In layman’s language, a contingent-claims market can be understood by comparing it with betting in a horse race. The state of the world corresponds to how the various horses will place, and a claim corresponds to a bet that a horse will win. If your horse comes in, you get paid in proportion to the number of tickets you purchased. But ex ante you do not know which state of the world will occur. The only way to guarantee payment in all states of the world is to bet on all the horses.
The state-preference model is an alternative way of modeling decision under uncertainty. Consumers trade contingent claims, which are rights to consumption, if and only if a particular state of the world occurs. In the insurance case, in one state of the world the consumer suffers a loss and in the other, she or he does not; however, ex ante he does not know which state will occur, but wants to be sure to have consumption goods available in each state.
In a corporate context Deman (1994) identified basically two theories of takeovers: (1) agency theory, and (2) incomplete contingent claims market. The latter theory hypothesizes that takeovers result from the lack of a complete state-contingent claims market. The main argument can be summarized briefly. If complete state-contingent claims markets exist, then shareholders’ valuations of any state distribution of returns are identical (because of one price for every state-contingent claim) and hence, they agree on a value-maximizing production plan. However, in the absence of complete-st ate contingent claims markets, any change in technologies (i.e. a change in the state distribution of payoffs) is not, in general, valued identically by all shareholders. Thus, majority support for such a change in plan may be lacking. Takeover is a contingent contract which enables a simultaneous change in technologies and portfolio holdings.
Merton (1990) describes some commercial examples of contingent claims which include: futures and options contracts based on commodities, stock indices, interest rates, and exchange rates, etc. Other examples are Arrow-Debreu (AW) securities, which play a crucial role in general equilibrium theory (GE), and options. Under AW conditions, the pricing of contingent claims is closely related to the optimal solutions to portfolio planning problems. Thus, contingent claims analysis (CCA) plays a central role in achieving its results by integrating the option-pricing theory with the optimal portfolio planning problem of agents under uncertainty.
One of the salient features of CCA is that many of its valuation formulae are by and large or completely independent of agents’ preferences and expected returns, which are some times referred to as risk neutral valuation relationships. Contributions to CCA have adopted both continuous and multiperiod discrete time models. However, most of them are dominated by continuous time, using a wide range of sophisticated mathematical techniques of stochastic calculus and martingale theory. There are several other facets of contingent claims, such as the option price theory of Black and Scholes (1973), and Merton (1977), general equilibrium and pricing by arbitrage illustrated in Cox et al . (1981), and transaction costs in Harrison and Kreps (1979). CCA, from its origin in option pricing and valuation of corporate liabilities, has become one of the most powerful analysis tools of intertemporal GE theory under uncertainty.
