Mesoscopic modelling of financial markets

We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investment alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model (Econ. Lett., 45, (1994), 103--111) using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupled with an equation for the price of the stock. From this model, under a suitable scaling, we derive a Fokker-Planck equation and show that the equation admits a self-similar lognormal behavior. Several numerical examples are also reported to validate our analysis

Valuing reload options

Over the past quarter century, the use of stock options as pay for performance has grown enormously. Option grants now account for 32% of CEO pay—more than twice that of salaries. In addition options are now being granted to many more employees than before. During this same time period, there have been numerous innovations in the features on compensation options. One of these features is the reload—the grant of new options to replace shares tendered in the payment of the exercise. Within the past year, the long-delayed FASB requirement that options be expensed for financial reporting has finally become a fact. It is incumbent upon financial researchers to provide methods to achieve the goal of valuing options, not only to serve the accounting needs, but also to provide ways of determining their true costs and incentive effects. This paper analyzes the various forms of reload options and provides simple Black-Scholes like formulas for evaluating them. Copyright Springer Science+Business Media, LLC 2006Exoctic options, Reload options, Incentive options,

Determinantes do fluxo de investimentos de portfólio para o mercado acionário brasileiro

Este artigo estuda como os fluxos de investimento para o mercado acionário brasileiro são afetados pelo retorno do índice Ibovespa, variação cambial, taxa SELIC e risco país. São utilizados dados mensais para o período entre 1995 e 2005 e verificadas as relações de causalidade e exogeneidade. Os resultados apontam para o comportamento racional do investidor estrangeiro, entrando no mercado após quedas e saindo após elevações. Os retornos defasados influenciam o fluxo. Há diminuição da posição do investidor estrangeiro quando a moeda doméstica se valoriza em relação ao dólar. A crise cambial de janeiro de 1999 afetou negativamente o investimento. A melhoria do indicador de risco país incentiva a entrada de investimentos. Os fluxos estão relacionados à taxa SELIC, que influencia a formação de expectativas. O índice de Sharpe positivo mostra que o maior risco do mercado brasileiro é compensado por maior rendimento. Após diversos testes diagnósticos, constata-se que o modelo proposto é adequado para inferência, mas não para a formulação de políticas e realização de previsões.<br>This work investigates the effects of equity returns, exchange rates, interest rates and a country risk measure on foreign portfolio investment flows to the Brazilian equity market. Data is monthly from 1995 to 2005. Causality and exogeneity relations are tested. The results point out the rational behavior of foreign investors, who enter the market after a fall and withdraw after a rise of the Bovespa index. Past returns are found to be important in the investment decision. When the domestic currency appreciates in face to the US dollar, foreign investors reduce their exposure to the Brazilian market. The evidence also indicates the exchange crises of January 1999 affected foreign investment. Inflows of investments are stimulated by better external debt evaluation and are also related to the Brazilian interest rate. The Sharpe ratio shows that the higher risk of the Brazilian market is rewarded by higher return. After several diagnostic tests, the model proposed is found to be appropriate for inference use, but not for prediction or policy purposes

Exoplanetary Atmospheres—Chemistry, Formation Conditions, and Habitability

Characterizing the atmospheres of extrasolar planets is the new frontier in exoplanetary science. The last two decades of exoplanet discoveries have revealed that exoplanets are very common and extremely diverse in their orbital and bulk properties. We now enter a new era as we begin to investigate the chemical diversity of exoplanets, their atmospheric and interior processes, and their formation conditions. Recent developments in the field have led to unprecedented advancements in our understanding of atmospheric chemistry of exoplanets and the implications for their formation conditions. We review these developments in the present work. We review in detail the theory of atmospheric chemistry in all classes of exoplanets discovered to date, from highly irradiated gas giants, ice giants, and super-Earths, to directly imaged giant planets at large orbital separations. We then review the observational detections of chemical species in exoplanetary atmospheres of these various types using different methods, including transit spectroscopy, Doppler spectroscopy, and direct imaging. In addition to chemical detections, we discuss the advances in determining chemical abundances in these atmospheres and how such abundances are being used to constrain exoplanetary formation conditions and migration mechanisms. Finally, we review recent theoretical work on the atmospheres of habitable exoplanets, followed by a discussion of future outlook of the field.M. Agúndez acknowledges funding support from Spanish MINECO through grants CSD2009-00038, AYA2009-07304, and AYA2012-32032 and from the European Research Council (ERC Grant 610256: NANOCOSMOS). J. Moses thanks the NASA Exoplanet Research program NNX15AN82G for support. Y. Hu is supported by the National Natural Science Foundation of China 435 (NSFC) under grants 41375072 and 41530423