To enter into contracts and make payments with respect to the contracts.
We assume that the model enjoys the no-arbitrage property either with respect to the null contract or for the trading desk and we consider the hedger who contemplates entering into the contract (mathcal {C}^{t} ) at time t.
By applying Definition 19 to the null contract (mathcal {N}= 0,0)), we deduce that any regular market model is arbitrage-free for the hedger with respect to the null contract.
The mayor, however, seems to have taken a war footing with respect to the teachers contract that expired last spring.
They first verify the no-arbitrage property of their trading model with respect to the null contract in the case of a nonnegative initial endowment x.
We introduce the concept of no-arbitrage with respect to the null contract and a stronger notion of no-arbitrage for the trading desk.
A minimal no-arbitrage requirement for an underlying market model is that it should be arbitrage-free with respect to the null contract.
(mathcal {M}) has the no-arbitrage property with respect to the null contract, (mathcal {M}) has the no-arbitrage property for the trading desk, (mathcal {M}) is nonregular and the extended model Open image in new window where S3=P K) does not have the no-arbitrage property with respect to the null contract.
If no primary arbitrage opportunity exists in the market model (mathcal {M}) then we say that (mathcal {M}) has the no-arbitrage property with respect to the null contract for the hedger with an initial endowment x.
We contend that the drawback of the definition of an arbitrage-free model with respect to the null contract is that it does not make an explicit reference to a class Open image in new window of contracts under study.
On the one hand, a natural definition of a hedger's fair value (see Definition 15) is consistent with the concept of no-arbitrage with respect to the null contract and thus it seems to be theoretically sound.
