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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Building curves using onshore or offshore JPY overnight rates?
I am trying to build Japanese Yen interest rate curves. When defining the curve instruments for the 'OIS' (discount) curve (aka TONAR), I am uncertain as to which rate to use for the overnight deposit ...
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Investment: Bond vs Equity
I was talking to a friend recently and he asked me the following question.
If I have a device which perfectly (with 100% accuracy) predicts that both a bond (e.g. AAA rated government bond) and the ...
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How can an inverted yield curve in a liquid market exist?
Take a liquid market like US T-bills, notes and bonds... Who would want a long-term security that yielded less than the short?
Even if someone is a long-term lender, why wouldn't they hold the ...
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Who determine Sport rate curve (Yield Curve)
My study was in a Mathematical modelling, we studied much about theory, equations, how to resolve equation, how to implement, but we don't understand well where these equations come from.
My ...
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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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How to price an European call on zero-coupon from the yield curve?
It is known that the price of an European call of maturity $T^*$ on zero-coupon of maturity $T$ is given by
$$p(0,T)= B(0,T^*)\mathbb E ^{\mathbb Q_{T^*}}\left[ (B(T^*,T)-K)^+\right]$$
where $B(0,T)...
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IR Yield Curve and Fixing Dates
Consider two FRAs.
3x6 , Effective 3 months from now, terminates in 6 months. The floating leg payer pays 3-month LIBOR. Fixing date for LIBOR 40 business days. To price this at par, the fixed leg ...
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Par Yield Curves vs Zero Curves
Does it make sense to look at par yield curve for German bonds in the current environment? Because low rates mean that a lot of bonds are trading above much above par (even around 150!).
I would ...
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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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Pricing a bond contract from the yield curve
When giving a particular class in financial mathematics for a student I saw a problem in a list of exercises that says:
How to calculate the price at 15 December 2010 of a bond paying a coupon of 11....
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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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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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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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Bloomberg Zero Coupon Rates
As some of your may know from my other posts, I am working on a Dynamic Nelson Siegel (DNS) based relative value trading model. On simulated data (which satisfies all the assumptions) of the DNS it ...
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OIS discounting pre and post crises
I have a Dynamic Nelson Siegel (DNS) based rv model.
I want to know if I can use pre and post-crises curves interchangeably in my calibration and out of sample testing. I.e. those without OIS ...
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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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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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Why is "full" Yield Curve (term structure of interest rates) 3 component based?
I am trying to understand bond-valuation and construction of yield curve. I don't have any exposure to bootstrapping or what-so-ever as of now. So it's appreciated to have an example but not too ...
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Calculating instantaneous forward rate from zero-coupon yield curve
I have a big dataset containing zero-coupon bond yields with different relative maturities. I fix a time horizon on my dataset and I want to calculate instantaneous forward rate. I'm going to write ...
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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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Looking for a pricing library supporting Mutli-curve Framework
I am looking for a builder of Yield curves by tenors (O/N, 1M, 3M, 6M, 12M) respect to a given discount curve based on multi-curve framework as described below :
Interest-rate Modelling with Multiple ...
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Interpolating spot rates given intermittent coupon-bond prices.
I'm trying to bootstrap spot rates given coupon-paying bond data. To simplify my problem, assume we are working with only 3 given data, the price/coupon rate on semi-annual bonds maturing in 0.5, 1, ...
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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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Economic indicators leading the yield curve
There is a lot of research on how the government yield curve can be used to predict the economy. The government yield curve is often seen as a leading indicator. But for which variables is the curve a ...
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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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How to manage evaluation date changes in QuantLib while using ImpliedTermStructure Class
I will not attach the whole code 'cause it would be just a huge waste of space and it would be not useful for this question's purpose.
What I am going to attach here is a snippet code and its output, ...
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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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Deriving the par-yield curve
Given for example 6 bond prices and their respective 6 cashflows over a time period of 6 years, I have managed to derive the zero-coupon yield curve using the bootstrap method.
However, it got lost ...
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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
$$-\frac{log Z(r,t;T)}{(T-t)}\approx-a+\left(\...
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Yield curve fitting example in Wilmott on Quant Finance p.528
In Wilmott on Quantitative Finance Vol. 2, p. 528, Section 31.4.2, is given a power series expansion for a zero coupon bond
$$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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How does the 2-factor Hull White model propagate the forward rates curve?
I've been trying to get a grasp on some of the basics of interest rate modeling, and am looking to simulate rates using the 2 factor Hull White model, which I am aware offers a more realistic model of ...
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Implied term structure from risky discount curve: does it make sense?
We know that, taken every discount curve, it's possible to calculate its forward rates according to our tenor preferences.
We know also that it's actually possible to extract an implied term ...
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"Friendly" papers about maximum smoothness yield curve modelling
I'm currently looking to implement some version of the yield curve modeling techniques in the maximum smoothness framework. The papers I have found so far explains the theory pretty well, but I find ...
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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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Zero Curve Calculation for AUD, CAD (post LIBOR scandal)
In the end of May 2013 British Bankers Association (BBA) stopped publishing LIBOR rates for Australian and Canadian dollars in a light of recent scandals.
LIBOR rates were essential for creating zero ...
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RQuantLib: any difference between FixedRateBond() and FixedRateBondPriceByYield() with flat term structure?
Please, consider the following functions from RQuantLib package:
FixedRateBond()
...
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Bond curve extrapolation
What are the best methods to extrapolate bond yields from an existing curve that doesn't extend quite this far?
For example, how would one come about finding a theoretical bond yield for a 40 or 50 ...
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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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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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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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Using the termstrc package in R
I am attempting to use the function estim_nss from the termstrc package in R to find the spot curve from constant maturity rates published by the Fed. I am using this package because I will need to ...
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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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About Option Adjusted Spread, rate curves and bonds comparison
I have few questions about using OAS as a measure of risk:
does OAS allow for comparison between bonds with and without embedded options (e.g. a callable bond against a plain vanilla one against a ...
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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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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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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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Bootstrapping spot rates from treasury yield curve
I'm attempting to construct a spot rate and forward rate curve from the 2011 daily treasury yield curve rates provided by the US Treasury. All US Treasury securities (1m, 3m, 6m, 1y, 2y, 3y, 5y, 7y, ...
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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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Which interest rate should I use for the discount rate in real-world pricing?
Suppose I want to compute the time value of money (present value, future value, etc). I need to put an interest rate into the calculation.
Which real world interest rate would best be used here, ...
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Why is an inverted yield curve a problem?
Immediately preceding the worst of the financial crisis, my professors all pointed out to me that the yield curve had inverted -- short-term yields were more risky than 20-year or 30-year Treasury ...
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