Pricing American Options Under High-Dimensional Models with Recursive Adaptive Sparse Expectations

49 Pages Posted: 11 Nov 2016 Last revised: 30 Aug 2018

See all articles by Simon Scheidegger

Simon Scheidegger

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne)

Adrien Treccani

University of Zurich

Date Written: August 28, 2018

Abstract

We introduce a novel numerical framework for pricing American options in high dimensions. Our scheme manages to alleviate the problem of dimension scaling through the use of adaptive sparse grids. We approximate the value function with a low number of points and recursively apply fast approximations of the expectation operator from an exercise period to the previous period. Given that available option databases gather several thousands of prices, there is a clear need for fast approaches in empirical work. Our method processes an entire cross-section of options in a single execution and offers an immediate solution to the estimation of hedging coefficients through finite differences. It thereby brings valuable advantages over Monte Carlo simulations, which are usually considered to be the tool of choice in high dimensions, and satisfies the need for fast computation in empirical work with current databases containing thousands of prices. We benchmark our algorithm under the canonical model of Black and Scholes and the stochastic volatility model of Heston, the latter in the presence of discrete dividends. We illustrate the massive improvement of complexity scaling over dense grids with a basket option study including up to eight underlying assets. We show how the high degree of parallelism of our scheme makes it suitable for deployment on massively parallel computing units to scale to higher dimensions or further speed up the solution process.

Keywords: American Options, Derivatives, Pricing, High-dimension, Adaptive sparse grids

JEL Classification: C61, C63, G12

Suggested Citation

Scheidegger, Simon and Treccani, Adrien, Pricing American Options Under High-Dimensional Models with Recursive Adaptive Sparse Expectations (August 28, 2018). Available at SSRN: https://ssrn.com/abstract=2867926 or http://dx.doi.org/10.2139/ssrn.2867926

Simon Scheidegger

University of Lausanne - School of Economics and Business Administration (HEC-Lausanne) ( email )

Unil Dorigny, Batiment Internef
Lausanne, 1015
Switzerland

Adrien Treccani (Contact Author)

University of Zurich ( email )

Sch├Ânberggasse 1
Z├╝rich, 8001
Switzerland

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