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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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9 votes
2 answers
16k views

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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5 votes
1 answer
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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). ...
Mathematician Joe's user avatar
-1 votes
1 answer
398 views

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 ...
Student's user avatar
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12 votes
3 answers
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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 ...
rex's user avatar
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5 votes
1 answer
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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 ...
moquant's user avatar
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3 votes
1 answer
440 views

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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1 answer
177 views

Explicit step by step curve construction using FRAs

I'm trying to understand a step by step process of building curve from the instruments to the final result, particularly how overlapped FRAs are used. i'm trying to build this in excel so I have a ...
Naim Hussain's user avatar
1 vote
2 answers
2k views

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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2 answers
585 views

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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2 answers
531 views

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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1 answer
260 views

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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29 votes
6 answers
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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 ...
athos's user avatar
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24 votes
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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 $X_t$ ...
Tom Artiom Fiodorov's user avatar
13 votes
1 answer
2k views

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 ...
qfin_newguy's user avatar
11 votes
1 answer
4k views

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. ...
RandomGuy's user avatar
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9 votes
1 answer
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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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1 answer
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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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4 votes
1 answer
6k views

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 ...
JVP3122's user avatar
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4 votes
1 answer
352 views

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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4 votes
1 answer
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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 ...
moquant's user avatar
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4 votes
1 answer
986 views

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 ...
user3212376's user avatar
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1 answer
1k views

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 ...
Joe's user avatar
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3 votes
3 answers
2k views

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) ...
access_nash's user avatar
3 votes
2 answers
1k views

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 ...
Qing's user avatar
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3 votes
1 answer
2k views

How to sum interest rate curves in QuantLib

C++ code taken from Bonds.cpp and slightly amended: ...
Lisa Ann's user avatar
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3 votes
0 answers
244 views

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 ...
Gogo78's user avatar
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2 votes
0 answers
167 views

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 ...
DVCITIS's user avatar
  • 237
2 votes
1 answer
1k views

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(...
ayoub's user avatar
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2 votes
2 answers
1k views

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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2 votes
1 answer
2k views

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, ...
Petter S's user avatar
2 votes
3 answers
3k views

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 ...
Trajan's user avatar
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2 votes
2 answers
6k views

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.
SW14's user avatar
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1 vote
2 answers
539 views

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 0 1 0.003 ...
user54908's user avatar
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1 vote
0 answers
222 views

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 ...
AleVis's user avatar
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1 vote
1 answer
310 views

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, ...
Shambhala's user avatar
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1 vote
1 answer
652 views

How does Bloomberg bootstrap CASH Instruments?

Given the following datas : If we do the bootstrap methodology for CASH Instrument we gotta : Calculate the DF associated to the Market Quoted Rate (2.91157). For the 3M Fixing we have : T = 0.26115. ...
TourEiffel's user avatar
1 vote
1 answer
10k views

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 ...
mickG's user avatar
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1 vote
1 answer
2k views

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 ...
Iliana's user avatar
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1 vote
2 answers
8k views

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-...
junior_pm's user avatar
0 votes
1 answer
2k views

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). ...
JVP3122's user avatar
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0 votes
1 answer
192 views

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{...
cici30725's user avatar
0 votes
1 answer
358 views

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 =...
Landscape's user avatar
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0 votes
1 answer
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Principal Component Analysis for attributing yield curve changes

I have calculated the Principal components using daily yield curve changes. After calculating these components, i noticed that 98% of the return can be attributed to the first 3 components. How do i ...
One Pablo's user avatar
0 votes
2 answers
1k views

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 ...
intern5ever's user avatar
-1 votes
2 answers
1k views

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 ...
Pythonista anonymous's user avatar