Signed, Sealed, Delivered: A Rough Path to Better Volatility Models
TL;DR for operators Options calibration has a familiar operational problem: the model that is fast enough to run every day is usually the model that assumes the market is behaving politely. The market, naturally, has other hobbies. This paper compares two ways of calibrating implied volatility surfaces. The first is the classical route: use model-specific analytical approximations for Heston and rough Bergomi. The second is the rough-path route: represent volatility as a linear functional of the truncated signature of a primary stochastic process.1 ...