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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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What pricing curve to use for different instruments?

When pricing derivatives, their price depends on some yield curve, which is used to discount future cash flows. But there are many yield curves, dependent on what they're bootstrapped from. There's ...
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When using quantlib's swaphelper to build a curve, is the fixing lag considered?

For example, EUR Annual (vs. 3M EURIBOR) swap has 2-Business-Days Fixing Lag. When interpolating with 1Y swap, the forward 3M Euribor rate starting date is the reset date(2023/6/14), not the reset ...
Michelle's user avatar
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Constructing a yield curve with unknown discount factors

There are some questions and answers on this site about yield-curve construction, but none of them address the case where in an EM market setting, one might only have annual observability of (say) IRS ...
Conductor's user avatar
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How to calculate zero rate for deposits in an interest rate curve in PiecewiseLinearZero method

I am trying to duplicate zero rates and discount factors from ql.PiecewiseLinearZero method. To simplify calculation, I only use one deposite rate: 3M Euribor 0.03822. I set evaluationDate as ql.Date(...
Michelle's user avatar
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Parallel shift in spot yield curve moves the IRR of a bond portfolio in the same direction: Analytical Proof

I am trying to prove that a parallel shift in the spot yield curve will as its effect have the IRR of a bond portfolio move in the same direction and by the same amount. I have tested this on few ...
Milan's user avatar
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swap curve calibration with interpolation using newton-like method

suppose 2 swap market quotes for 1Y and 2Y and that swap payments occur semi-annually. calibrating / obtaining the discount factors means finding 4 unknowns / discount factors that reproduce the ...
baluch_stan's user avatar
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Double interpolation continuity

I am trying to use double interpolation(linear and forward quartic) but the interpolator is the zero coupon so at each time i need to convert the instantaneous forward rate to zc my problem is at the ...
Bred 's user avatar
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3 answers
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Does PCA for yield curve has any tangible value?

I am aware of an abundant literature on Principal Component Analysis (PCA) application for yield curves. All of these papers to me look merely a statistics-oriented results. Most of the papers argue ...
Sane's user avatar
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Yield to Maturity (YTM) to Zero Coupon Yield Curve (ZCYC) Forward Rate and Discount Factor mismatch in QuantLib

I have a set of YTM data for various tenors, and I'm constructing a ZCYC using the QuantLib library. However, when I calculate the forward rates and discount factors from the ZCYC and compare them ...
Roshan Yadav's user avatar
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Construct DeFi yield curve

I was wondering if anyone knows how to construct a yield curve for cryptocurrencies (for yTokens like yDAI and yETH for example). It'd be best if yield curves could be dynamic (though I think it could ...
Jenn Gunawan's user avatar
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Shape of Yield curve of ZCB under no-arbitrage

Sorry if the question is somewhat elementary, but I have thought about it for a while and I cannot figure out where my mistake is. Suppose we are in are in an arbitrage-free market in which risk-free ...
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Interpolation by central bank cometee meeting dates

I want to have an interpolation, to the yield curve, In the term up to a year, the forward daily curves will be the same between central bank cometee meeting dates (to be precice, the implemantation ...
Zeev's user avatar
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Cubic Spline Interpolation partial derivative to the point

Still didn't figure out this, so looking for some help, kindly apppreciated. By this blog https://blog.timodenk.com/cubic-spline-interpolation/index.html, the piecewise cubic spline interpolation is ...
imyafeng's user avatar
1 vote
2 answers
259 views

Yield curve and bond price

I am confused about how the yield curve is built and how it relates to the pricing of bonds. First what I don't understand is that when people talk about the yield curve, which yield curve are they ...
yield_curve_and_bonds's user avatar
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Explicit step by step curve construction using FRAs

I'm trying to understand a step by step process of building curve from the instruments to the final result, particularly how overlapped FRAs are used. i'm trying to build this in excel so I have a ...
Naim Hussain's user avatar
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How to compute discount factor from yield curve when there are two daycounts in play?

