Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [annuity]

The tag has no usage guidance.

2
votes
1answer
152 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\,\...
-1
votes
1answer
49 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, ...
0
votes
1answer
64 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
0answers
279 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 $$\frac{C(T)}{2}\sum_{t=1}^{2T}d\Big(\frac{t}{2}\Big) + d(T) = 1$$ $$\implies\frac{C(T)}{2}A(T) + d(T) = 1,$$ ...
7
votes
2answers
816 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 the issues ...
3
votes
0answers
524 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
votes
1answer
173 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
vote
1answer
445 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{...
-3
votes
1answer
54 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
2answers
1k 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))}^...
0
votes
1answer
215 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
2answers
71 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 ...
1
vote
0answers
51 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?
3
votes
2answers
121 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 ...