Seminar in Finance

This talk surveys recent research tackling the inherent challenges of path dependence in finance. First, we present the Functional Taylor Expansion (FTE), at the junction of Dupire’s Functional Itô Calculus and path signature. The FTE is a powerful tool to linearly decompose path functionals from future scenarios. Among many applications, the FTE leads to new Greeks–notably the Libra, enabling fast computation of risk measures.

We then move to a unified, occupation-time framework that enables finite-dimensional Markovian lifts. We demonstrate the omnipresence of occupation times across financial instruments, and on the modeling side, introduce Local Occupied Volatility (LOV). By design, the LOV model guarantees perfect calibration to European vanilla options while offering additional flexibility to fit other instruments or capture stylized facts of volatility.

Partly based on joint work with Bruno Dupire (Bloomberg).

The talk will be mainly based on these works: 

1. https://link.springer.com/chapter/10.1007/978-3-031-97239-3_6 (Open Access)

2. https://www.sciencedirect.com/science/article/pii/S0304414926000220?dgcid=author

Above link gives open access until March 25. Otherwise the (extended) preprint can be found here
https://arxiv.org/pdf/2311.07936