Let's say I have a yield curve, i.e. a series of times $t_1, ..., t_n$ and associated rates $r_{t_1}, ..., r_{t_n}$, such that my discount factors are $DF_{t_i} = (1+r_{t_i})^{(-t_i)}$. The curve has ...
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Bootstrapping adjustment for coupon

I struggling to get why in bootstrapping I need to divide the YTM by 2 (for semiannual coupons) and not adjust the power for the semiannual period. Please see below example. Consider two bonds with a ...
Finance_student's user avatar
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Relationship Between the Equity Funding Curve and Equity Forward Curve

am trying to understand the core concepts of Equity Forwards Curve, Funding Curve and yield Curves (most sources online seem to focus on Interest rate related examples, so any sources for equity ...
ESN's user avatar
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Why isn't the volatility version of the Nelson-Siegel model in the same shape as the original yield model?

If we compare the form of the original model: https://edisciplinas.usp.br/pluginfile.php/3180059/mod_resource/content/0/Nelson%2C%20Siegel%20%281987%29%20-%20Parsimonious%20Modeling%20of%20Yield%...
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Benchmark Treasury Curve Data

I want to calibrate US treasury bonds to get a benchmark curve as an exercise. I know that choice of bonds may be discretionary. But can you point me to any good public data source where I can get ...
Gary's user avatar
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Relationship of par-curve and zero-curve/spot-curve

I've been trying to bootstrap the zero-curve from a swap curve composed of ESTR OIS swaps. Theory says when the par-curve is upward sloping, the zero-curve will be above the par-curve and vice-versa. ...
Energy Media's user avatar
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How Zero Discount factors are calculated in Oracle and Wellstreetprep?

I've some inquiries that may be naive related to ZDF. I have got a look at those two resources for zero discount factors: Oracle - Zero Discount Factors Wallstreetprep - Discount Factor ...
user's user avatar
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Bootstrapping the zero-curve/spot-curve from incomplete swap curve par-rates

TL;DR: I have an incomplete set of swap rates and want to bootstrap the zero-rate curve, what can I do? I'm trying to construct a spot-rate/zero-rate curve from a swap curve (i.e. par-rate quotes) ...
Energy Media's user avatar
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177 views

Mathematical meaning of an inverted yield curve

I am currently working on rates model. I would like to understand, mathematically, what does it mean to have an inverted yield curve? And I am asking myself for a certain model, how can I generate an ...
StochasticMan's user avatar
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33 views

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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139 views

Methods for Constructing a Yield Curve

I wonder if the Raw interpolation (known as linear on the log of discount factors) can handle negative interest rate due to the inverted yield curve? I understand using the linear on log of rates and ...
Riskquant's user avatar
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Liquidity Preference Hypothesis and Yield Curve

Unlike under the Expectation Hypothesis (for which the forwards are perfect predictors of the expected short rates), for the LPH forward=expected short rates + LP and consequently the expected short ...
Maurizio Marinaro's user avatar
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116 views

QuantLib FittedBondDiscountCurve does not produce expected rates

I am using the QuantLib library to fit yield curves. For a $\\\$100$ face bond, with price equal to $\\\$100$, and coupon equal to $\\\$0$, I would expect it to provide a zeroRate of $0.0\%$. However, ...
Trevor J Richards's user avatar
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226 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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Quantlib Bond yield jump on front end of the curve

I'm trying to build up a US treasury curves using Bills and bonds with the FixedRateBond class, however when I compared the ParYield from .bondYield() and zero_rate from yield curve instance. The ...
ETH's user avatar
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Constructing the FedFunds Yield Curve with jumps at FOMC meetings

When constructing the FedFunds yield curve I want to define the curve based on two separate interpolation schemes. The first on the short end being LogLinear on the discount factors between FOMC ...
ml4irs'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
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153 views

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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swap carry/rolldown mid-period

Pretty much all discussions and examples I have seen discussing carry and roll down for fix-flt interest rate swaps are ones where the forward date coincides with the coupon dates on both legs. It ...
Magnyz's user avatar
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Curve optimization to predict monetary policy path (OIS Curve)

This is a question about a relatively undeveloped market (Chile) in which Camara the O/N rate is daily compounded (OIS Curve). The available instruments in the market are short term rates ie 1m 2m 3m ...
SwapperAtPar's user avatar
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Dynamic Nelson-Siegel model with time-varying scale factor lambda: how to ensure the non-negativity of the state variable?

