An Explicit Finite Difference Approach to the Pricing Problems of Perpetual Bermudan Options

Abstract

Perpetual Bermudan options, Optimal stopping problems, Explicit finite difference methods, Linear complementarity problem, PSOR algorithm, Linear programming methods, Interior point methods,

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

“…Before showing the numerical results, we would like to emphasis that the ultimate goal of this paper is to price PBOs under the LJDR process. The parameters of option contracts examined in Table 1 are adapted from Table 2 of Ju (1998) and Table 4 of Muroi and Yamada (2008). Therefore, the accuracy and efficiency of our method can be clearly discerned when comparing with those PD-process-based methods.…”

“…With this setting, we calculate values of 500-year Bermudan options when Δt equals 0.0001, 0.00005, and 0.00001. The parameters of option contracts examined in Table 1 are adapted from Table 2 of Ju (1998) and Table 4 of Muroi and Yamada (2008). In addition, we consider the time interval between two exercisable time points, τ, to be 0.004 (daily), 0.02 (weekly), 0.083 (monthly), 0.25 (quarterly), 0.5 (semiannually), and 1 (annually).…”

“…Alobaidi, Mansi, and Mallier (2014) discretize the integrals in the Wiener-Hopf method to obtain a linear system and solve the system by the value-matching condition. Lattice-based solutions, such as binomial tree and explicit finite difference models, have been proposed by Lin and Liang (2007) and Muroi and Yamada (2008), respectively. Lattice-based solutions, such as binomial tree and explicit finite difference models, have been proposed by Lin and Liang (2007) and Muroi and Yamada (2008), respectively.…”

“…Ma and Luo (2012) express the expected payoff from holding a PBO as a sum of iterative integrals, since holders of the PBO will eventually earn the exercise value at one of the future exercisable time points. Lattice-based solutions, such as binomial tree and explicit finite difference models, have been proposed by Lin and Liang (2007) and Muroi and Yamada (2008), respectively.…”