Multi-Level Monte Carlo Using Quasi-Random Numbers

• Activity Number: 255 - Contributed Poster Presentations: Section on Statistical Computing
• Type: Contributed
• Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Lu Vy* and Erin Austin and Yaning Liu
• Companies: University of Colorado Denver and University of Colorado Denver and University of Colorado Denver
• Keywords: quasi-MC; multi-level; estimator; pricing; estimation

Abstract

When modeling the value of an asset, the model complexity often exceeds the grasp of an analytic solution. When this is the case, simulation becomes the best alternative. What began in the Los Alamos Laboratories as Monte Carlo estimation evolved over the next 70 years to become something ubiquitous in financial mathematics. Today, Monte Carlo computational methods are so heavily used that pseudo-random numbers alone hardly suffice. Predicting the modern market requires efficiency, and to this end, a number of variance reduction techniques emerged. In this paper, we juxtapose two: these are a quasi Monte Carlo method utilizing random start digitally scrambled Halton sequences and the multi-level Monte Carlo estimator. We apply their combined advantages to various mathematical models in finance, including option pricing models, and compare the results with traditional Monte Carlo estimation.