Modeling Returns of Stock Indexes through Fractional Brownian Motion Combined with Jump Processes and Modulated by Markov Chains

Carpinteyro, Martha and Venegas-Martínez, Francisco and Martínez-García, Miguel Ángel (2018): Modeling Returns of Stock Indexes through Fractional Brownian Motion Combined with Jump Processes and Modulated by Markov Chains.

Abstract

We develop a mathematical model useful to describe the stochastic dynamics and return distribution of the stock indexes of world’s main economies (USA, Eurozone, UK and Japan) and of the main emerging markets (China, Brazil, and México) incorporating risk factors as: idiosyncratic volatility, market volatility, and regime-switching volatility. It is assumed that the returns of the stock indexes are driven by fractional Brownian motions combined with Poisson processes and modulated by Markov chains. To do that, we calibrate Jump-GARCH models and estimate Markov regime-switching stochastic volatility models. The proposed models properly describe the stochastic dynamics of the returns of the stock indexes under study during 1994-2017. The main empirical finding is that the USA stock market stays in high volatility most of the time and presents more jumps than other indexes, and that Brazil stock market has the biggest intensity of jumps during 1994-2017. The outcome supports the hypothesis of long-term memory of stock markets.

Resumen: Esta investigación desarrolla un modelo matemático útil para describir la dinámica estocástica y la distribución de los rendimientos de los índices bursátiles de las principales economías del mundo (EE.UU. Zona Euro, Reino Unido y Japón) y de los mayores mercados emergentes (China, Brasil y México) mediante la incorporación de factores de riesgo como: volatilidad idiosincrática, volatilidad del mercado y volatilidad de cambio de régimen. Se supone que los rendimientos de los índices bursátiles son conducidos por movimientos fraccionales brownianos combinados con procesos de Poisson y modulados por cadenas de Markov. Para lograr este objetivo se calibran modelos Jump-GARCH y se estiman modelos de volatilidad estocástica de cambio de régimen markoviano. Los modelos propuestos describen adecuadamente la dinámica estocástica de los rendimientos de los índices bursátiles bajo estudio durante 1994-2017. Los principales hallazgos empíricos reflejan que el mercado de capitales de EE.UU. se mantiene en alta volatilidad la mayor parte del tiempo y presenta más saltos que los otros índices y el mercado accionario de Brasil presenta grandes saltos con mayor intensidad. El resultado sostiene la hipótesis de memoria de largo pazo en el mercado de capitales.

• Item Type: MPRA Paper
• Language: English
• Keywords: Stock index return, fractional Brownian motion, Markov regime-switching, jump processes.
• Subjects: G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets

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