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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Basic LIBOR curve question
I'm new to the quant finance and have a very basic question about LIBOR curve.
LIBOR is published every day for 4 different tenors (1M, 3M, 6M, 1Y), and each rate means how much annual interest ...
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Question on yield curve fitting from Wilmott on Quant Finance p.529
My last question is related.
At the top of p. 529, it says,
"From the Taylor series expansion for $Z$ we find that the yield to maturity is given by
$$-\frac{log Z(r,t;T)}{(T-t)}\approx-a+\left(\...
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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.
1) I wish to know what exactly 'Dual Curve Bootstrapping' is (If someone could explain it in clear ...
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Par Yield, Bond Yield and Zero Rate
In the Hull's book, chapter 4.4, it says :
The par yield for a certain bond maturity is the coupon rate that
causes the bond price to equal it's par value.
Then for this question (4.18) :
“...
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Why QuantLib computes the fixed-leg swap rate by this formula?
I'm trying to understand how QuantLib creates (bootstraps) a yield curve from a vanilla swap at the source level. I have the following test code:
...
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Does Nelson-Siegel require adjustments to yield curve input data?
I am attempting to gain a better understanding of the limitations of the Nelson-Siegel model as described in Estimating the Yield Curve Using the Nelson-Siegel Model.
As I have been playing around ...
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QuantLib error with qlPiecewiseYieldCurveData() on qlPiecewiseYieldCurve() with ZeroYield and ForwardRate
I'm using QuantLibXL to build a discount curve, a zero yield curve and a forward curve of the EURIBOR rate (QuantLibXL is downloadable here).
I've built an object of class ...
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Estimating a Yield Curve in a country without Bond Stripping
I am currently working under estimating a Yield Curve. From my understanding common procedures to construct a yield Curve like Nelson Siegel have the input of a series of different zero rates and ...
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What's the logic behind 3-10 UST yield inversion predicting recession?
Is there causality, behavioral or logical explanation behind this indicator or is it just purely an observation based on correlation? My guess is that there are existing derivatives with clauses that ...
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What is the yield on an infinitely lived ZCB?
I guess the price of a Zero-Coupon Bond with infinite maturity should go to zero, what about its yield?
I am asking this because I was dealing with the yield curve and its asymptotic properties when $...
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Cost of Carry Bear Flattener
I was reading a report last week that
“the carry on a 2s5s gilt curve flattener is negative to the tune of
10bp over 6 months”
and I realised I have little understanding of this concept and how ...
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487 views
What does 5 year OIS actually mean?
I am aware that OIS is the new reference/risk-free rate for collateralized cashflows. OIS is by definition an overnight rate (annualized, I assume). So once I have constructed my OIS yield curve, what ...
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Investor rationale behind inverted yield curve
I just had a question regarding investors/markets rationale behind the cause of the yield curve. Assuming that investors believe that rates will be lower in the future and are pessimistic about the ...
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Bond strategy in rising rate environment
During a period of rising interest rates, it makes sense for investors to either swap out their longer term bonds for shorter ones, or simply invest in shorter maturity bonds in order to reduce ...
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Cash vs Deposit Rates
When constructing a yield curve for derivatives purposes, what is the difference between cash and deposits rates?
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Weights Blowing up in PCA
I'm using daily settlement data to get yield levels for a couple of products. From this data I am doing PCA on a rolling collection of the yield levels. I have been using sci-kit learn's PCA function, ...
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Calculate the “ten year zero rate” given two bonds with two prices
I have a little question and need some help with the notation. So, the question goes as follows:
A bond with a maturity of ten years that pays annual coupons of 8% has a price of \$90. A bond with ...
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What's Hedge Curve Template
what's a Hedge Curve Template (HCT)? How does it help value a bond?
It appears to me it normally is used together with another curve where x,y-axis being maturity dates and discount factors ...
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Brazilian break even inflation curves
Brazil has had historically two sets of inflation bonds, the NTN-B and NTN-C series each with a different inflation index. The NTN-C is no longer issued.
When creating historical break even ...
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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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How is the integral relationship between current yield curve and forward yield curve derived?
$$y(\tau) = \frac{1}{\tau} \int_{0}^{\tau} du \Big(f(u)\Big)$$
As far as I understand the forward rate is the future rate based on the expectation hypothesis. But it is unclear how many years into the ...
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Relative order of curve for coupons for Upward Sloping Yield
Why would the forward curve be above zero and coupon bond yield be at the bottom for a sloping up yield curve.
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Is there really a negative roll yield for futures in contango?
I am trying to wrap my head around how ETFs that track futures work (whether its USO tracking WTI futures or VXX tracking VIX futures).
I have read online about how for normal contango environments, ...
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Equations for multicurve calibration with OIS discounting
I am trying to calibrate my forecast and discount curves using the multi-curve approach with OIS discounting. To do so, I have a implemented multivariate Newton-Raphson root finder. I am finding a bit ...
