Speaker: Julien Guyon, Quantitative Research Group, Bloomberg LP
ABSTRACT
In this talk we will introduce the particle method and show how it solves a wide variety of smile calibration problems:
- calibration of the local volatility model with stochastic interest rates
- calibration of stochastic local volatility models, possibly with stochastic interest rates and stochastic dividend yield
- calibration to the smile of a basket of multi-asset local
volatility-local correlation models, possibly with stochastic volatility, stochastic interest rates, and stochastic dividend yields
- calibration of path-dependent volatility models and path-dependent correlation models
The particle method is a Monte Carlo method where the simulated paths interact with each other to ensure that a given market smile is fitted. PDE methods typically do not work for these high-dimensional models. The particle method is not only the first available exact simulation-based method. It is also robust, easy to implement, and fast (it is as fast as a standard Monte Carlo algorithm), as many numerical examples will show. As of today, it is the most powerful tool for solving smile calibration problems. Icing on the cake: there are nice mathematics behind the scenes, namely the theory of McKean stochastic differential equations and the propagation of chaos.