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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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56 views

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 ...
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495 views

Why is carry divided by DV01 to scale it?

If I understand correctly, 6M carry in a fixed-floating interest rate swap should be the difference between the fixed and floating leg. When I read this on Page 2: https://corporate.nordea.com/api/...
2 votes
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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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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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1 answer
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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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1 answer
148 views

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 ...
2 votes
3 answers
345 views

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 ...
2 votes
1 answer
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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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1 answer
78 views

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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1 answer
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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 ...
33 votes
3 answers
59k views

What is the Swap Curve?

What is the so-called Swap Curve, and how does it relate to the Zero Curve (or spot yield curve)? Does it only refer to a curve of swap rates versus maturities found in the market? Or is it a swap ...
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594 views

Bootstrapping semi annual bond

I have a bond that pays out semi-annually. The coupon is 0.14, which means it pays 0.7 after 6 months, and then 100.7 after another 6 months. I need to find the discount factors by bootstrapping. Is ...
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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 ...
5 votes
3 answers
345 views

How would you build a yield curve for a cryptocurrency with only a perpetual futures market?

Assuming that hourly/daily funding rates are autocorrelated and revert to a long term mean, then perhaps the following would work: Use the average of the last N day funding rate as as predictor of the ...
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1 answer
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Converting US Treasury CMT to Discount Yields

I'd like to convert the US Treasury Constant Maturity series (par, semi-annual coupon, Actual/365 daycount convention) into Discount Factors (for appropriate comparison for certain money-market series,...
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2 answers
112 views

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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1 answer
765 views

Yield Curve Flattening Trade

Relatively simple question, but came upon it in class and have not been able to come up with an answer: The two-year bond yield is equal to 4% while the 10-year one is equal to 10%. You want to put ...
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2 answers
6k 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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1 answer
1k views

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. ...
2 votes
1 answer
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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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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 ...
3 votes
2 answers
1k views

Construct a butterfly interest rate portfolio to eliminate PCA exposures

I have data from 2012 to 2016 for interest rates whose term range from 2 month to 30 years, a total of 10 Principal components can be calculated. Then I want to construct a portfolio, $$WFLY = w_1 *5Y ...
1 vote
1 answer
188 views

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
1 answer
114 views

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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233 views

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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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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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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372 views

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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2 answers
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 ...
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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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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 ...
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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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115 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, ...
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225 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 ...
3 votes
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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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How to measure Steepener/Flattener/Butterfly sensitivity? (in 01)

This seems like a simple concept but I'm a bit lost. How can I calculate the dollar value sensitivity for a yield curve slope or butterfly position? I understand how DV01 can be calculated, but it ...
2 votes
2 answers
539 views

QuantLib: How to bootstrap Yield Curve using 3M futures - Python

I need to bootstrap a yieldcurve with 3M futures, using a cubic spline if possible. Using, for example 3M Euribor, how do I bootstrap the yield curve using python? I have a vector of dates and a ...
2 votes
1 answer
499 views

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 ...
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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 ...
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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 ...
1 vote
1 answer
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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 ...

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