Neural Network Methods in the 2BSDE Formalism for Solving the High-Dimensional Black--Scholes Equation with Transaction Costs
In briefNeural network solver for high-dimensional Black-Scholes pricing with transaction costs
SummaryThe paper formulates a 2BSDE system for a (D+1)-dimensional Black-Scholes PDE under the Leland transaction cost model, which accounts for the sign of the curvature. The system takes the curvature's speed (its derivative) as input. A single ResNet neural network learns both the PDE solution and the free degrees of freedom in the curvature matrix. It prices derivatives such as call options and butterfly spreads on geometric baskets, achieving a time-averaged RMSE below 0.1 for D=10 and D=100.