Option-pricing surrogates move past price alone: BeTINN cuts Heston sensitivity errors too

BeTINN extends a conditional neural solver's modulation from time alone to joint conditioning on time and the Heston model parameters, and keeps a joint residual pathway that processes the full state-time-parameter input directly. The earlier TINN let effective network weights vary along a single time direction, with model parameters entering the backbone only as ordinary inputs, so adaptation across the solution family had to be learned implicitly. In capacity-matched comparisons near 3.6 thousand parameters, BeTINN has the lowest mean absolute error on normalized option value, first-order sensitivities and second-order curvature; against TINN in paired seeds it wins on price, Delta and Vega in all six seeds and on Gamma in five of six.

Each modulated parameter group varies along several learned adaptation directions, and the conditioning network outputs only scalar coefficients over them, so effective weights lie in a low-dimensional affine subspace rather than being generated freely. Single-direction time-induced parameterization confined each group's time variation to one learned direction, where overly strong conditioning becomes a bottleneck and weak conditioning approaches an unconstrained joint-input network. For Heston the conditioning vector holds time and five model parameters while the backbone receives state and time; ablations show that parameter conditioning, gating, Fourier features or the joint residual pathway alone do not reproduce the full configuration's joint accuracy, and removing the joint residual pathway raises price, Delta and Gamma errors.

The main evaluation is the zero-dividend Heston stochastic-volatility pricing equation, where one surrogate must cover an eight-dimensional joint input, and reference values and sensitivities come from a semi-analytic solution used only for evaluation. Cross-PDE checks cover parametric Burgers and Wave without equation-specific architecture tuning.

Spearman correlations between validation physics loss and the four predictive errors range from 0.578 to 0.698, a moderate association, and architectures with similar validation loss can still differ in solution and derivative errors. Derivative fidelity is assessed empirically, with no formal guarantee of monotonicity, convexity or arbitrage consistency beyond the physics constraints; on parametric Wave the fixed configuration shows no systematic advantage over simpler baselines.