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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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Typo in Wilmott's Forward rate formula?

I am going through the 2nd edition of Paul Wilmott on Quantitative Finance, and came across the following, Shouldn't the last equality be $$ F(t;T) = y(t;T) + \color{red}{(T-t)}\frac{\partial y}{\...
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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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RQuantLib: any difference between FixedRateBond() and FixedRateBondPriceByYield() with flat term structure?

Please, consider the following functions from RQuantLib package: FixedRateBond() ...
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True or false: roll-down return is negative when a bond is trading at a premium

These three sources all say that the bond roll-down effect is negative if the bond is trading at a premium: https://www.investopedia.com/terms/r/rolldownreturn.asp https://corporatefinanceinstitute....
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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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Using Python Quantlib's FittedBondDiscountCurve as Evaluator of Parametric Curve - Errors

I am using Quantlib's FittedBondDiscountCurve in Python 3.7 and setting MaxIterations to 0, and giving a guess_solution, which then turns the routine into an evaluator for the parametric form I choose,...
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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 ...
A.L. Verminburger's user avatar
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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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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 ...
Quanti's user avatar
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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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Interpreting SOFR OIS Curve from CME

I have a doubt regarding the daily SOFR OIS Curve published by CME. https://www.cmegroup.com/trading/interest-rates/cleared-otc-sofr-swaps.html#sofroiscurve If we refer to the curve dated 22 Jul 2022.....
Rohit Gajare's user avatar
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Term premium with daily vs monthly time series

I have estimated the term premium for the Polish Government Bonds (POLGBs) using the methods described by Adrian et al. (2013) (often referred to as ACM). The underlying yields are interpolated from ...
borninthenorth's user avatar
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Yield to maturity of amortized bond

I have an amortized bond with maturity at 30.04.2023, a semiannual frequency, 10% coupon rate, 30Е/360 day convention, and a clean price of 104.9367. Also, there are two amortization payments: 300 at ...
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Building Yield Curve using different instruments

I'm trying to back out the LIBOR curves on Bloomberg. And I am using exactly the same instruments as BBG, i.e. 3-month LIBOR, followed by 6 EuroDollar Futures contracts (ED1, ..., ED6), and finally ...
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Robust standard errors OLS for term structure

Suppose i have estimated the following model with OLS: $y_{1,t+1} - y_{1,t} = \alpha + \beta y_{1,t} + \epsilon_{t+1}$. Where $y_{1,t}$ is the 1 month zero-coupon yield at time t. What would be an ...
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Why does adding a negative risk premium to the short rate avoid the occurrence of inverse yield curves?

I am reading about the Vasicek One Factor short rate model and how to implement a change in measure from a risk-neutral to real-world measure, when I came across this comment: Adding a negative risk ...
coffee-raid's user avatar
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How to optimise Fixed Income portfolio (Yieldbook) based on YTM, duration, rating and exchange rate

I have a fixed income portfolio built up in the Yieldbook and BBG Port. However due to some bad performance of my portfolio compared to the benchmark I would like to build up an optimisation which ...
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Par rates, zero rates and forward rates curves in swaps

I'm new to the concept of swaps, I'm having hard time understanding what each curve relationship with a swap derivative traded in the market. Can someone please explain this? Thank you.
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How to interpret DV01 in terms of PCA equivalent?

I have computed the PCs for daily changes in the UST yield curve over the last 5 years using the covariance matrix and can explain 94% of the variance using the first two components, which is good ...
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Yield Curve Trading Strategy Explaining Books

Recently I really enjoyed being here while getting great recommendations. Would like to thank you all. Could you please recommend some books/papers on trading strategies, lets say yield curve ...
TryingtobeQuant's user avatar
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116 views

Strategy in steepening curve environment, stable spreads - HotS interview problem

The following problem was found in "Heard on the Street": You construct a yield curve for (coupon-bearing) treasuries. A particular five-year corporate zero-coupon bond has a default risk ...
Lepidopterist's user avatar
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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 ...
Dhruv Mahajan's user avatar
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How do traders determine when points in a yield curve are at 'fair value'?

