Extending the Cox-Ross-Rubinstein algorithm for pricing options with exponential boundaries

It is a common belief that the standard binomial algorithm of Cox-Ross-Rubinstein (CRR) cannot be used to deal with barrier options with multiple or time-varying boundaries. We propose an extension of the CRR model to evaluate options with exponential boundaries. The essence of the extended binomial model relies upon the construction of a binomial tree for the underlying asset price dynamics, characterized by sets of nodes that mirror the barriers evolution. As a result, a very easy algorithm is derived that produces accurate prices with respect to the corresponding continuous time values. Moreover, numerical results show that the performance of the extended binomial algorithm is superior to that of the trinomial algorithms usually employed to price these options.