Volume 7, Issue 3
Primal-Dual Active Set Method for American Lookback Put Option Pricing

Haiming Song, Xiaoshen Wang, Kai Zhang & Qi Zhang

East Asian J. Appl. Math., 7 (2017), pp. 603-614.

Published online: 2018-02

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  • 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.

  • Keywords

American lookback option, linear complementarity problem, variational inequality, finite element method, primal-dual active set method.

  • AMS Subject Headings

35A35, 90A09, 65K10, 65M12, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-603, author = {}, title = {Primal-Dual Active Set Method for American Lookback Put Option Pricing}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.060317.020617a}, url = {http://global-sci.org/intro/article_detail/eajam/10767.html} }
TY - JOUR T1 - Primal-Dual Active Set Method for American Lookback Put Option Pricing JO - East Asian Journal on Applied Mathematics VL - 3 SP - 603 EP - 614 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.060317.020617a UR - https://global-sci.org/intro/article_detail/eajam/10767.html KW - American lookback option, linear complementarity problem, variational inequality, finite element method, primal-dual active set method. AB -

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.

Haiming Song, Xiaoshen Wang, Kai Zhang & Qi Zhang. (2020). Primal-Dual Active Set Method for American Lookback Put Option Pricing. East Asian Journal on Applied Mathematics. 7 (3). 603-614. doi:10.4208/eajam.060317.020617a
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