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25 votes
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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 ...
Chris Taylor's user avatar
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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 ...
Pontus Hultkrantz's user avatar
13 votes
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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 ...
Yassine Q.'s user avatar
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"...
Jan Stuller's user avatar
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10 votes
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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 ...
Helin's user avatar
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10 votes
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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 ...
AlRacoon's user avatar
  • 6,642
9 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 ...
Helin's user avatar
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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....
emot's user avatar
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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: ...
Helin's user avatar
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7 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 ...
Kermittfrog's user avatar
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7 votes
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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 ...
Helin's user avatar
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6 votes
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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 ...
Helin's user avatar
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6 votes
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Construct a butterfly interest rate portfolio to eliminate PCA exposures

Let $S$ be your risk sarray, expressed in pv01, for each of your (implied) 10 instruments. You restrict the array to all zeroes except those corresponding to the 5Y, 7Y and 10Y risks, e.g. if 1Y:10Y ...
Attack68's user avatar
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6 votes
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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, ...
Magic is in the chain's user avatar
6 votes
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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 ...
Attack68's user avatar
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6 votes
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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 ...
Dimitri Vulis's user avatar
6 votes
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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 ...
David Duarte's user avatar
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6 votes
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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, ...
Jan Stuller's user avatar
  • 6,223
6 votes
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Parameters in Nelson-Siegel model and Nelson-Siegel-Svensson model

The Nelson-Siegel model has four parameters: $\beta_0$, $\beta_1$, $\beta_2$, and $\lambda$. These parameters have the following restrictions: $\beta_0$, $\beta_1$ and $\beta_2$ can be any real ...
Hans-Peter Schrei's user avatar
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 ...
Helin's user avatar
  • 11.8k
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 ...
Helin's user avatar
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5 votes
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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 ...
Fred's user avatar
  • 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 ...
caverac's user avatar
  • 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 ...
Enrico Schumann's user avatar
5 votes
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What does 5 year OIS actually mean?

When people say OIS swap they mean an exchange of some sort of fixed cash flow and in return the receipt of daily OIS based on the "Fed Effective Rate" (FEDL01 Index on Bloomberg). The floating ...
JoshK's user avatar
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5 votes
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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 ...
Dimitri Vulis's user avatar
5 votes
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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 ...
ir7's user avatar
  • 5,053
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-...
Enrico Schumann's user avatar
5 votes

Advice for automating swap curve construction

I first present the bare basics of single curve bootstrapping in part 1, then I try to come up with some ideas in part 2. (bare) Basics of single curve bootstrapping As I understand it, for a common ...
Kermittfrog's user avatar
  • 6,967
5 votes
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Graeme West's VBA code Monotone Convex

As mentioned by Bob in the comments, if you follow the github issue, you'll get the link to the Graeme West's Excel sheet for monotone convex interpolation. The link is now dead, but a quick search on ...
autoencoder's user avatar

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