New answers tagged forward
It is the former. Martingales are defined by filtration and probability space. The probability space for the filtration need not be the same as the probability space for the martingale. I think? That's what my prof said (iirc).
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 ...
The negative solution does not satisfy $P(T,T)=P(t,t)=1$
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