Maximum likelihood approach for several stochastic volatility models

Details Maximum likelihood approach for several stochastic volatility models Maximum likelihood approach for several stochastic volatility models

2012-04-16

arxiv.org/abs/1204.3556v1

Economy

Quantitative Finance

Computational Finance

10 pages, 13 figures

Scientific paper

Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility follow a two-dimensional diffusion process where volatility is the stochastic diffusion coefficient of the log-price dynamics. We apply this method to the expOU, the OU and the Heston stochastic volatility models and we study their performance in terms of the log-price probability, the volatility probability, and the mean first-passage for the log-price. The approach has some predictive power on the future returns amplitude by only knowing current volatility. The assumed models do not consider long-range volatility auto-correlation and the asymetric return-volatility cross-correlation but the method still arises very naturally these two important stylized facts. We apply the method to different market indexes and with a good performance in all cases.

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