In this presentation, I discuss new simulation algorithms for the Heston model. These algorithms are based on recent results showing that the Heston model presents an explicit weak solution that can be used for simulating volatilities and option prices. Most often, efficient simulation is done under an artificial reference probability and then converted to the real probability with the appropriate likelihood. The resulting simulation algorithm can therefore be seen as the analog of a weighted particle filter. It is then natural to introduce some type of resampling to improve the performance of the simulation algorithm. Here we focus on recently developed branching algorithms which have the advantage of preserving the historical property of the particle system. Through numerical results, we illustrate the increased performance and accuracy due to branching. We also compare the resulting simulation algorithm to popular Heston simulation methods.

Anne MacKay is an Assistant Professor in the Department of Mathematics at Université du Québec à Montréal since June 2016. She was previously a postdoctoral fellow at Risklab, at ETH Zurich. Her research is at the intersection of actuarial science and financial mathematics, and is generally focused on the risk management of long-term financial guarantees. She received her Ph.D. in Actuarial Science from the University of Waterloo in 2014.