We are interested in constructing new martingales that share the same marginal distributions as an existing
martingale. The new martingales, known as mimics of the original martingale, preserve the prices of
European vanilla options but might have different properties. In this talk, I will review some previous results on
martingales mimicking and discuss martingales formed by functions of Brownian motions that admit a universal mimicking property. Specifically, we identify those martingales for which, with essentially any deterministic time change, the resulting time-space-transformed process remains a martingale and preserves the one-dimensional marginal distributions.
Joint work with Kais Hamza, JieYen Fan, and Fima Klebaner.