral;

Pricing exotic options under local volatility.

Optimal; Optimal portfolio selection; Portfolio; Selection; Cash flow; Capital at risk; Risk; Pricing; Options;

A Structural Econometric Investigation of the Agency Theory of Financial Structure

We estimate a structural model of financing choices in presence of managerial moral hazard, financial distress costs and taxes. In the theoretical model, firms with low cost of managerial effort, and high financial distress costs and non--debt tax shields, find it optimal to issue equity. Correspondingly the likelihood that a given firm issues equity is the probability that its managerial cost of effort is below an upper bound, reflecting its financial distress cost and non debt tax shields, as well as the other deep parameters of the model. Similarly we characterize the likelihood of issues of debt and convertible bonds. Using maximum likelihood analysis, we confront this theoretical model to data on financing choices by French firms in 1996. We find large costs of financial distress, equal on average to 41.2\% of the value of the firm when it is in distress. We also find large agency costs, equal to 40.26\% of the value of the investment project. In contrast, we find that tax shields do not play a significant role in the financing decision.

Solution of the Fokker-Planck equation with boundary conditions by Feynman-Kac integration.

In this paper, we apply the results about d and d-function perturbations in order to formulate within the Feynman-Kac integration the solution of the forward Fokker-Planck equation subject to Dirichlet or Neumann boundary conditions. We introduce the concept of convex order to derive upper and lower bounds for path integrals with d and d- functions in the integrand. We suggest the use of bounds as an approximation for the solution.Feynman-Kac integration; Functions; Integration; Path integral; Perturbations theory; SDE;

Modeling soil moisture-reflectance

Spectral information on soil is not easily available as vegetation and farm works prevent direct observation of soil responses. However, there is an increasing need to include soil reflectance values in spectral unmixing algorithms or in classification approaches. In most cases, the impact of soil moisture on the reflectance is unknown and therefore ignored. The objective of this study was to model reflectance changes due to soil moisture in a real field situation using multiresolution airborne Spot data. As the direct observation of soils is only possible in the absence of vegetation, the effective remote sensing of soil moisture is limited to a few days each year. In such a favorable time window, modeling the soil moisture- reflectance relationships was found possible. The proposed exponential model was not valid when all soil categories were considered together. However, when fitted to each category, the RMS error on moisture estimates ranged from 2.0% to 3.5% except for silty soils with crusting problems (6%). Results also indicated that, when the soils have similar colors (i.e. same hue), soil categories can be partly grouped and the model can be simplified, using the same intercept coefficients. This study has potential application for the definition of a more generalized model of the soil reflectance. It shows that the impact of soil moisture on reflectance could be higher than differences in reflectance due to the soil categories