41 votes
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What is the Swap Curve?

Garabedian, Typically, the "swap curve" refers to an x-y chart of par swap rates plotted against their time to maturity. This is typically called the "par swap curve." Your second question, "how it ...
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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 ...
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  • 5,628
16 votes
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Deriving Interest Rates

There are two parts to your question and I'd like to answer them separately. Curve Construction On a daily basis, you can observe prices on a large variety of instruments, whose prices are driven by ...
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16 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 ...
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12 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 ...
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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"...
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9 votes
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Calculating instantaneous forward rate from zero-coupon yield curve

Your overall approach is correct. However to my knowledge it is formally more appealing to work with a parameterized and smoothed yield curve. Basically one assumes that the yield curve can be ...
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9 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 ...
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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....
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8 votes
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How can an inverted yield curve in a liquid market exist?

There are many reasons why a yield curve can be inverted. A default-free yield curve reflects a combination of - market expectation of future short-term interest rates; bond risk premium: usually ...
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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....
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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: ...
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6 votes
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Does Nelson-Siegel require adjustments to yield curve input data?

The NS model should be fit directly to bond prices. If you have the prices of all the Treasuries, you should use those directly. See this paper for how the Fed does it http://www.federalreserve.gov/...
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6 votes
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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 ...
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6 votes
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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 ...
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6 votes
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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 ...
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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 ...
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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 ...
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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 ...
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6 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 ...
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6 votes

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 ...
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5 votes

Who determine Sport rate curve (Yield Curve)

US Treasuries start trading BEFORE they're actually issued, in the so-called "When-Issued" market. This market allows investors to purchase the new issues for "forward settlement." Because these bonds ...
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5 votes

Why is "full" Yield Curve (term structure of interest rates) 3 component based?

@Arrigo's answers are quite good; I'll try to beef up his points a bit more. Yield curves should be constructed using instruments of similar credit risks. If you're building a US Treasury yield curve,...
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5 votes
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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5 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 ...
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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 ...
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