All Questions
Tagged with fixed-income convexity
20
questions
0
votes
1
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74
views
Proving that Convexity approx. equals Duration squared but something goes wrong?
I am trying to derive a formula for bond convexity that I saw in a textbook which states that
$$\text{convexity} = \frac{\text{Macaulay duration}^2 + \text{Macaulay duration} + \text{dispersion}}{(1+\...
- 281
2
votes
2
answers
575
views
Quantifying the impact of rates change on bond prices
How can I quantify the impact of a change in interest rates on bond prices?
I know that in a classical textbook setting the answer would be to compute the modified duration of the bond and, to account ...
- 45
1
vote
2
answers
235
views
Are there names from the third term onwards in the Taylor approximation for bond pricing?
The first terms are duration and convexity, but are there common names for the terms beyond this?
- 11
4
votes
1
answer
264
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How am I supposed to understand the following statement on the convexity adjusted rate
Given, a numéraire $(N(t))_{0\leq t \leq T}$ and an index $(X(t))_{0\leq t\leq T}$ that is a $\mathbb Q^{N}$-martingale, we consider the natural payoff $V_{N}(T)$, where it pays
$$V_{N}(T):=X(T)N(T) \...
- 93
0
votes
1
answer
90
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Duration and convexity of an open term loan/bond!
Imagine an open term loan with monthly interest payments of [x]% and the principle due when the loan is closed. Both the lender can call the loan, and the borrower can return the loan (with no penalty)...
- 1
1
vote
1
answer
500
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Duration and Convexity
I am searching to estimate the evolution of my portfolio duration following a yield increase/decrease.
Can i use the convexity?
I mean IR delta x (- convexity) = Duration delta
Is it correct?
Thanks a ...
0
votes
0
answers
547
views
How to calculate the new price of a bond using duration rule and duration with convexity rule?
A bond with a 30 year maturity, par value of $1000 and is 8% p.a. coupon is selling at an yield to maturity of 8% p.a. The modified duration of the the bond at its yield is 11.26%, and its convexity ...
1
vote
2
answers
733
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Bond Convexity and Maturity
What the reasoning for why bond convexity increases with maturity. Heuristic explanations are somewhat better as I would like a fundamental understanding.
Also what causes a more convex bond to be ...
- 2,532
1
vote
1
answer
2k
views
High convexity vs low convexity bond definition
Isn't high convexity always better than low convexity bond from the formula that $$\frac {ΔB} B=-D \frac {Δy} {1+y} + \frac 1 2 CΔy^2$$
Since $\frac 1 2 CΔy^2$ is positive no matter what so the price ...
- 111
3
votes
0
answers
685
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Modified duration and convexity of a bond in R
A soft question:
Are there any existing packages in R that allows one to compute the modified duration and convexity of bonds in R? If there isn't, how can one go about doing so (with formulas) with ...
- 205
1
vote
1
answer
3k
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Derivation of convexity formula
Let's say that I have a bond that pays coupon on a semi-annual basis. Therefore, the price of this bond can be calculated using the following formula:
$$ P = \sum_{i=1}^N \frac{CF_i}{(1 + YTM/2)^{...
- 1,850
0
votes
1
answer
939
views
Convexity for historical bond data
I'm trying to write a program to calculate the convexity of a bond. The bigger idea is, that if I have access to the actual price for each point in time, I should be able to calculate various features ...
- 174
0
votes
1
answer
597
views
A very simple question about convexity of a bond
I was always under the impression that, ceteris paribus, higher the coupon rate, higher the convexity of the bond.
But Investopedia says the following:
"zero-coupon bonds have the highest degree ...
- 277
2
votes
1
answer
791
views
From continuous compounding to simple compounding - convexity adjustment
I have derived the convexity adjustment expression for futures rates using the Ho-Lee model, to arrive at the following:
$$
ForwardRate = FuturesRate - \frac{1}{2}\sigma^2T_1T_2
$$
where $T_1$ refers ...
- 223
0
votes
2
answers
644
views
Bond Duration hedging with long convexity
How do you build a duration-neutral bond portfolio which is long convexity? can you give me an example?
- 255