25
votes
Accepted
Shape and geometry of the yield curve
You can't make any concrete statements about the monotonicity, convexity or even sign of the yield curve.
Yields are almost always positive, and in the past (2007 and earlier) you could find people ...
- 5,778
19
votes
What does instantaneous forward mean?
1. Observable instruments, spot rates, and forward rates
First remember that something observable means that you can observe/find the rate in the market by looking at traded rate instruments or ...
- 1,246
12
votes
Accepted
What does instantaneous forward mean?
Given a forward rate, for example:
$ F(t, T, T+\delta)$
The instantaneous forward rate $f(t,T)$ fixed in $t$ is the limit when $\delta \rightarrow 0$ of your forward rate.
If the relation between ...
- 136
12
votes
Swap curve construction
I think your question can be split into two parts: (i) how to value a swap mathematically and (ii) how swaps actually work as a traded product.
Part (i):
As noob2 pointed out, "theoretically"...
- 5,723
10
votes
Accepted
Why Fed Funds Rate's is higher than U.S. treasury yield on the short term (< 2M)
There currently is an excess supply of cash looking for short term investments. Money market funds have been receiving a lot of subscriptions. The Feds reverse repo facility has been reaching new ...
- 5,652
9
votes
Accepted
Do we use the Nelson-Siegel model to calculate the yield curve?
In the beginning, we had a plot of yields of individual bonds against time to maturity, the crudest form of "yield curve."
Years later, people began hand-drawing a smoothed line through these yields ...
- 11.2k
9
votes
Why the 3M Zero Rate is not equal to the 3M Cash Rate? On Bloomberg yield curve bootstrapping
Market Rate, for this particular case, is a rate quoted on ACT/360 basis, start date = 21/06/2022, end date = 21/09/2022 on ACT/360 basis means year fraction 92/360. Discount Factor is $1/(1+92/360*2....
- 846
8
votes
Is trading mean reversion of small principal components of prices profitable?
Within the fixed income space, there's a lot of literature on PCA trading.
The first 2-3 principal component factors (PCs) can typically explain 90-99% of the total variances in yield curve movement....
- 11.2k
7
votes
Why 10-year versus 2-year spread?
The short answer is that using 2y/10y is not a requirement and many other combinations are commonly used (e.g., 3m/10y, 1y/10y, fed funds/10y). According to a note published by the New York Fed:
...
- 11.2k
7
votes
Accepted
Data on historical, cross-country nominal yield curves
First, a quick comment on Bloomberg symbols such as USGG10YR. These are actually yields on "generic bonds"; typically these are benchmark, on-the-run ...
- 11.2k
6
votes
Accepted
Why QuantLib computes the fixed-leg swap rate by this formula?
fixedLegBPS is the basis-point sensitivity of the fixed leg, that is, how much its NPV changes when the fixed rate changes by one basis point: it's calculated as ...
- 6,263
6
votes
Accepted
Quantlib bootstraping fails on 5y swap
You're not the first to trip on this, and unfortunately the fact that the provided example is from a different era doesn't help.
Quite simply, you're not writing rates correctly. The 5-years swap ...
- 6,263
6
votes
Accepted
Arbitraging upward sloping yield curve
This is what banks have been doing for hundreds of years. They borrow short term (mainly through deposits and interbank lending) and lend long term (e.g. mortgages).
I would not call it arbitrage, as ...
- 1,335
6
votes
Yield curve trading
Please refer to the picture below for what each trade is betting on.
As an example, in a bull flattening trade, you're betting that rates will decline AND the yield curve will flatten. The flattening ...
- 11.2k
6
votes
Accepted
YTM of "very-seasoned" bond issues
There is a liquidity premium between on-the-run treasury issues and off-the-run issues with similar characteristics. This is why when building a yield curve, typically on-the-run issues are used to ...
