Questions tagged [yield-curve]

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Intuitive explanation of geometric mean

Suppose that the 10 Year Treasury Yield Rate varies every trading day during the year X1 (which in practice is accurate) what is the intuitive explanation behind calculating the geometric mean using ...
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785 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 ...
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5k 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.
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232 views

ESTER replacement for EONIA/EURIBOR

Does anybody know what impact the replacement of EONIA with ESTER ( Euro Short TErm Rate ) will have on discounting existing or new derivatives once EONIA will be restricted as of Jan 2020? I'm ...
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79 views

Why should central bank intervention cause inverted yield curve to be less effective as a recession signal?

Pimco's new CIO Dan Ivascyn believes that the inverted yield curve has become less effective as a signal of impending recession. https://www.bloomberg.com/news/articles/2017-06-22/pimco-s-ivascyn-...
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Is it possible to derive a reasonable USD yield curve using only publicly/freely available data sources?

Background I'm a corporate financial analyst with a small derivatives portfolio (amortizing interest rate swaps and FX forwards) looking to value these derivatives "properly" (which, in my case, ...
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2k views

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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196 views

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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151 views

Curve steepner and convexity

Can someone please explain why a curve steepener trade has a negative convexity? And are the gains from the steepness of the curve offset by the negative convexity?
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886 views

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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711 views

Details of calibration of Hull-White model

Consider the one-factor Hull-White model $$ \mathrm{d}r(t) = (\theta(t)-\kappa r(t))\mathrm{d}t + \sigma\mathrm{d}W(t) $$ When one calibrates the model to market data one chooses $$ \theta(t) = \...
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811 views

High convexity vs low convexity bond definition

Isn't high convexity always better than low convexity bond from the formula that $$\frac {ΔB} B=-D \frac {Δy} {1+y} + \frac 1 2 CΔy^2$$ Since $\frac 1 2 CΔy^2$ is positive no matter what so the price ...
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343 views

Build a swap curve / Swap Hedging

I’m going through the exercise of building a swap curve. I understand I need libor rates for the short-end, futures for the medium-end, and swap rates for the long-end. Should I be using bid, mid, ...
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938 views

Is the “swap curve” synonymous with the “yield curve”?

Looking at the swap curve construction here: http://www.bankofcanada.ca/wp-content/uploads/2010/01/wp00-17.pdf it seems to be constructed in an identical fashion as the yield curve as described here:...
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116 views

Interest rate risk using copulas

In order to simulate an interest rate yield curve, can I just estimate a covariance matrix of historical key rate data, simulate with a normal copula, spline my simulated key rates, then price my ...
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1answer
1k views

Deriving a 3M libor curve from 6M libor swaps and 3M-6M libor basis swaps

If I had a set of 6M Libor instruments and another set of 3M-6M basis swap instruments, how would I derive the 3M Libor curve? Just bootstrap the 6M curve and the basis curve and add up the zero ...
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455 views

How to get real interest rate from Nominal spot rates?

I have the nominal spot rates. Based on the Fisher equation , how to get the real interest rate ($r$) and the "expected inflation" ($\pi$) ?
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152 views

Yield curve interpolation at (very) short horizons

I'm struggling to find much information about yield curve interpolation for sub-yearly horizons. Say, one-two months. It seems to be the area where the curvature is usually nontrivial, while after ...
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307 views

“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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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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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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522 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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155 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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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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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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216 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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434 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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852 views

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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1answer
1k 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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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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58 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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1answer
121 views

stress testing zero coupon yield curve

i'm currently trying to stress test the zero coupon yield curve using daily observations from 2003 to 2019. Each Zero coupon yield curve originate from an actuarial curve with 37 tenors that range ...
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228 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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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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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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Custom Frequency termstrc Package

Termstrc package in R by default uses yearly coupon frequencies. Dataset i am working with is semi-yearly coupon bonds. Here are the variables it takes into the model ...
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131 views

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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152 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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291 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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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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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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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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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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1answer
432 views

QuantLib FittedBondDiscountCurve fitResults [Error]

I try to use FittedBondDiscountCurve with NelsonSiegelFitting, but I faced with error when call fitResults() method: ...
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162 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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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 ...