International audienceThe article focuses on the leverage effect modeling as a form of stochastic processes through the volatility model. It states that leverage effect is characterized by a subsequent stock price dropping and increase in volatility. It mentions that the first model that describes the volatility and price relations known as Constant Elasticity of Variance Model (CEV) was developed by Cox
International audienceIn the aftermath of the 2008 financial crisis, the need to consider more realistic risk models for derivative products has received renewed attention. We introduce a dynamic model for the pricing of European-style options with various attractive features such as a mixture of heavy-tails and Gaussian distribution along with a leverage effect property. We test the model on FTSE 100 stock index options during the period of January 2008 to June 2009. Our empirical results show that the model adequately fits the volatility smile dynamics particularly during stress periods. Furthermore, we find that the leverage effect form is driven by the sticky-strike rule
The correlation matrix is the key element in optimal portfolio allocation and risk management. In particular, the eigenvectors of the correlation matrix corresponding to large eigenvalues can be used to identify the market mode, sectors and style factors. We investigate how these eigenvalues depend on the time scale of securities returns in the U.S. market. For this purpose, oneminute returns of the largest 533 U.S. stocks are aggregated at different time scales and used to estimate the correlation matrix and its spectral properties. We propose a simple lead-lag factor model to capture and reproduce the observed time-scale dependence of eigenvalues. We reveal the emergence of several dominant eigenvalues as the time scale increases. This important finding evidences that the underlying economic and financial mechanisms determining the correlation structure of securities depend as well on time scales.
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