Lévy processes — stochastic processes with jumps — are the bedrock of modern financial modeling. From the Variance Gamma model to the CGMY framework, these models have replaced Brownian motion in capturing the reality of financial returns: asymmetry, fat tails, and sudden discontinuities. But what if we told you these processes don’t just live on probability distributions — they live on manifolds? ...
One of the most sacred assumptions in financial modeling is the existence of a traded risk-free asset. It anchors discounting, defines arbitrage boundaries, and supports the edifice of Black–Scholes. But what happens when you remove this pillar? Can we still price options, hedge risk, or extract information about funding conditions? In a striking extension of the Lindquist–Rachev (LR) framework, Ziyao Wang shows that not only is it possible — it may reveal financial dynamics that conventional models obscure. ...