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while it is true that $$\lim_{T\to\infty} Z(t, T) = \lim_{T\to\infty} e^{-r(T-t)} = 0$$ this is when $r$ is independent of time to maturity, a flat and constant yield curve. In practice, we use yield curves which vary depending on what day they are estimated and what maturity the ZCB is. If in fact $r(t, T)$ depends on today and the maturity then the ...


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This is something that banks don't do very well (in my opinion), but we can look to the insurance industry for help. Insurance liabilities often span decades, and the regulation has come up with something called the Ultimate Forward Rate (or UFR). It's currently a hotly debated topic with the advent of Solvency II (insurance regulation) coming into effect ...


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First, it's not true that a market sector is cheap whenever the forward curve lies above the par curve. In fact, whenever the yield curve is upward sloping, the forward curve will always lie above the par curve. Conversely, when the yield curve is downward sloping, forwards will always lie beneath the par curve. In the example you quoted, Ilmanen chose a day ...



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