I am a bit confused about what the implication of "no-arbitrage" in popular term struchture models (such as affine term struchtre models or HJM models) are?

Is it solely a restriction on the cross-section of bonds/yields in the sense that at time $t$ arbitrage oppurtunities are excluded or does it also provide a restriction on the time series dimension of bonds/yields? I am confused since e.g. the HJM model provides a dynamic equation for the evolution of forward rates through time and I am unsure if this only implies that for each point in time $t$ oppurtunities are excluded or does it also imply that the dynamic evolution of bonds/yields cohere such that arbitrage oppurtunities are excluded?


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In the typical HJM model, during a single time step forward rates evolve according to their individual volatilities and according to pairwise correlations which can be specified. That arrangement is arbitrage free within the time step. In addition, different time steps are independently generated. This latter feature ensures that the model does not generate arbitrage possibilities through its "dynamic evolution", as you say. Does that address your question?

  • $\begingroup$ Yes, it does address my question and it is also corresponds to what I concluded. However, I found the following sentence in a paper of Duffee (2002): "No-arbitrage implies the existence of an equivalent-martingale measure, which imposes the restrictions of Duffie and Kan (1996) on this cross-sectional mapping." It confused me because he only writes cross-sectional mapping (and not time-series dimension) $\endgroup$ – Piotter Nov 24 '18 at 19:40

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