Modelo exponencial para opÃÃes: aplicaÃÃes ao Ãndice Ibovespa

AUTOR(ES)
DATA DE PUBLICAÇÃO

2007

RESUMO

In this thesis we perform an empirical analysis of the Brazilian stock and options markets. In the first part of our study we carry out a statistical analysis of the Ibovespa stock index of the SÃo Paulo Stock Exchange. It is shown that the daily returns of Ibovespa follow not a Gaussian distribution but rather an exponential law, in addition, this exponential distribution remains valid for returns calculated for time scales varying from one day up to 30 days. Using intraday quotes on the Ibovespa (15 minute intervals), it is found that this exponential distribution holds true for returns down to a 3 hours intervals, in agreement with previous study performed in our group. However, for short time scales, it is observed that the empirical distributions exhibit a less-than-exponential decay, with strong evidences of power-law tails. We then tested two important theoretical distributions that exhibit power-law decay, Levy distribution and the so called q-Gaussian distribution (also known as Tsallis distribution), to see which of them best matches the empirical data for the 15 minutes returns of the Ibovespa. It was found that the q- Gaussian distribution gave a better fit in the least-square sense. In the second part of the thesis, we study two relevant models of option pricing, namely, the standard Black-Scholes model and an empirical model that assumes an exponential distribution for the returns. Both models yield an analytical solution for the price of a European call option, which can be easily compared with the quoted market prices. More specifically, we make a comparative study between the market prices for call options on the Ibovespa stock and the corresponding predictions of both the Black-Scholes model and exponential model. It is shown that the exponential model gives a better fit to the empirical data for times close to the option expiration date, whereas for longer periods before expiration the Gaussian (Black-Scholes) model gives a better description of the market prices. This finding is in agreement with the results found in the first part of the thesis, where it was observed that for short time scales the Ibovespa returns obeys an exponential distribution

ASSUNTO(S)

econofÃsica mercado financeiro modelo de precificaÃÃo de opÃÃo econophysics option price model processo estocÃstico fisica financial markets retornos de alta-freqÃÃncia

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