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Quantlib FuturesRateHelper triggers not a valid IMM date error
I'm beginning to use QuantLib with Python SWIG, and trying to build a EUR yield curve.
I face this error which frankly I don't understand; I looked at the code of bool IMM::isIMMdate in imm.cpp and ...
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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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Bond (yield curve) dynamics in the Forward-LIBOR-market-model
The standard Libor-Forward-Market-Models provides a way of modelling the evolution of forward rates in time.
However the model does not seem to be well suited for the modelling of zero-bonds. But ...
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Yield Curve Volatility
Let you have several issuers, and let each issuer have its yield curve built up with liquid plain vanilla fixed rate bonds.
Each yield curve has its slope and its curvature, and they obviously change ...
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Do we use the Nelson-Siegel model to calculate the yield curve?
Suppose we are to plot a yield curve for a list of bonds. Do we use the Nelson-Siegel fitted yield curve since that's with the case for zero coupon bonds? Or do we in fact use bonds with different ...
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Bootstrap yield curve with QLNet / Quantlib
I am trying to grasp QLNet (C# version of Quantlib, all the functions of Quantlib have the same name and work the same way, so if you just know Quantlib, you can still help me), especially for pricing ...
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Arbitraging upward sloping yield curve
I read from various sources that yield curve is normally upward sloping. If that's the case, if we borrow short term and lend long term, won't we always make money on average?
Let's say 1-year ...
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What do these maturity codes mean?
In fitting a curve I found that people are using the following tenors:
U1 Z1 H2 M2 U2 Z2 2Y
Could you please let me know what exact time periods they stand for? Is there a web page describing ...
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3M curve vs 6M Curve, which one to use for valuation of IR Derivatrives
Sorry, this might be basic for some of you but I'm very confused when it comes to know which curve (6m or 3m) we can use for valuations of swaps and swaptions. Could someone please explain when to use ...
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Yield curve trading
I have a problem in understanding following strategies:
bullish flattening trades
bearish flattening trades
bullish steepening trades
bearish flattening trades
Can anyone give me an explanation ...
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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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Choosing which interest rate model to go with?
I've been assigned with the task of modelling zero rate curve. I did it with two models: Vasicek and CIR. Looking at the two curves produced, I can see that one is closer to the observed curve than ...
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If 10s20s steepener have equal DV01 weighting on each swap then why does convexity play a role in MtM
Receiver Swap 10yrs
Notional: 1,000,000
DV01: +1,300
Tenor: 10yrs
Rate: 4%
Payer Swap 20yrs
Notional: 500,000
DV01: -1,300
Tenor: 20yrs
Rate: 5%
Looking at this fictitious example, I want to ...
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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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Recommended Instruments (and sources) for Constructing Money Market Yield Curves
What instruments are the current industry recommendations for constructing money-market yield curves in some major currencies?
The switch after the crisis to multi-curve methods is well documented on ...
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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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Reconstruct yield curve from principal components
I am currently building a model which aim is to model shocks to the yield curve (i.e. 25bps hike in the short rate).
Currently I am looking at a swap curve from which I derive the PCs. Assessing the ...
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Corporate Bond Yield Curve
I am an intern in a mutual fund and they have asked me to create in house yield curve for different type bonds in their portfolio
I need to know on what basis are different yield curves made. For ...
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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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1answer
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Derivation of the Nelson-Siegel model and proof of arbitrage
1. I am looking for a derivation of the Nelson-Siegel model
$y(m)=a+b\left( \frac{1-e^{-\lambda m}}{\lambda m}\right)+c\left( \frac{1-e^{-\lambda m}}{\lambda m} -e^{-\lambda m} \right)$
It is ...
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Discount Factors to Zero Rates
I have obtained a Ibor-6Months curve using bootstrapping techniques. For the short-term of the curve I used spot, for the middle-term FRAs and for the long-term IRS.
The curve that I have obtained is ...
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Comparison of multicurve calibration methods
It seems that there are mayor softwares around offering a multicurve framework based on bootstrap. I find this puzzling nowadays, given the distinct advantages of best-fit optimization methods and ...
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yield curve basics
Suppose we observe the following term structure (of annualised spot rates):
0-3 Months $\rightarrow$ 4.0%.
0-6 Months $\rightarrow$ 4.2%.
0-9 Months $\rightarrow$ 4.4%.
Question1) How can we ...
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Curve building for a swap
I'm a student learning how to build a swap curve, I've deposit 6m rate = 5%, fra 6-12m rate = 5.8% and 12m-18m rate= 6% and swap 2y =7% and 3y swap rate = 7.5%.
I get the correct discount factors for ...
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Convexity in interest rate curve bootstrapping
Whether the bootstrapping is a multicurve one or not, one can use futures quotes. One link these quotes to corresponding (synthetic) forwards (that can be expressed as known functions of zero-coupons) ...
