The Single Period Binomial Model

Derivatives pricing and investment management seem to have little in common. Even at the organizational level, they belong to two quite separate parts of financial markets. The so-called sell side, represented mainly by the investment banks, among other things offers derivatives products to their customers. Some of them are wealth managers, belonging to the so-called buy side of financial markets. So far, the only universally accepted method of derivative pricing is based upon the idea of risk replication. Models have been developed which allow for perfect replication of option payoffs via implementation of a replicating and self-financing strategy. We call such models complete. The option price is calculated as the cost of this replication. Adjustments to the price are later made to cover for risks due to the unrealistic representation of reality. More accurate description of the market is given by the so-called incomplete models in which not all risk in a derivative product can be eliminated by dynamic hedging. However, this potential model advantage is hampered by another difficulty. Namely, the concept of price for a derivative contract is not uniquely defined. Many