American pandemic options under a stochastic SIR model with degenerate diffusion

• The valuation of American pandemic options under SIR dynamics yields a degenerate free-boundary problem. • A coordinate-rotated upwind scheme stabilizes transport-dominated boundary dynamics. • Numerical tests confirm first-order spatial accuracy and non-negativity. • Volatility exhibits a dual effect on optimal exercise timing across epidemic phases. We computationally study the valuation of American-style contingent claims written on epidemic indicators under a stochastic Susceptible–Infectious–Recovered (SIR) model with degenerate diffusion. Epidemic dynamics evolve on a constrained triangular state space induced by population conservation, where the diffusion coefficient vanishes along the boundary corresponding to the exhaustion of susceptible individuals. This structural degeneracy gives rise to a nonlinear free-boundary problem formulated as a Hamilton–Jacobi–Bellman variational inequality. We first establish the well-posedness of the stochastic SIR model by proving the existence, uniqueness, and positivity of solutions. The American pandemic call option is then formulated as an optimal stopping problem, leading to a variational inequality defined on the triangular domain. Our primary contribution lies in a coordinate transformation that aligns the degenerate diagonal boundary with the computational grid. This eliminates staircase artifacts, reduces spurious oscillations near the boundary, and enables a consistent treatment of the boundary transport dynamics. Such stability is important in financial applications, since oscillatory artifacts may lead to economically inconsistent option values. Numerical experiments show that the option value is concave with respect to the infectious population, reflecting the saturation effect inherent in SIR dynamics. Furthermore, we find that higher volatility creates a trade-off between two opposing effects: it suppresses the epidemic’s growth potential on one hand, while simultaneously supporting the option value through financial convexity on the other.