Questions tagged [yield-curve]
A yield curve is a plot of yields for various bonds (often government bonds) versus the bonds' maturities. We also often plot swap and other LIBOR rates to get the (related) swap curve.
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What is the Swap Curve?
What is the so-called Swap Curve, and how does it relate to the Zero Curve (or spot yield curve)?
Does it only refer to a curve of swap rates versus maturities found in the market? Or is it a swap ...
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Swap curve construction
I am new to this area so my question might be basic to many but please answer.
For valuing interest rate swaps how will we define which curve to take, like sometimes we use usd 3m curve, or usd 3mv 6m ...
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Setting input parameters for Nelson Siegel Svensson model
I am trying to determine the parameters for the Nelson Siegel Svensson model and am solving a Non-Linear Optimization problem to do this.
I am trying to solve:
$$
\min_\theta{\sum{(p_i - \hat p_i)^2}...
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Best method for interpolating yield curve? [Multiple questions]
I'm building a spot curve for US Treasuries. My original selection of cash treasury include all the on-the-run bills, notes, bonds from 6 months to 30 years, as well as some selected off-the-run ...
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What is Dual Curve Bootstrapping? And how to do it, with an example?
I am starting to explore this area. My ultimate aim is to build a 3 month LIBOR forward curve.
I wish to know what exactly 'Dual Curve Bootstrapping' is (If someone could explain it in clear words).
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Stress testing fixed income Yield curve with Nelson Siegel
I am attempting to stress test the Zero coupon Yield curve using The Nelson Siegel model as described in the following papers :
Generating Yield Curve Stress-Scenarios
Representative Yield Curve ...
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How to value a long term interest rate swap if the floating leg is USD-LIBOR
To value an IRS, you require a spot/zero curve. If I am correct this zero curve will be the USD-LIBOR curve. However, if you have e.g. a 10-year swap that you are trying to value 2 months into the ...
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Deriving Interest Rates
I am trying to teach myself about interest rate swaps, how they are priced, etc... Easy enough - just comparing cash flows of fixed and floating rate bonds.
However, what I'm struggling with is how ...
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Dual Curve Bootstrapping - When to OIS discount?
I am a new quant and I am trying to understand some of the specifics of dual curve bootstrapping. For concreteness, suppose I want to build a Libor forward curve.
From what I understand
OIS ...
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Yield to Maturity
For a bond with market price $P_t$ and fixed payments $c_n$, I'm told the yield to maturity is given by the solution $Y$ to the equation
$P_t=\sum_{n=1}^N c_n e^{-Y(t_n-t)}$.
Firstly, I'm not great ...
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How do you construct a zero coupon curve from the current market yield curve?
If I was to take the current market yield to maturity and tenor for all bonds for a particular issuer how can I convert this curve into a zero-coupon curve?
For example if we were to get the yield and ...
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Quantlib yield curve - zerorate output differs from expectation
I was creating an yield curve using zeroRate, when I read back the value from the created yield curve - it differs from expectation.
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Data on historical, cross-country nominal yield curves
Various central banks publish their fitted nominal yield curve estimates: the Fed, BOE, SNB, BOC, ECB (cf: Bundesbank), RBA, Russia, RBI.
(I couldn't find for BOJ; Brazil; BOK; or PBOC. Links for ...
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which market instruments are used to strip the SOFR curve under 1 year?
which instruments are used to strip the SOFR curve for the short term of the curve(below 1 y) ?
there are no swaps with maturity under 1 year, right?
thanks
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how to derive yield curve from interest rate swap?
According to some textbooks, to derive the yield curve, quote
overnight to 1 week: rates from interbank money market deposit,
1 month to 1 year: LIBOR;
1 year to 7 years: Interest Rate Swap;
7 ...
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Why isn't the Nelson-Siegel model arbitrage-free?
Assume $X_t$ is a multivariate Ornstein-Uhlenbeck process, i.e.
$$dX_t=\sigma dB_t-AX_tdt$$
and the spot interest rate evolves by the following equation:
$$r_t=a+b\cdot X_t.$$
After solving for $X_t$ ...
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Musiela parameterization
I have a question regarding the proof of the Musiela parametrization for the dynamics of the forward rate curve. If $T$ is the maturity, $\tau=T-t$ is the time to maturity, and $dF(t,T)$ defines the ...
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Shape and geometry of the yield curve
Let the initial yield curve $T\mapsto y(0,T)$ be given for a term structure family of bonds $B(0,T)$ having different maturities. I am trying to figure out the geometric properties of the yield curve. ...
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Where do swap rates and/or long-term forward rates come from?
I apologize if this is supposed to be obvious, but ... . Libor spot rates are quoted up to a year, beyond that one can use Eurodollar futures to continue to build the curve. Let's say up to 3 years. ...
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How does one estimate theta in the Ho-Lee model from a yield curve?
I have a yield curve constructed using linear interpolation with data points every 3-months for US treasuries.
I would like to use that calibrate a Ho-Lee model, but I can't wrap my head around how ...
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Duration: Parallel shift in yield curve assumption
General Intro
I'm trying to really understand the assumptions of dollar duration for a portfolio of bonds. In particular I don't fully understand that the assumption that there are parallel shifts ...
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Yield curve fitting example in Wilmott on Quant Finance p.528
In Wilmott on Quantitative Finance Vol. 2, p. 528, Section 31.4.2, is given a power series expansion for a zero coupon bond
$$Z(r,t;T)=1+a(r)(T-t)+b(r)(T-t)^2+c(r)(T-t)^3+\dots$$
then it says to ...
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Attributing the change in NII to Shift, Twist and Butterfly
The movement of the zero rate curves can be decomposed into a shift movement (the level of interest rates) and a twist movement (the slope of the curve) and butterfly (the curvature of the curve). If ...
