On pricing options with stressed-beta in a reduced form model

We consider the valuation of options with stressed-beta in a reduced form model. Under this two-state beta model, we provide the analytic pricing formulae for the European options and American options as the integral forms. Specifically, we provide the integral representation of the early exercise premium of an American put option. We use the quadrature method to evaluate the integral forms and we measure the performance of our pricing framework comparing the benchmarks set by the trinomial tree method. It turns out that our pricing framework with the quadrature methods are computationally efficient and accurate. We also calibrate the market data successfully.