Estimando a Densidade da Taxa de Câmbio Usando Modelos Paramétricos: o Caso do Brasil

Marcos Massaki Abe,Eui Jung Chang,Benjamin Miranda Tabak

doi:10.12660/rbfin.v5n1.2007.1164

Abstract

Este artigo emprega uma técnica paramétrica desenvolvida recentemente para extrair previsões de densidade para a taxa de câmbio doméstica, usando o mercado de opções cambiais. Os resultados empíricos sugerem que o mercado de opções contém informação útil sobre a densidade futura da taxa de câmbio. Estes resultados sugerem que previsões de densidade usando o mercado de opções podem adicionar valor à gestão de carteiras e de risco, e podem ser úteis para reguladores financeiros avaliarem estabilidade financeira.

Highlights

Recent research in the financial literature has investigated whether optionimplied distributions are useful in providing information regarding the future distribution of underlying asset prices (see Clews (2000) and Melick and Thomas (1997))
This paper argues for the use of the generalized beta density of second kind (GB2) for exchange rate returns in call option pricing models for the following reasons: 1. we have to estimate a small number of parameters, avoiding problems such as overfitting the data; 2. the parameters of the GB2 permit general combinations of the mean, variance, skewness and kurtosis, enabling the shape of the density to be flexible; 3. the real-world density has a closed form when one assumes the GB2 density, and 4; 4. recent literature suggests that the GB2 density forecasting accuracy performs quite well (see Tunaru and Albota (2005))
Density forecasting is essential for risk and portfolio management

Summary

Introduction

Recent research in the financial literature has investigated whether optionimplied distributions are useful in providing information regarding the future distribution of underlying asset prices (see Clews (2000) and Melick and Thomas (1997)). One of the most used distributions to extract density forecasts is the mixture of lognormals (see Ritchey (1990) and Melick and Thomas (1997)) These authors argue that the risk-neutral density of the asset price when options expire can be defined as a mixture of lognormal densities. Using data that covers the period from 2000 to 2005, the results of the study suggest that a parametric method, using the generalized beta density of second kind, is useful for density forecasting. This paper argues for the use of the generalized beta density of second kind (GB2) for exchange rate returns in call option pricing models for the following reasons: 1.

Risk neutral density

Data Sampling and empirical results

Findings

Conclusions