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QuantLib Python Swap Yield Curve Bootstrapping Dates and Maturities
This is somewhat related to the question I asked here but simpler. I am trying to bootstrap a yield curve from swaps, and am having a problem with the dates/maturities that are coming out. The code ...
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Monetary Policy and the Yield Curve PART TWO
The Fed has a number of tools/targets with which they manage monetary policy. I'm looking to refine a concise summary of them and looking for guidance/correction/validation.
Think I understand these ...
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How to sum interest rate curves in QuantLib
C++ code taken from Bonds.cpp and slightly amended:
...
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PCA for Risk bucketing
I'm working on a project to justify the use the certain tenors (2y, 5y, 10y, 30y) for risk bucketing. I'm a little stuck after calculating the principal components. Just to describe my approach-
a) ...
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Dual curve construction
I'm new to curve construction for swaps pricing concept and I am having hard time to understand dual curve construction and what difference it from single curve ? how do we construct it ? can someone ...
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Accrual in Default Derivation of Credit CDS Curve
In Trading Credit Curves Part I by JP Morgan we have that each point on a credit (CDS) curve represents:
$$PV(\text{Fee Leg}) = PV(\text{Contingent Leg})$$
which is
$$S_n \sum_{i=1}^{n}\Delta_i ...
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Par and Zero Coupon Yield Curves
The government par yield curve shows a marginally lower yield than the Government zero coupon curve.
What is the reason for this in general.
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Monetary Policy and the Yield Curve PART ONE
As I understand it, the Fed has 3 tools for moving interest rates to combat inflation/unemployment: the discount rate, Fed Funds rate and open market operations.
I'm trying to understand how the ...
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Construct a butterfly interest rate portfolio to eliminate PCA exposures
I have data from 2012 to 2016 for interest rates whose term range from 2 month to 30 years, a total of 10 Principal components can be calculated.
Then I want to construct a portfolio, $$WFLY = w_1 *5Y ...
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Forecast 3m LIBOR USD. Budget purpose
How can I calculate/budget/find a expectation for the 3 month LIBOR for the next 3monts-4 years?
I am calculating a CF scenario on USD 3month Libor + margin. With swaps and fixed rate this is easy, ...
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Why we should specify the evaluation date when using Quantlib yield curve? And why updating the evaluation Date is time consuming
I was runing some tests using the yield curve structure in quantlib mainly: PiecewiseYieldCurve
It seems that I have to fix the evaluation date using such a line :
Settings::instance().evaluationDate(...
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Principal component analysis for yield curve
I have Treasury yield data across 11 maturities for past 1 year. I have used a code in MATLAB for PCA on change in yield curve. Now, I have covariance matrix of daily/monthly yield curve changes, ...
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How does one calculate carry-roll-down theoretically assuming expectations of short-term rates are realised
I am not asking for an explanation that is hugely quantitative, but rather one that is more intuitive.
I am aware that there are different assumptions that one could take when it comes to carry-roll-...
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Calculating the short rate from the discount curve
I'm currently looking at some code that implements the Hull-White model. As one of the inputs, the code accepts a table of discount factors at various dates.
Time in Years
Discount Factor
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0.003
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Building a Nelson-Siegel curve
I originally posted this on Mathematics, but was told my question is better suited here.
I want to graph a yield curve with an extended version of the Nelson-Siegel-Svensson. I have the issue date, ...
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Stub rate and first fixing in IRS
I have 2 questions that probably are related.
Suppose there is an IRS that pays a 2% fixed rate every 6 months and receives the Libor 3 months (but paid every 6 months).
The swap starts today (March ...
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Applications of PCA to yield curve analysis
One of the applications of Principal Component Analysis in Finance is to analyse the shape of the yield curve.
But what conclusions can be drawn exactly from performing this exercise? Does it help us ...
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Spot rate dominates the yield to maturity if the yield curve is normal
Let $y_{k}$ denote the yield-to-maturity of a $k$-period coupon bond. Let $S(k)$ denote the $k$-th period spot rate. If $y_{1}<y_{2}<y_{3}<\cdots$, then $S(k)\geq y_{k}$ for all $k\in \mathbb{...
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Zero Coupon Bond - Price and Yield when interest rate is a diffusion process and 0 "price of market risk"
Given that the price of market risk (or market price of interest rate risk) is $\lambda(r_t, t)=0$ and that we have the following dynamics of the interest rate (under the physical measure $P$.
$$dr_t =...
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Convert US Treasury par yields to spot rates
I'm devising a methodology to transform par yield to spot rates, I'd like to stick with pure python as much as possible so not really after Quantlib (or other libraries) examples.
In particular I want ...
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Constructing a USD LIBOR curve
USD_LIBOR rates are only published up to 12 months.
how would you approach constructing the curve to at least a 30-year tenor, to price for example an interest rate swap.
I have heard that swaps can ...
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How to measure Steepener/Flattener/Butterfly sensitivity? (in 01)
This seems like a simple concept but I'm a bit lost. How can I calculate the dollar value sensitivity for a yield curve slope or butterfly position? I understand how DV01 can be calculated, but it ...
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QL-Python Bootstrapping Yield Curve FuturesRateHelper throwing off results
I'm trying to perform a bootstrap of a yield curve from deposit rates, futures, and swaps, and the interpolation is "blowing up" for the futures maturities being off by two orders of magnitude (100x). ...
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QuantLib Python: how to calculate the npv of irregular cashflows?
I am trying to learn QuantLib for Python but I must say I am banging my head against the documentation (I also bought Ballabio's python cookbook) - maybe it's me, but even finding the most basic ...
