This thesis focuses on a mathematical model developed to replicate and compute the implied volatility index by simply using the stock exchange daily returns as starting point. First, the thesis defines the theoretical background, introducing the main properties of volatility. Second, it describes the relationship between the VIX and the US stock market index SaP500, denoting their most relevant features. Third, it presents the model, by giving its mathematical background, the computation formula and by optimizing its parameters, in order to apply it unconditionally to several stock market indexes. The results suggest that the model reproduces, with a very high coefficient of determination the past data of the implied volatility indexes under review, enabling to recalculate their unknown past values. It achieves therefore the goal of recreating quickly and simply the implied volatility index, without the need of a basket of options.First, the thesis defines the theoretical background, introducing the main properties of volatility. Second, it describes the relationship between the VIX and the US stock market index Saamp;P500, denoting their most relevant features.

Title | : | Implied Volatility Model for Stock Market Indexes |

Author | : | Leonardo Falconi, Lorenzo Camponovo |

Publisher | : | - 2014 |

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