Year: 2017
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 3 : pp. 603–614
Abstract
The pricing model for American lookback options can be characterised as a two-dimensional free boundary problem. The main challenge in this problem is the free boundary, which is also the main concern for financial investors. We use a standard technique to reduce the pricing model to a one-dimensional linear complementarity problem on a bounded domain and obtain a corresponding variational inequality. The inequality is discretised by finite differences and finite elements in the temporal and spatial directions, respectively. By enforcing inequality constraints related to the options using Lagrange multipliers, the discretised variational inequality is reformulated as a set of semi-smooth equations, which are solved by a primal-dual active set method. One of the major advantages of our algorithm is that we can obtain the option values and the free boundary simultaneously, and numerical simulations show that our approach is as efficient as some other methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.060317.020617a
East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 3 : pp. 603–614
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: American lookback option linear complementarity problem variational inequality finite element method primal-dual active set method.
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