If Not Now, Then When? Model Risk in the Optimal Exercise of American Options

Battle Count: 138

Highly relevant for practitioners trading American-style derivatives (e.g., equity-linked notes, convertible bonds, Bermudan options). The findings demonstrate that calibration to European option prices—even full surface calibration—does not eliminate model risk in exercise decisions, which is critical for desks managing American option portfolios. The recalibration analysis directly addresses common market practice. However, the paper is primarily theoretical/numerical rather than providing actionable trading signals or strategies.

High implementation complexity due to: (1) 2D PDE solution for Heston model with mixed derivative requiring ADI splitting schemes, (2) Brennan-Schwartz algorithm for variational inequalities, (3) Dupire local volatility calibration via constrained quadratic programming with bicubic spline interpolation, (4) Monte Carlo simulation with Milstein discretization, (5) non-uniform grid construction with sinh transformations, (6) cubic spline interpolation for exercise boundaries. The Modified Craig-Sneyd scheme and proper handling of boundary conditions add further complexity. Recalibration analysis requires ~5 million calibrations.

The paper provides detailed parameter values (Table 1), comprehensive numerical methodology descriptions including finite difference schemes, ADI splitting, calibration procedures (Andersen and Brotherton-Ratcliffe), and boundary conditions. Appendices A-D contain full implementation details for FD schemes, one-dimensional model numerics, Heston model numerics, and Longstaff-Schwartz validation. However, no code repository is provided, and the specific grid parameters and interpolation details would need to be carefully replicated.