# Tag Info

2

Most practitioners think of option prices in terms of implied volatility. It is easier to interpret and to model. One can consider the implied volatility surface as a random field : $\Sigma : \Omega \times \mathbb{R}_+ \times \mathbb{R}_+ \to \mathbb{R}_+$ and apply PCA. The first 3 eigenmodes correspond to absolute level (ATM vol), slope in the strike ...

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I would personally go for a normal returns, because you do not make any assumptions about the data or returns. When we use log returns we assume that prices are distributed log normally (which, usually is very far from the truth). Moreover if you will investigate different distribution you will not use the log returns features like time additivity or ...

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Model them individualy and as a group. When you model them as a group you are essentially building a stock index that you can compare the performance of individual stocks to and can then calculate a subgroup beta for each stock. You can also calculate a beta coefficient for the group as a whole to the wider market. Since I assume that you are modeling them ...

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