I'm trying to estimate a Dynamic Nelson-Siegel-Svensson (DNSS) model with time-varying scale factors lambda_{1} and lambda_{2}. I am therefore estimating the lambdas as state variables (same as the ...
Jessica F.'s user avatar
1 vote
1 answer
70 views

Overlay Analysis of US Yield Curve

Let's define the US yield curve as the O/N fed funds rate, then the on the run 2/3/5/7/10/20/30y us treasury notes and bonds, represented by their yield to maturity as of today T. What I am trying to ...
PHH's user avatar
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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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1 answer
142 views

Recommended books/resources for IRRBB risk metrics calculation

Any recommendations for books/resources/videos/on-demand courses for in-depth IRRBB-related risk metrics calculation etc? Yield Curve Risk, Basis Risk, Repricing Risk, Optionality Risk, Value at Risk, ...
Pat's user avatar
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1 vote
1 answer
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Zero Curve Interpolation Does Not recover Node point input rates

I having an issue with interpolation in QuantLib Python. Please see the code below for a minimum working example ...
Tomi Adewusi's user avatar
1 vote
0 answers
96 views

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
1 vote
2 answers
454 views

Different maturities but same tenor to obtain the yield

My question is in regards to obtaining the yield of a specific tenor at any date (for example, when constructing the yield curve). For example, when calculating the yield for a specific zero-coupon (...
bond-pricer's user avatar
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251 views

QuantLib Yield Curve Bootstrapping Fails with Bracketing Error

I'm trying to build the yield curve simply using Treasury yields one would get by querying the FRED API, but as my code below will show, I'm told on the 1st iteration that there was failure at the 4th ...
pmse234's user avatar
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What does volatility process mean and how is it different from volatility?

I have been reading the paper "Bridging P-Q Modeling Divide with Factor HJM Modeling Framework" by Lyashenko and Goncharov (2022). On Equation 5 of page 4 of the paper, I came across the ...
Dishay Mehta's user avatar
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58 views

How do I obtain the RMSE from a QuantLib curve estimation?

I'm estimating yield curves in Python using the QuantLib package and the included Nelson Siegel, Svensson, specifications. I can get the estimated parameters, but I would like to see a measure of the ...
ibbore's user avatar
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1 answer
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BootStrap with quantlib USD SOFR (vs. FIXED RATE) swap curve

I struggle to understand why my market rates does not match my bootstrap model. So I wonder why the spread is that high between market & model. ...
TourEiffel's user avatar
2 votes
0 answers
234 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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4 votes
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Parameters in Nelson-Siegel model and Nelson-Siegel-Svensson model

I am trying to determine the parameters for the Nelson Siegel and Nelson Siegel Svensson model and try to solve SE=$\sum_{i=1}^{n_{i}}(y_{t_{i}}-\hat{y}_{t_{i}}(X))^{2}$ where $y_{t_{i}}$ denotes the ...
Martin N.'s user avatar
2 votes
1 answer
485 views

Factor loadings in Nelson-Siegel model

The Nelson-Siegel model has the following form $y(\tau)={}_{1}X+{}_{2}X\frac{1-e^{-\lambda{\tau}}}{{\lambda{\tau}}}+{}_{3}X\left ( \frac{1-e^{-\lambda{\tau}}}{{\lambda{\tau}}}-e^{-\lambda{\tau}} \...
Martin N.'s user avatar
2 votes
1 answer
81 views

Mean level of the state variables under the risk-neutral measure in Arbitrage-free Nelson Siegel

I do not understand why mean levels of the state variables under the risk-neutral measure, $\theta^{\mathbb{Q}}$, in Arbitrage-free Nelson-Siegel is set to zero. It should follow from the following ...
Martin N.'s user avatar

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