How to use self-similarities to discover similarities of path-dependent options (Q2725586)

The author considers options on foreign exchange in the Garman-Kohlhagen framework. Is is shown how self-similarities can be used in order to find the relations between lookback, Asian, passport, and imperfectly hedged European options and to establish the fact that the valuation formulas for all these options are remarkably similar in nature. E.g. a Partial Differential Equation (PDE) based derivation (combining self-similarity, splitting, and Laplace transforms) of the standard valuation formula for Asian calls is given. It turns out that, in general, there is an interesting duality between the PDE approach (using the concept of self-similarity) and the probabilistic approach based on the concept of Lévy's local time.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00019].