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Least Squares regression was first introduced for the pricing ofAmerican-style options, but it has since been expanded to include swing optionspricing. The swing options price may be viewed as a solution to a BackwardDynamic Programming Principle, which involves a conditional expectation knownas the continuation value. The approximation of the continuation value usingleast squares regression involves two levels of approximation. First, thecontinuation value is replaced by an orthogonal projection over a subspacespanned by a finite set of $m$ squared-integrable functions (regressionfunctions) yielding a first approximation $V^m$ of the swing value function. Inthis paper, we prove that, with well-chosen regression functions, $V^m$converges to the swing actual price $V$ as $m \to + \infty$. A similar resultis proved when the regression functions are replaced by neural networks. Forboth methods (least squares or neural networks), we analyze the second level ofapproximation involving practical computation of the swing price using MonteCarlo simulations and yielding an approximation $V^{m, N}$ (where $N$ denotesthe 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 squaresregression. 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 theswing value function with respect to cumulative consumption, which is alsoproved in the paper and has not been yet explored in the literature before forthe best of our knowledge.

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