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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233 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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175 views

daycount of the yield curve

Complete characterization of an interest rate requires a few elements: day count compounding frequency the rate itself start date and end date That said, I notice that day counts are never displayed ...
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91 views

Concentration risk in Rates

What are some good ways to assess the concentration risk for a rates curve or by currency when volumes traded by instrument are not easily available? For ex, if for some currencies, the PV01 at ...
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153 views

Construction of synthetic deposits

I'm looking at the paper "Everything You Always Wanted to Know About Multiple Interest Rate Curve Bootstrapping But Were Afraid To Ask". It describes how to construct synthetic deposits in order get a ...
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979 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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199 views

Does the YTM for a zero coupon treasury equal the treasury yield curve value for it's maturity?

The title is my question. I think the answer is yes, but I am unsure about it.
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55 views

Why 10 year treasury yield expectation note priced in bond prices?

A lot of large firms are predicting that the 10 year treasury yield is going to rise. My question is that if such prediction has any substance, shouldn't the current 10 year yield rise accordingly, as ...
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2k views

In what economic scenario do yield curves bull flatten or bear steepen?

Bull steepening and bear flattening have the common belief that in bad news, treasuries catch a bid and short end rallies more because most bad news are short lived. In good news, treasuries sell off ...
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227 views

Generating random yields

I would like to test different methods for fitting a yield curve, like the Nelson-Siegel, cubic splines etc. I would like to generate random yield to maturity data, that somehow reflects the common ...
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2k views

What is a Basis Swap Curve?

I know what a Swap Curve is. But I don't understand what a Basis Swap Curve is and how it is constructed? Need some guidance on this.
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527 views

Forward Curves and Par Yield Curves

I'm recently reading a research paper on the yield curve by Salomon brothers and in it it states that when the forward curve is above the par yield curve, it is seen as cheaper. If for example, the ...
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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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2k views

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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27 views

Quantlib Yield Curve given spot and forward rate

Is it possible to create a yield curve, given the spot rate and the forward rate?
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56 views

Risk-Neutral covariance matrix of arbitrage-free Nelson Siegel

For my thesis on a Bayesian sampling routine for a modification on arbitrage-free Nelson-Siegel I came across an equation that involves a matrix exponential within an integral, i.e. $\int_{0}^{\Delta ...
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125 views

pca for yield curve

I used Principe component analysis on yield curve data this was the result ...
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198 views

Matching the yield on a bond with the zeroRate on a curve in Quantlib

I am using QuantLib to generate a US Treasury curve from 1y, 3y, 5y, and 10y yield quotes. However, after building the curve and running zeroRate on it, it ...
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29 views

Retrieve SYC from Par yields

Currently studying about fixed income and the construction of the Spot yield curve, but I do not know whether my intuition is right. Suppose we have a firm that has traded Bond for different ...
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449 views

PCA predicted yield curve moves do not match (closely) realized yield curve moves

I have a need to set-up a methodology to decompose the x-day yield curve moves into its underlying (3) PCAs. Specifically, for an example, to generate the 1-day moves in the EUR-swap yield curve; ...
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84 views

Duration and yield

I have some basic questions about mainly duration and yield. 1) Almost no-one defines what yield they are talking about when talking about duration and discount rate, I've seen some talk about ...
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472 views

Interview question on interest rate spread trade

Consider this interview question: Tell me how you'd construct a risk neutral cross country trade on the 2 year – 10 year interest rate spread in Germany and the U.S. What does "risk neutral" mean ...
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60 views

Using above par zero coupon bond to build a zero coupon curve

Should I discard bonds above par (zero coupon bond with market price over par value) when I build a zero coupon curve? Most of the academic textbooks use bonds below par as inputs to build Zero ...
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150 views

basic difference between interest rate models

I am reading up on interest rate models, but currently confused about difference in the two types of models: no arb models like ho-lee, vasicek etc. others like nelson siegel, pca models etc. While ...
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232 views

Yield curve estimaton using linear regression

Assuming that there are not any zero coupon bonds in the market, then someone has to use the prices of regular bonds with same maturity and characteristics (risk,issue etc.) to obtain the yield curve. ...
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358 views

Simulation curves; PRIIPS category 3

Once the yield matrix has been computed, the eigenvectors must be calculated to project the yield matrix on the 3 main dimensions. Tehen is wasted to calculate the yield matrix to be used for the ...
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173 views

How are short rate models used to construct the whole of the yield curve? [closed]

There are a number of short rate models that give $r(t)$. How can those be used to construct the whole of the yield curve $y(t,T)$ (where $y(t, 0) = r(t)$)?
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277 views

Decreasing Forward FX rate curve

i've constructed a Forward FX curve using the formula: $F= Spot \frac{(1+I_b*n/N)}{(1+I_c*n/N)}$ when i get these Forward rates for 1 month, 3, 6 till 1 year i got a decreasing forward Fx Curve How ...
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Discretizing the conditional variance in the Arbitrage Free Dynamic Nelson Siegel model

for my thesis I am trying to fit the correlated factor arbitrage free dynamic Nelson Siegel model to yield data. I use the Kalman filter to model this but since the model is in continuous time, I need ...
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166 views