While on my last day on an internship last summer, I heard on the morning call a UK rates trader say something along the lines of: "Most of the curve is at fair value at the moment, so nothing ...
ODP's user avatar
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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 ...
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Turn of the year

I understand the basics of "Turn of the year" effect. But I am wondering why does this effect sometimes cause overnight rates around year end to dip below normal overnight rate levels (i.e. negative ...
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Data source for a corporate bond yield curve?

Yield curves are a valuable tool for economic analysis. It is particularly interesting to analyse the difference between Government Debt yields and Corporate Debt yields (credit spreads). This gives ...
DVCITIS's user avatar
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1 answer
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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 ...
georgeb's user avatar
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Multiple factor Hull-While and yield curve deformation

I am currently studying rate models and I understand that the One-Factor model has some incompleteness: The yield-curve can only be shifted. But I don’t understand what parameter controls this shift ( ...
Adel Chakir's user avatar
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180 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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Can I use Nielson Siegel to 'interpolate' par yield

The NS model initially set a parametric form for forwards and we can get equivalent zero rates. If I have a few par yields, can I simply fit the par yields to the NS form or the NS form of the zero ...
HoldBreath's user avatar
1 vote
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107 views

Apply monotone convex interpolation to swap rate input data

I'm trying to apply Hagan & West's monotone convex interpolation to a 6m EURIBOR (forward) curve using ESTR (already bootstrapped) for discounting. In their paper Hagan & West use discrete ...
BerndSchmitz's user avatar
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building an em fx forward curve with forward spreads

Like the title suggests, I'm trying to build a forward curve for exchange rates in USD/em currencies. I have certain forward points already, but they're in spreads and ideally, I'd like to construct ...
quantwannabe's user avatar
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197 views

Onshore vs offshore curve construction

Can anyone guide me to links or literature regarding onshore vs offshore curve construction? What kind of instruments do you use? Take for CNH (offshore) (vs) CNY (onshore curves) for example: For CNY ...
Benedict's user avatar
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YTMs of Ukrainian Bonds are much greater than published yield curve suggests

I noticed that the yields to maturity of Ukrainian government bonds seem to be much greater (multiple times greater in some cases) than the avaialible yield curves suggest, and I'm trying to ...
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Data on historical, cross-country REAL yield curves (i.e. inflation-linked bonds)

I asked here about data on a data source for historical yield curves for many countries. Many central banks (linked there, in Helin's answer) publish estimates for their nominal yield curves. But most ...
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Replicating Bloomberg's zero rates bootstrapping

I'm interested in manually replicating the bootstrapping procedure that Bloomberg uses to built ICVS179 (RUB vs MosPrime 3M) curve up to a two years tenor as of October 12th 2021. These are the market ...
Hasek's user avatar
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Including Exogeneous variables in short rate models

I am trying to use short rate models (e.g. Vasicek, CIR or Hull-White) to forecast next one or two months yield curve. In this context, is there a way that I can include some exogenous economic or ...
Hamed's user avatar
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How to obtain the discount curve under Vasicek interest rate for discounting cash flow?

Suppose that the spot rate is governed by a Vasicek model. We know that there is an analytical solution for the zero-coupon bond. I guess the discount curve is constructed by the Yield curve in which ...
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Hedging Options assuming a non-constant Yield Curve

I have read most of Shreve's Stochastic Calculus for Finance II. In it, the author prices various option types assuming an interest rate that is constant with respect to time. We can expand this model ...
user54908's user avatar
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Short rate models practical textbook

Currently working on a validation and testing of a yield curve model (one factor short rate model). Have been reading Andersen and Piterbarg, and Mercurio and Brigo. Good for true understanding, but ...
deblue's user avatar
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Quantlib Yield Curve given spot and forward rate

Is it possible to create a yield curve, given the spot rate and the forward rate?
Malekik's user avatar
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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 ...
Gert van Dasler's user avatar
1 vote
0 answers
960 views

Calibrating Vasicek model for historical data

I need to to estimate the parameters of vasicek model to predict the zero curve. My database has 4k daily observations of zero rate for 37 maturities. My question is do I have to estimate the model ...
Sizirr01's user avatar
1 vote
0 answers
251 views

pca for yield curve

I used Principe component analysis on yield curve data this was the result ...
Pelumi's user avatar
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513 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 ...
user2728814's user avatar
1 vote
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67 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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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; ...
Kiann's user avatar
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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 ...
Simon Nicholls's user avatar
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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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