# 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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### Shocking an OTR curve to price an OFF THE RUN

I would like to shock an OTR curve in a certain way and reprice an off-the-run bond after that shock. I have a yield curve that I want to shock. This yield curve is the YTM of the OTR bonds. The way I ...
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### Coupon effect and US economy [closed]

When people talk about the health of the US economy they look at the yield curve. The yield curve can mean may different things. It can be the Zero coupon curve, the forward yield curve, the yield to ...
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### Bootstrapping Par Curves from Spot and their values with respect to each other

Context I am trying to code a general algorithm to 'convert' a spot curve to a par curve for any given curve. This is part of a larger problem - where I need to calculate par rate for any given spot ...
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### OIS curve, why a multi-curve framework is needed

I don't understand why multi-curve framework is now needed. Here is my understanding: The OIS curve is now the curve considered risk-free, and it's used to discount the cashflows for example to value ...
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### Empirical factors vs PCA factors representation

I have performed a Principal Component Analysis on Matlab on a time series of US Treasury yields from 1990 to the present, which determines a $n \times m$ matrix $Y$, where $n = 8577$ are the ...
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### PCA on yield curve - Matlab

Consider that I have a dataset of 8964 daily observation of US yields from 1990 to May 2024. These yields are related to each maturity from 3 months, every 3 months, to 30 years, for a total of 120 ...
1 vote
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### Correlation between Yield Curve PCA components and Level - Slope - Curvature

I found a piece of the following book: Yield Curve Modeling and Forecasting That states that when extracting the PCA components from the yield curve and projecting the data along these axis we find a ...
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### Modeling Yield Scenarios and Curve Shocks for Bonds

I would like to do the following: Given a basket of bonds I want to generate different yield scenarios at a future time $T$ for the different bonds in my basket. I also want to see how I can shock the ...
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### Yield curve steepner or flattener trades

Hi if anyone will kindly help to clear up some confusion that i might have. Market is currently placing bets on a curve steepener trade due to Trump's potential election success. Steepener trade is ...
1 vote
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### Derivatives data vendors for individual user [duplicate]

I am looking for a market data vendor that I can utilize for my personal research or practice. Among the market data vendors that provide the swap rate required for bootstrapping, are there any ...
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### Quantlib Python Yield Curve Construction Inconsistent

Why is it that my first method of looping through dates and creating curves on each date, fails on a specific day, but when creating a curve using only that dates data it does not? I created a repo ...
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### Bootstrapping SOFR swap curve

I want to know key tenors of SOFR swap for building discounting curve for pricing derivatives. To build a similar curve to that of Bloomberg ICVS & SWPM, Which instruments should I use? Which ...
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### Bootstrapping a yield curve based on instruments with different spot lags

Recently I've had to pay closer attention to the minutiae of interest market conventions regarding fixing and settlement dates, and there's something I'm really struggling to get. If I understand it ...
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### What pricing curve to use for different instruments? [duplicate]

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 ...
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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 ...
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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(...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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### 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 ...
1 vote
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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 ...
1 vote
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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) ...
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### 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 ...
1 vote
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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 ( ...
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### 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 ...
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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 ...
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### 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, ...
1 vote
301 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 ...
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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 ...
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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 ...
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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 ...
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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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