Pricing Ladder Options with Combinatorics

Exotic options are popular financial derivatives that play essential roles in financial markets. How to price them efficiently and accurately is very important both in theory and practice. The lattice model is usually used to price them. The prices computed by the lattice converge to the theoretical value under the continuous-time model. But the lattice model may produce quite slow convergence; and when it comes to such options as barrier options, the lattice often produces wild oscillation and huge amounts of computational time are required to achieve acceptable accuracy. This paper introduces combinatorial techniques to help improve the performance in pricing a special barrier option, the ladder option. Through a computer experiment, it is proved that our B. Q. LI, H. J. ZHAO and J. LEI 106 algorithm based on combinatorics compares favorably against popular lattice methods, which take at least quadratic time.