A comparative study of tree - based models and their applications in modern nance

Abstract

The Binomial option pricing model plays an integral role in modern nance due to its simplicity to implement and pedagogical value. There are two ways of extending the Binomial model on one source of underlying risk. The rst is to expand the number of possible states after each time step which results in the multinomial model. The second is to increase the number of sources of underlying risk. In this dissertation, the extension of the Binomial model in both cases is discussed. Numerical investigation is done to evaluate convergence patterns and computational intensity of a number of non-vanilla options. These include rainbow, basket and digital options, as well as convertible bonds. Theoretical and actual convergence is discussed and compared.