Pricing Bermudan Option with Variable Transaction Costs under the Information-Based Model

Abstract

The Bermudan option pricing problem with variable transaction costs is considered

for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an optimal

stopping problem, which is the val ue function of a stochastic control problem

given by a non-linear second order partial differential equation. The theory of

viscosity solutions is applied to solve the stochastic control problem such that

the value function is also the solution of the corresponding Bellman equation.

Under some regularity assumptions, the existence and uniqueness of the solution of the pricing equation are derived by the application of the Perron

method and Banach Fixed Point theorem.