An analysis of least squares regression and neural networks approximation for the pricing of swing options

Christian Yeo

Papers from arXiv.org

Abstract: Least Squares regression was first introduced for the pricing of American-style options, but it has since been expanded to include swing options pricing. The swing options price may be viewed as a solution to a Backward Dynamic Programming Principle, which involves a conditional expectation known as the continuation value. The approximation of the continuation value using least squares regression involves two levels of approximation. First, the continuation value is replaced by an orthogonal projection over a subspace spanned by a finite set of $m$ squared-integrable functions (regression functions) yielding a first approximation $V^m$ of the swing value function. In this paper, we prove that, with well-chosen regression functions, $V^m$ converges to the swing actual price $V$ as $m \to + \infty$. A similar result is proved when the regression functions are replaced by neural networks. For both methods (least squares or neural networks), we analyze the second level of approximation involving practical computation of the swing price using Monte Carlo simulations and yielding an approximation $V^{m, N}$ (where $N$ denotes the Monte Carlo sample size). Especially, we prove that $V^{m, N} \to V^m$ as $N \to + \infty$ for both methods and using Hilbert basis in the least squares regression. Besides, a convergence rate of order $\mathcal{O}\big(\frac{1}{\sqrt{N}} \big)$ is proved in the least squares case. Several convergence results in this paper are based on the continuity of the swing value function with respect to cumulative consumption, which is also proved in the paper and has not been yet explored in the literature before for the best of our knowledge.

Date: 2023-07
New Economics Papers: this item is included in nep-cmp
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2307.04510 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2307.04510

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().