Questions tagged [annuity]

The tag has no usage guidance.

3 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
3
votes
0answers
594 views

Properties of Geometric Brownian Motion Integrated w.r.t. Time (i.e., distribution of a Yor Process)

Let $S_t$ be a process which follows a Geometric Brownian Motion: $\frac{dS_\tau}{S_\tau} = \mu \,d\tau + \sigma \,dW_\tau$ By Ito's lemma, we have: $S_T = S_t e^{(\mu-{\sigma^2 \over 2})(T-t) + \...
1
vote
0answers
475 views

Why is the annuity factor proportional to the CV01?

For an asset with par amount of one unit (with a semiannual payment regime) we have $$\frac{C(T)}{2}\sum_{t=1}^{2T}d\Big(\frac{t}{2}\Big) + d(T) = 1$$ $$\implies\frac{C(T)}{2}A(T) + d(T) = 1,$$ ...
1
vote
0answers
52 views

Pricing with-profit/smoothed bonus annuity using Black-Scholes

Would this be possible? Subsequently, would the pricing of such an annuity be somewhat similar to pricing a lookback option?