Moreover, we show that the resulting continuous tenor model is arbitrage-free and belongs to the class of affine term structure models.
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.
We show that the continuous tenor model is arbitrage-free, that the analytical tractability is retained under the spot martingale measure, and that under mild conditions an interpolating function can be found such that the extended model fits any initial forward curve.
An explicit example of a market model, which is arbitrage-free in the sense of Definition 10, but suffers from this deficiency, is analyzed in Section 4.2.3.
But where there is regulation there is arbitrage.
A minimal no-arbitrage requirement for an underlying market model is that it should be arbitrage-free with respect to the null contract.
The following result gives a sufficient condition for a market model to be arbitrage-free for the trading desk.
Then the market model Open image in new window is arbitrage-free for the trading desk.
Regrettably, the class of models that are arbitrage-free in the sense of Definition 14 seems to be too encompassing and thus it is still unclear whether the valuation irregularities mentioned in the preceding section will be completely eliminated (for an example, see Section 4.2.3).
The goal is to identify a class of nonlinear market models, which are arbitrage-free for the trading desk and, in addition, enjoy the desirable property that if a given contract can be replicated, then the cost of replication is also the fair price for the hedger.
The Vasicek model is one of the earliest no-arbitrage interest rate models based upon the idea of mean reverting interest rates.
