Questions tagged [annuity]

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Deferred mortality probabilities (mortality table)

My question has to do with drawing correct conclusions regarding deferred mortality probability from a mortality table. I am looking at the table below (source). In it, the $q_x$ (2nd columns) is ...
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Find a relationship between the present value and future value of an annuity [closed]

The following is a previous examination question in Financial Mathematics: If $A, r, n, PV$ and $FV$ represents the ordinary annuity (annuity immediate) amount, rate of interest, number of years, ...
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185 views

Present Value versus. Future Value of an Annuity Due

To determine the present value of an annuity due, 1 is added to the discount factor of the ordinary annuity. However, to determine the future value of an annuity due, 1 is removed from the discount ...
1 vote
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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 $$\frac{C(T)}{2}\sum_{t=1}^{2T}d\Big(\frac{t}{2}\Big) + d(T) = 1$$ $$\implies\frac{C(T)}{2}A(T) + d(T) = 1,$$ ...
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Put-call parity for cash settled swaptions

The Euro swaption market is changing from cash to physical settlement quotation in July 2018 $-$ see e.g. "Euro swaptions market prepares for pricign revamp (Risk, 2018)". When describing ...
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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) + \...
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962 views

Increasing Annuities [closed]

Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the first month, 4 at the end of the second month, and for each month thereafter the payment increases by 2. The nominal ...
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1 vote
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Is there a formula for present value of a growing annuity with yearly payment growth and monthly payments? [closed]

I have seen formulas that have cracked the future value of growing annuity where there are monthly payments and yearly growth rates. But given a future value, is it possible to derive the present ...
79 views

NPV of two annuities

For exam preparation we are given some past papers, however there are no solutions and I would like to know if my logic is correct for the following question: Assume you are 25 years old. An ...
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1 vote
58 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?
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