- 11.2k
6
votes
Accepted
Par Yield, Bond Yield and Zero Rate
Let's assume we have yearly cash flows, and let's focus on just two years - year 1 and year 2. Let $R_1$ and $R_2$ represent the zero rates of year 1 and year 2. So if you want to borrow for one year, ...
- 6,154
6
votes
Accepted
3M curve vs 6M Curve, which one to use for valuation of IR Derivatrives
You use the curve that describes the floating rate index to estimate the floating rate cashflows, a swap against floating 3M uses a 3M curve to forecast the cashflows.
And then you use a discounting ...
- 8,412
6
votes
Accepted
Bootstrap with QuantLib: Fair Swap or zero NPV
The problem is that you are not pricing the same thing, and for two reasons:
The vanilla instruments you are pricing should start on spot date and have a maturity with that start as reference
The ...
- 5,535
6
votes
Accepted
Use of interest rate swaps in liability-driven investing
Based on a Bloomberg article by Matt Levine, this is how it works:
Pension funds have long-term liabilities: say a liability of £100 in 30 years from now. This liability will have a net present value, ...
- 5,723
5
votes
Accepted
Bootstrap yield curve with QLNet / Quantlib
While @Baruch Youssin answers correctly in the general sense, the first part of his answer isn't what happened in the example code.
While QLNet is a port of QuantLib, it's not a direct port. Your ...
- 2,255
5
votes
Constructing yield curve directly from yield-to-maturity data
Unless all of your yields are par yields (yield of bonds trading at par), you'll get very unreliable results if you fit your curve using yields alone. This is because yields can be distorted by the ...
- 11.2k
5
votes
Best method for interpolating yield curve? [Multiple questions]
Typically, the yield curve used for performing relative value analysis should be built from off-the-run bonds.
Different vendors select different bonds, but starting with all outstanding Treasury ...
- 11.2k
5
votes
Accepted
What curve are you shifting when you calculate DV01 for a swap?
Let's step back and look at the reason for making a DV01 calculation first before answering the question;
The reason for making a DV01 calculation is to quantify what market movements has impact on ...
- 86
5
votes
Principal Component Analysis of yield curve change
To put things in context, if $\{{\bf X}_i\}_{i=1}^n$ is a set of variables and $\{{\bf Y}_j\}_{j=1}^n$ denote the principal components of ${\bf X}$ then
$$
{\bf X}_j = \mu_j + \sum_{k=1}^n{\bf Y}_k ...
- 311
5
votes
Estimating a Yield Curve in a country without Bond Stripping
You do not need zero rates to estimate a parametric
model of the yield curve, such as Nelson-Siegel.
Suppose for instance that you have a cross-section of
bond prices. Then:
For given parameters for ...
- 2,976
5
votes
Accepted
What is Dual Curve Bootstrapping? And how to do it, with an example?
A multi-curve means that you observe the discounting instruments (such as fed funds) and projection (libor, swap curve) and solve for all of them simultaneously; as opposed to bootstrapping separately ...
- 11.3k
5
votes
Accepted
Swap curve construction
I think I understand the question, but maybe not.
In USD market, the most liquid IR swaps have floating leg reset quarterly from 3Mo LIBOR. (The fixed leg is semi-annual. Ths will change when LIBOR is ...
- 11.3k
5
votes
Accepted
Choosing which interest rate model to go with?
Calibrate to many observed curves, over all kinds of shapes: flat, normal, inverted, and humped, and measure and compare the model fitting errors. If you can't find all the shapes in history, make ...
- 4,968
5
votes
How to compute par yield from zero rate curve?
For simplicity, let us assume continuously compounded zero rates and periodically compounded par yields. If you have to work with continuous rates, you may adapt the formulas accordingly.
Using the ...
- 6,195
5
votes
How to minimize Nelson-Siegel parametric form
When we worked with that model several years go, we used Differential Evolution and it worked very well. See Calibrating the Nelson-Siegel-Svensson Model. At least in the standard version, a best-of-...
- 2,976
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