Bass Construction with Multi-Marginals: Lightspeed Computation in a New Local Volatility Model

Abstract

The local volatility model is widely used as this is the unique one-factor Markov model perfectly calibrated to a continuum of vanilla options in strike and expiry. It requires unfortunately an arbitrage-free interpolation of implied volatility in expiry and a time-consuming Euler discretization scheme for its simulation. In this paper, we construct a new local volatility model, based on the extension of the Bass construction, which is (1) perfectly calibrated to vanilla options on market expiries and (2) is also a one-factor diffusion which can be discretized exactly as it requires only the simulation of a standard Brownian motion, providing very fast calculations.