In my humble opinion, Economics is mainly based on Equilibrium approach, while Finance is mainly based on Non-arbitrage approach..
The "equilibrium approach" can be used to value an asset or derivative under a very wide range of circumstances. Unfortunately, it is necessary to know something about the preferences of market participants (or agents), particulary their attitudes to risk. The "no-arbitrage approach" relies on the existence of a special kind of ultra-stable equilibrium to find a value for a derivative. The advantage of this approach is that it does not require any knowledge of agents' preferences. However, this approach can only be used under certain narrow assumptions. Equilibrium A market for some good or service is said to be in equilibrium at some price if the quantity offered for supply at that price is equal to the quantity demanded at that price. There may only be one price at which supply and demand can be equalised, in which case the equilibrium is said to be unique. Conversely there may be several prices at which supply and demand can be equalised (multiple equilibria) or no price at which supply and demand can be equalised (non-existence). An equilibrium may be either stable (in which case a market at an equilibrium price will quickly revert to that equilibrium price following a small price shock) or unstable (in which case the market price will rapidly move away from that equilibrium price following a small price shock). The amount of a good that is offered at various prices can be described by a supply curve (typically a function mapping price onto quantity offered for supply). Similarly, a demand curve describes the relationship between price and quantity demanded. The shapes of these curves determine whether an equilibrium exists, is unique, is stable or unstable. The shapes of these curves are determined in turn by the preferences of market agents and the constraints they face (such as the budget constraint for households). In finance, the supply and demand curves for assets and other financial quantities (such as implied volatility and interest rates) are also determined by agents preferences, particularly their attitudes to risk. Equilibrium models include the CAPM, in which financial assets are valued under the assumption that agents are mean-variance optimisers, i.e. that agents attitude to risk is to optimise the expected return in terms of variance of returns. Equilibrium pricing is a very general technique, however it does require some knowledge of the risk preferences of market agents. No-arbitrage pricing No-arbitrage pricing relies on the existence of a special kind of ultra-stable equilibrium known as an arbitrage. The advantage of this method is that it does not require any knowledge of agents' preferences. However, no-arbitrage pricing can only arise under a particular set of circumstances (or under a certain set of assumptions) relating to market completeness (see below). An arbitrage is a trading position either (1) that pays a positive cashflow on day one and requires no further cash to be paid or (2) that can be established at zero cost and that leads to one or more positive cashflows in the future. Black and Scholes used Merton's idea of no-arbitrage pricing in their paper on valuing European style options. If it can be shown that the pay-off of a derivative instrument can be exactly replicated using some combination of other existing instruments, then the price today of that derivative instrument must be the same as the price of that combination of other instruments. The other instruments (also known as the "replicating porftolio") give the same pay-off as the derivative instrument, so if the price of the derivative is different from the price of the replicating portfolio then an arbitrage would be possible. The existence of an arbitrage opportunity would in turn give rise to theoretically unlimited buying or selling by agents setting up arbitrage positions. This activity would swiftly restore the price of the derivative to its no-arbitrage value. In terms of equilibria, it can be seen that a no-arbitrage price is a unique ultra-stable equilibrium price. The only difficulty is that no-arbitrage pricing relies on the possibility of arbitrages. This in turn relies on the existence of a replicating porftolio. It can immediately be seen that no-arbitrage pricing can only be applied in circumstances where it is possible to form a portfolio that replicates the pay-off of the derivative under all circumstances. More formally, it requires that the market for the instruments in the replicating portfolio be complete, which, baldly speaking, means that these instruments trade continuously and without frictions such as transaction costs or taxes. In practice, bid-ask spreads mean that there will be a range of prices for which it is not possible to arbitrage some particular derivative. This range is sometimes known as the "arbitrage band", particularly with reference to stock index arbitrage. In cases of bid-ask spreads or other forms of market incompleteness it is not possible to form a portfolio that is exactly equal to the pay-off of the derivative under all states of the world. However, it may be possible to form a portfolio whose value is greater than or equal to the value of the derivative in all states of the world. Such a portfolio is known as a "super-replicating portfolio". The use of super-replicating portfolios enables no-arbitrage pricing arguments to be used in markets that are "nearly" complete. i.e. even if markets are not textbook complete, it is still possible to form a range of prices for a derivative such that arbitrage is not possible, thereby giving a range of prices for the derivative without recourse to agents' risk preferences. Summary No-arbitrage pricing can be used only where the markets for the underlying assets are complete. However, it is still possible to use no-arbitrage pricing for markets that are "nearly" complete either (1) by assuming away the incompleteness (useful for developed markets with, for example, very small transaction costs) or (2) by use of super-replicating portfolios. No-arbitrage pricing has the enormous benefit of allowing derivatives to be valued without any knowledge of agents' risk preferences. Equilibrium pricing can be used to value any security or asset, including derivatives on non-traded underlyings (e.g. derivatives on hedge funds) or derivative models with non-traded stochastic parameters (such as stochastic volatility models). Unfortunately the equilibrium approach requires assumptions to be made about agents' risk preferences.
[此贴子已经被作者于2005-7-28 10:51:42编辑过]
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