Analysis methods of the Russian financial market volatility for a wide class of models
Abstract
Analysis methods of the Russian financial market volatility for a wide class of models
Incoming article date: 25.12.2016The article considers a problem of the Russian financial market modeling and suggests wide classes of diffusion and jump models. The authors examine the adequacy of the diffusion models by means of quadratic variation analysis on the Russian financial market, which is used to construct the volatility index, the most important quantitative risk indicator in the financial market. It is shown that the existing volatility indexes RTSVX and RVI worse approximate the realized variation than the alternative index, based on the implied variation integration. Further analysis of power variation of log-returns for RTS index shows that Levy processes with unbounded variation without diffusion component better describe the dynamics of the Russian financial market. A new model-free formula for the volatility index is proposed in the class of Lévy processes. The new formula suggested is based on the variation representation via market option prices.
Keywords: mathematical modeling, numerical method, mathematical finance, volatility index, option, Levy process, diffusion model, quadratic variation, RTS index, derivatives market.