Hot answers tagged term-structure
5
Regarding your first question.
You can try to argue in the following manner. Using the fact that $E_{Q^t}[P(t,T)|\mathcal{F}_s]P(s,t)=P(s,T)$, then:
$$p(s)=\lim_{T\to\infty}P(s,T)^{\frac{1}{T}}=\lim_{T\to\infty}(P(s,t)E_{Q^t}[P(t,T)|\mathcal{F}_s])^{\frac{1}{T}}=\lim_{T\to\infty}E_{Q^t}[P(t,T)|\mathcal{F}_s]^{\frac{1}{T}}$$
as ...
2
Regarding your first question, let me reformulate $p(s)$:
$p(s)=(\frac{P(s,T)}{P(s,t)})^\frac{1}{T}=
\frac{e^{-\frac{(T-s)R(s,T)}{T}}}{e^{⁻\frac{(t-s)R(s,t)}{T}}}.$
Now, because $R(s,t)$ is finite, the term $e^{⁻\frac{t-s}{T}R(s,t)}$ converges to 1 for $T\to\infty$. On the other hand, the term $e^-\frac{(T-s)R(s,T)}{T}$ converges to ...
1
I would look at the following metrics when quantifying "liquidity" in listed options:
bid/offer spread
number contracts traded and from that follows notional traded (in the option not underlying)
frequency of bid/offer adjustments relative to changes in the underlying delta.
frequency of liquidity added/removed on the bid and offer side even when no ...
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