Basis Function Choices in Least-Squares Monte Carlo Option Pricing

Summary

The document introduces basis-function selection in Longstaff–Schwartz least-squares Monte Carlo pricing for options on multiple underlyings. In this approach, continuation values are approximated with basis functions during backward induction, which determines an exercise policy. The author notes that an approximate policy can be suboptimal and yield a lower bound on the option price.

The question is why radial basis functions, commonly used to approximate unknown functions, appear less often in the literature than polynomial bases such as Chebyshev, Laguerre, and Legendre. The document frames the methodological issue but gives no answer, empirical comparison, or evidence explaining the reported preference. It therefore identifies a practical research question rather than establishing that radial basis functions are unsuitable or that polynomial bases are universally superior.

Key ideas

• Least-squares Monte Carlo approximates continuation values using basis functions in backward induction.
• The chosen approximation influences the exercise policy for an early-exercise option.
• A suboptimal exercise policy can produce a lower bound on the option price.
• The document asks why radial basis functions seem less common than polynomial bases but does not answer the question.
• It provides no comparative results establishing which basis family performs better.

Tags

# Are radial basis functions popular in least squares monte carlo option pricing?


# Are radial basis functions popular in least squares monte carlo option pricing?












In a Longstaff-Schwarz setting option on several underlyings can be priced using least squares monte carlo. Using suitable set of basis functions, continuation values can be approximated using backward induction, which gives suboptimal policy and a lower bound on option price.

However choice of basis functions is sometimes not trivial. Since RBFs are used quite often for approximating unknown functions I thought that RBFS should be popular choice for approximating continuation values for option pricing. However when I started searching, looking at different articles it seems like nobody uses RBFs, instead different polynomials (Chebyshev, Laguerre, Legendre) are used to approximate continuation values.

Could you please explain what is the reason for neglecting RBFs?

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