
arXiv: 0809.3375
AbstractWe study in details the skew of stock option smiles, which is induced by the so‐called leverage effect on the underlying B i.e. the correlation between past returns and future square returns. This naturally explains the anomalous dependence of the skew as a function of maturity of the option. The market cap dependence of the leverage effect is analyzed using a one‐factor model. We show how this leverage correlation gives rise to a non‐trivial smile dynamics, which turns out to be intermediate between the “sticky strike” and the “sticky delta” rules. Finally, we compare our result with stock option data, and find that option markets overestimate the leverage effect by a large factor, in particular for long dated options. Copyright © 2009 Wilmott Magazine Ltd
FOS: Economics and business, Statistical Finance (q-fin.ST), Physics - Data Analysis, Statistics and Probability, Quantitative Finance - Statistical Finance, FOS: Physical sciences, Pricing of Securities (q-fin.PR), Quantitative Finance - Pricing of Securities, Data Analysis, Statistics and Probability (physics.data-an)
FOS: Economics and business, Statistical Finance (q-fin.ST), Physics - Data Analysis, Statistics and Probability, Quantitative Finance - Statistical Finance, FOS: Physical sciences, Pricing of Securities (q-fin.PR), Quantitative Finance - Pricing of Securities, Data Analysis, Statistics and Probability (physics.data-an)
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