In the paper by D. Filipović (1999), he summarizes that "all consistent Ito processes have essentially deterministic dynamics". It seems to me that the paper assumes Ito processes for each of the parameters of the Nelson-Siegel forward rate curve, and then concludes that by doing so, there does not exist any interest rate model that ensures the absence of arbitrage.

Question 1 So does this mean, if I were to assume stochastic processes for the parameters of the Nelson-Siegel, I would essentially obtain bond prices/yield curve values that would allow for arbitrage opportunities and are thus, theoretically unsound? Or am I looking at this the wrong way?

Would appreciate any insight by someone who has read the paper and/or has much idea about the relevance of "consistency" in an interest-rate model?

Question 2 (not really specific to this paper alone): It says that if the drift and volatility coefficients of an Ito process $Z$ are progressively measurable, then $Z$ is not Markov. Why is this? Is it because $Z$ becomes a semimartingale?



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