In this chapter, we looked at a number of numerical procedures in derivative pricing the most common being options. One such procedure is the use of trees, with binomial trees being the simplest structure to model asset information, where one node extends to two other nodes in each time step, representing an up state and a down state respectively. In trinomial trees, each node extends to three other nodes in each time step, representing an up state, a down state, and a state with no movement respectively. As the tree traverses upwards, the underlying asset is computed and represented at each node. The option then takes on the structure of this tree and, starting from the terminal payoffs, the tree traverses backward and toward the root, which converges to the current discounted option price. Besides binomial and trinomial trees, trees can take on the form of the Cox-Ross-Rubinstein, Jarrow-Rudd, Tian, or Leisen-Reimer parameters.

By adding another layer of nodes around our tree, we...