QuantLab Research

Classical solvers, scientific ML & operator learning.

A controlled comparison of finite-difference methods, PINNs and DeepONets for American option pricing, evaluated on accuracy, computational cost and repeated-query efficiency.

Experiment 01

American Put — Solver Accuracy

CRR provides the reference solution. Projected Crank–Nicolson is compared with two PINN formulations across a common spot-price grid.

Method	MAE	RMSE	Max error	ATM error	Training / solve	Inference
CRR benchmark	0.000000	0.000000	0.000000	0.000000	59.252751 s	—
Projected Crank–Nicolson	0.001386	0.002399	0.008078	0.006499	0.051331 s	—
PINN V1 obstacle_penalty	0.577899	0.907986	1.704741	0.096848	24.408700 s	0.005155 s
PINN V2 fischer_burmeister	0.124013	0.148751	0.357380	0.129387	44.907313 s	0.005575 s

American put pricing comparison between CRR, projected Crank Nicolson, PINN V1 and PINN V2. — The full pricing functions are compared over the same spot-price interval rather than at a single at-the-money point.

Absolute pricing errors for projected Crank Nicolson and PINN models. — Absolute error relative to the high-step CRR benchmark reveals where each solver performs well and where approximation quality deteriorates.

Training loss curves for American option PINN V1 and PINN V2. — The obstacle-penalty and complementarity-aware formulations are compared through their optimisation trajectories.

Experiment 02

Operator Generalisation

DeepONet learns the mapping from option parameters and evaluation coordinates to American put values generated by the classical solver.

MAE

0.199122

RMSE

0.259732

Median error

0.161657

95% error

0.538324

Max error

1.232681

Branch operator

Pricing problem

strikeratevolatilitymaturitydividend_yield

Trunk operator

Evaluation coordinates

spottime

American option DeepONet training loss. — Training loss for the operator network learning a family of American-put pricing solutions.

American DeepONet predictions compared with projected Crank Nicolson target prices. — Predicted American option values are compared with projected Crank–Nicolson targets on previously unseen parameter sets.

Experiment 03

When does operator learning pay off?

DeepONet has an expensive offline stage but very cheap online inference. This experiment measures the point at which repeated pricing queries recover that upfront cost.

Projected CN

1.545e-2

seconds / query

DeepONet

6.735e-7

seconds / query

Measured online speedup

22933.34×

Break-even

2,053

approximate pricing queries required before the offline data-generation and training cost is recovered.

Data generation

3.04 s

Training

28.66 s

Total offline cost

31.70 s

Interpretation

Classical solvers remain the accuracy baseline.

The scientific-ML methods are evaluated not simply on whether they reproduce an option price, but on whether their additional training cost is justified by generalisation and repeated-query performance. This makes the comparison fundamentally about computational regimes rather than declaring one method universally superior.

Classical solvers, scientific ML & operator learning.

American Put — Solver Accuracy

American put solution comparison

Error profile across spot

PINN training convergence

Operator Generalisation

Pricing problem

Evaluation coordinates

DeepONet training convergence

Out-of-sample operator predictions

When does operator learning pay off?

Classical solvers remain the accuracy baseline.