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.