Topic 1: Forwards and Future Contracts
Arbitrage in financial markets
The absence of arbitrage in investment decisions occurs when strategies entailing zero risk have the risk-free rate of return. Therefore zero payoffs are result of zero initial invest- ments. This definition of arbitrage is a generalization of the law of one price (LoOP) that asserts that two assets traded in the same market under the same conditions should have the same price. Hence if two assets have different prices there exists an arbitrage opportu- nity by buying the asset at the lower price and selling it at the higher price. Individuals adopting this strategy make a profit out of nothing (without taking any risk). It is obvious that this strategy cannot persist long by the driving forces of the market.
The concept of absence of arbitrage places restrictions on asset prices to be consistent with market equilibrium. Arbitrage itself does not provide criteria for investors to choose their portfolios and in turn cannot determine asset prices. This assumption on market behavior just rules out the existence of prices incompatible with equilibrium market con- ditions.
Arbitrage is defined by the actions seeking secure profits in investment decisions but without bearing any risk. An arbitrage portfolio satisfies the following conditions.
The wealth of the initial portfolio is zero. Assets can be held in positive and negative amounts but the net value of the portfolio is zero.
The portfolio is risk-free and provides positive or at least null payoffs in every state of the nature.