No-arbitrage bounds

Under the absence of arbitrage absence is understood any possibility of (economic) arbitrage. This term was coined especially for the financial markets. Due to the international electronic trading on these markets and the rapid global dissemination of new information to market participants the prices of their products fit in so quickly that arbitrage opportunities usually exist only for very short periods. Most thereby the transaction costs are higher than those achievable through arbitrage profits.

Importance

The absence of arbitrage is one of the basic assumptions of modern financial mathematics: In equilibrium models, the prices are determined as endogenous variables, that is, the prices will be adjusted depending on the supply and demand quantities until the market is in equilibrium. This process of adjustment has no effect on the prices of other goods. In the 1980s, the shortcomings of these models have become apparent as the based on them yield curves for fixed income derivatives did not correspond to the actual curves and thus to trade useless were, as they are not the law of the single price (English law of one price ) corresponded.

Arbitrage -free (even Engl. No- arbitrage or arbitrage - free ) models, however, determine the prices exogenous, ie market prices flow into the model directly, and their derived yield curves correspond to reality. The first interest rate structure compliant reviews have been made ​​possible by the work of Thomas Ho and Sang- Bin Lee and later David Heath, Robert Jarrow, and Andrew Morton. All currently used in practice for the evaluation of derivatives models are arbitrage-free.

Formal representation

Formally, the no- arbitrage condition can be described as follows: There is no portfolio with the value zero at time t0 = 0, that at t1 > t0 a certain non-negative value and with positive probability has a positive value.

Definitions

The following table shows the different no-arbitrage definitions in their demands to be read from left to right more. No free lunch means that there can be no position in which there is a safe consumption today, without getting anything in return today or tomorrow. No free lottery, that there can be no position in which one has a chance to win without having committed any money.