Questions tagged [annuity]
The annuity tag has no usage guidance.
26
questions
0
votes
1
answer
42
views
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 ...
- 101
0
votes
1
answer
61
views
How do I determine the ideal selling price for a cash flow that rises with inflation?
Let's say I own a parking space. I have two options:
I can rent out this parking space for $1,000/month. I am assuming that the rent will keep pace with inflation, which we'll call 2% over the long ...
0
votes
0
answers
62
views
Example of a simple transparent indexed annuity?
I am working on a University project where I need to provide a 2-page overview of
An indexed annuity, which uses zero coupon bonds and options; the underlying of the options are a broad market index.
...
- 153
0
votes
1
answer
103
views
Calculating present value of a bond (understanding a step)
Our professor calculated the present value of a bond with $T=10$ years, $FV=10,000$€, $C=700$€ p.a. and an expected rate of return $r$. He wrote $$\begin{align}PV&=C\cdot\sum_{n=1}^{10}\frac{1}{(1+...
- 109
0
votes
1
answer
56
views
How to simply calculate future value of periodic contributions to an index fund account?
So, for the sake of simplicity, ignoring taxes, expense ratio, volatility or anything else other than known values for the following five variables:
Starting contribution (dollars)
Annual ...
-3
votes
1
answer
32
views
Finding the period for annuities [closed]
I've got a question relating to annuities which I'm stuck on.
You intend to retire when you are 60 and predict you will die when you are 90. You want 50,000 a year for a comfortable retirement, and ...
0
votes
1
answer
51
views
Hypothesis regarding a recursive annuity loan
I have a question regarding an annuity loan calculation and I would like to prove whether the hypothesis I am stating is correct:
Consider an annuity loan $L_{1}$, with a principal of $T_{1} = 100$ ...
- 113
0
votes
1
answer
214
views
How to price an Annuity
When we price a fixed rate bond using Quantlib, we generally take below approach -
...
- 858
1
vote
0
answers
59
views
Why are cashflows "modelled backwards in time"?
A am currently reading a manual on how to use some actuarial modelling software to project the expected liability payments made under an annuity contract. In this guide, the following statement is ...
- 175
0
votes
2
answers
109
views
What is the present value of an immediate annuity over 12 years with 4 yearly payments and an interest of i = 2%?
See the question above, the result should be 10.689.
I tried using the temporary annuity-due formula (see below):
$$
\ddot{\mathbf{a}}_{n}^{[m]}=\frac{1-v^{n}}{d^{[m]}}
$$
where:
$$
d^{[m]}=m \cdot\...
- 3
3
votes
1
answer
579
views
Constant Maturity Swap dates and conventions
Let's note $L(t,T_i,T_{i+1})$ the libor rate observed at $t$, fixing at $T_i$ with delivery at $T_{i+1}$.
The natural delivery date for this rate is $T_{i+1}$, so a vanilla swap with no pay lag would ...
- 31
1
vote
1
answer
536
views
Calculation of Combined IRR
How to calculate combined IRR for two different cost of funds? The emi (Equated Monthly Installment) amount, whether it is calculated separately or based on the combined IRR should be same. I tried ...
- 11
3
votes
1
answer
6k
views
Swaption annuity factor
In H. Corb's book about interest rate swaps and oder derivatives, the present value of an T into n payer swaption is given via
$A\sigma\sqrt{T}\left[\frac{1}{\sqrt{2\pi}}e^{-\frac{d^2}{2}}+d\,\...
- 31
-1
votes
1
answer
73
views
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, ...
- 101
0
votes
1
answer
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
1
vote
0
answers
3k
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
$$\frac{C(T)}{2}\sum_{t=1}^{2T}d\Big(\frac{t}{2}\Big) + d(T) = 1$$ $$\implies\frac{C(T)}{2}A(T) + d(T) = 1,$$
...
- 439
8
votes
2
answers
4k
views
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 ...
- 8,169
3
votes
0
answers
1k
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) + \...
- 3,015
-1
votes
1
answer
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 ...
- 1
1
vote
1
answer
3k
views
Mark to Market of a CDS Contract and Risky Annuities
From JP Morgan's Trading Credit Curves 1 and we have that:
The MTM of a CDS contract is (for a sell of protection) therefore:
$$\text{MTM} = (S_{\text{Initial}}-S_{\text{Current}}).\text{Risky ...
- 2,562
-2
votes
1
answer
174
views
Problems with Money Weighted Rate of Return [closed]
The market value of a small pension fund’s assets was 2.7m on 1 January 2000 and 3.1 m
on 31 December 2000. During 2000 the only cash flows were:
Bank interest and dividends totalling 125,000 ...
4
votes
2
answers
4k
views
Cash-settled swaptions
I was wondering, what is the motivation behind the payoff of the cash swaptions being multiplied by the swap annuity?
$$c(S_{\theta, T})=\sum_{i=\theta+1}^{T}\tau_i\frac{1}{{(1+S_{\theta,T}(\theta))}^...
- 41
0
votes
1
answer
292
views
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 ...
-1
votes
2
answers
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 ...
- 109
1
vote
0
answers
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?
- 83
2
votes
4
answers
704
views
How to calculate interest rate in this problem?
Problem: A loan of £12,000 is issued and is repaid in instalments of £300 at the end of each month for 4
years. Calculate the effective annual rate of interest for this loan.
What I tried-
But ...
- 137