MCFAM Seminar - From option values to additive models

Speaker: Lorenzo Torricelli

Abstract: We have recently found that certain simple no-arbitrage vanilla option values yield to implied price distributions of logistic type which are known to be infinitely-divisible. When a no-arbitrage term function is also supplied, the corresponding family of distributions  determines an additive pure jump process for the underlying security price, which turns out to be a martingale. The use of additive processes in finance dates back to little more than a decade and has proved to successfully model derivative prices on a large number of asset classes. We insert in such literature with a focus on parameter parsimony and simplicity of valuation, while at the same time being able to capture returns  skewness, kurtosis,  self-similarity and other important stylized facts.  

In order to improve the empirical performance of the models, it is possible to augment the logistic distributions with an additional skew parameter. This amounts to study martingale additive processes in the boarder class of generalized logistic and generalized Beta distributions. A second extension is obtained by randomizing the logistic scale parameter, an idea similar in spirit to stochastic volatility and Lévy subordination.