How would the introduction of option affect the market? In the well known binomial and Black-Sholes pricing models, one uses the noarbitrage principle to derive option prices. The principle implies that option can be replicated by stock and bond and is, therefore, a redundant asset. However, there are various types of options introduced to the financial market everyday, and their role becomes increasingly important in today’s financial activities. In the following, we review some of the discussions on the role of option and how option affects the market.
In an Arrow-Debreu[1] economy with uncertainty, if there exists a financial market with a sufficiently large number of linearly independent financial instruments, the market becomes complete and the welfare theorems are satisfied as in an economy without uncertainty.
When there are not enough independent financial assets in the market, the introduction of new options, provided that these options can not be replicated by existing assets, can improve welfare. When the market is incomplete, Detemple and Selden [4] point out that an additional financial derivative introduced to the existing market will interact with its underlying assets; thus, options are no longer redundant. New options increase the flexibility in allocating the future incomes for agents and aggregately affect the wealth distribution in the market.
Besides the incompleteness of the financial market, different beliefs in future stock prices may also be a reason to trade options. In the article of Hayne E. Leland [8], the author explains why agents choose to buy different options, and attributes it to the different beliefs agents have in the future process of stock prices. His discussion, however, is not undertook in the context of a general equilibrium model.