Daily yield to maturity using `uniroot` in R: error

So, I'm trying to compute the daily yielt to maturity on basis of data retrieved from Datastream. The data comprises EMU Treasury bonds with Prices, Coupon and Maturity date. In R the matrices are ...
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Multi-factor affine yield models reference (a la Duffie and Kan)

http://www.darrellduffie.com/uploads/pubs/DuffieKan1996.pdf I was trying to read above paper on the topic of multi-factor affine models, but I presume the contents have been dealt with more ...
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355 views

Find Z-Spread in R

I am new to the quant finance community... I have a series of bond cash flows, its market prices and also the spot rates for the timing of those cash flows. How to find the Z-Spread that matches its ...
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181 views

Bonds with embedded options pricing via binomial model

Notation: t - time; G(t) - zero-coupon yield curve; $r$, $r_d$, $r_u$ - interest rates. The task is to find market price of a bond for today, while knowing the price of a number of other bonds. ...
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112 views

HJM model, existence of arbitrage:

The Setup: Suppose I know the yield curve of a Bond satisfies: f (0, t) = 0.04 for t ≥ 0 and f (ω, 1, t) = 0.06, t ≥ 1, ω = ω 1 , 0.02, t ≥ 1, ω = ω 2 , where Ω = {ω 1 , ω 2 } with P[ω i ] > 0, i = 1,...
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Moody's seasoned corporate bond yields

The Fed publishes Moody's seasoned corporate bond yields here. These yields are not broken out by maturity. According to this website, the yields represent "long-term" bonds, with minimum and ...
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state space for affine yield curve

i would like to reproduce in R the working paper " Affine free arbitrage class of Nelson Siegel term structure". The authors considering the equation of nelson siegel plus an adjustment term(C(t,T)) ...
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128 views

affine arbitrage free class of nelson siegel yield curve

I'm studying statistics for finance at university. Last week i read the working paper on "The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models". I would like to reproduce in R ...
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115 views

Smoothening yield curve by minimizing forward curve slope

I am using government bullet bond data and have bootstrapped a yield curve by solving the following optimization which minimizes unweighted price error: $$\text{min}\sum_i\left(P_i-\sum_t\frac{F_{it}}...
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2k views

Zero rate vs. yield on coupon bearing bond

in Hull's solutions manual of Options, Futures & Derivatives (8th edition), there's question 4.7, in which is asked to put the following in descending order: a) the five-year zero rate, b) the ...
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116 views

Term Structure and short rates

If I have a term structure/yield curve given by: $$f(t, T) = f(0, T) + σ^2t(T − \frac{t}{2}) + σB_t $$ and want to find the short/spot rate $r_t$, is this simply: $$f(t,t) = f(0,t) + \sigma^2t(t-\...
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194 views

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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Discount Curve Vs Forward Curve

This could be a trivial question, but would I like to clear the concepts. Our firm started sourcing the Murex Trades which has all the variety of Derivative products. I noticed that the Curve ...
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108 views

Meaning/importance of “yields” (bonds) [closed]

After reading many articles on bond yields (yield-to-maturity) I'm still not getting what they are used for by investors. I understand the math behind its evaluation, but, say, what exactly I can tell ...
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Value of a 30 year bond using the Yield curve

If I buy a $1 30 year bond with 4% coupon payment, would my cash flow be: $$ V^{30}(t) = \frac{$1 \times0.04}{1 + R(t, 1)} + \frac{$1 \times0.04}{1 + R(t, 2)} + \cdots + \frac{$1 + $1 \times0.04}{1 + ...
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1k views

Constructing yield curve directly from yield-to-maturity data

I'm trying to use Bloomberg yield-to-maturity data for sets of sovereign bonds of different maturities to fit to a yield curve. I looked into using the QuantLib library (the FittedBondCurve ...
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Relationship Between Yield Curve and STRIP Prices

Suppose at different maturities (e.g., 1 year from now, 2 years from now, 3 years from now, etc.), the price of a STRIP security is consistently decreasing as the maturity increases all else held ...
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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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IR parity theorem

I wonder how post crisis multiple curve approach influences the ir parity theorem: $${\displaystyle (1+i_{\$})={\frac {E_{t}S_{t+k}}{S_{t}}}(1+i_{c})}$$ Let's say that $i_\$$ is USD Libor 3m rate ...
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How to compute treasury yields as reported in the online financial newspapers?

I am trying to compute treasury yields (with different data) similar to what has been done by bloomberg, yahoo finance, msn money, and wall street. I find the data reported by these are not the same ...
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Using Forward or Spot rates for NPV?

I have to calculate the NPV for Capital Budgeting in a project with annual cash flows discounted by a risk - free interest rates 1.Instead of using a constant interest rate, should it better to use ...
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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 ...