# Drift-Invariance of Hypothesis Spaces

Discount curves are usually estimated day by day with kernel ridge regression, but a good daily fit does not guarantee that the estimated curves can serve as states of a continuous-time arbitrage-free model. This work asks whether the finite-dimensional hypothesis space of kernel ridge regression is invariant under the risk-neutral drift of the discount curve for every grid of cash flow dates. Apart from kernels whose Hilbert space has dimension at most two, only the family built from the Segal–Bargmann kernel qualifies; for that kernel the estimate is an affine combination of flat discount curves, and the drift-invariant subspaces that allow dimension reduction correspond to sub-grids of the cash flow dates.

Discount curves are usually estimated day by day with kernel ridge regression, but a good daily fit does not guarantee that the estimated curves can serve as states of a continuous-time arbitrage-free model. This work asks whether the finite-dimensional hypothesis space of kernel ridge regression is invariant under the risk-neutral drift of the discount curve for every grid of cash flow dates. Apart from kernels whose Hilbert space has dimension at most two, only the family built from the Segal–Bargmann kernel qualifies; for that kernel the estimate is an affine combination of flat discount curves, and the drift-invariant subspaces that allow dimension reduction correspond to sub-grids of the cash flow dates.