A simple iteration algorithm to price perpetual Bermudan options under the lognormal jump‐diffusion‐ruin process

We propose an analytical‐form framework for pricing perpetual Bermudan options (PBOs) under the lognormal jump‐diffusion‐ruin model of Merton (1976). We first analytically derive the holding and early exercise values of PBOs. The optimal exercise boundary of the PBO, determined by equating the holding and early exercise values, is then solved using an iteration algorithm. We finally evaluate the PBO by taking the expectation of the option prices at the subsequent exercisable date and discounting it at the risk‐free rate. The numerical results indicate that our method is far more efficient than the competing methods in the literature for pricing PBOs.