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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Treasury futures and the TUT spread historical volatility
I'm doing a study at Rutgers on the TUT spread. The TUT spread is composed of 2 2-year treasuries and 1 10-year treasury per spread. I was trying to estimate the historical volatility of the spread, ...
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Yield curve bootstrapping: direct market rates vs discount factors interpolation
From my understanding, there are (most generally speaking) two approaches for bootstrapping the yield curve (with an exact method). We can either interpolate between the market quotes (interbank ...
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Question from Duffie and Kan (1996)
Going through Duffie and Kan (1996) I came up with a question.
After Eq. $(3.4)$ the claim the following:
By $(2.4)$, we also know that $\mathcal{D} F (X_t, t) - R(X_t) F(X_t, t) = 0$. Since $F$ is ...
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Yield curve PCA: levels or daily moves?
I have tried using both yield curve levels as well as daily moves (absolute change) while doing PCA. Using both types of input/dataset gives me roughly the same shape in terms of principal components ...
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Formula to calculate the sensitivity of a bond to curve steepening
https://github.com/jerryxyx/TreasuryFutureTrading/blob/master/README.pdf
On page 2 of the pdf above, the sensitivity of a bond to increases in the slope of the curve, is given as $\ln(T)$, where $T$ ...
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Is the ytm curve same as the par curve? [duplicate]
probably a v basic Q, but what is the difference between the ytm curve and the par curve, and given the ytm curve I see in the market how do I build a corresponding par curve
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Zero Coupon Bond - Price and Yield when interest rate is a diffusion process and 0 "price of market risk"
Given that the price of market risk (or market price of interest rate risk) is $\lambda(r_t, t)=0$ and that we have the following dynamics of the interest rate (under the physical measure $P$.
$$dr_t =...
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Spot rate dominates the yield to maturity if the yield curve is normal
Let $y_{k}$ denote the yield-to-maturity of a $k$-period coupon bond. Let $S(k)$ denote the $k$-th period spot rate. If $y_{1}<y_{2}<y_{3}<\cdots$, then $S(k)\geq y_{k}$ for all $k\in \mathbb{...
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Principal component analysis on a yield curve
When conducting principal component analysis on the yield curve, PC1 = constant (level shift), PC2 = Slope, PC3 = Curvature. How do you interpret PC>3, e.g. PC 4?
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Can I use spot rates bootstrapped from a swap curve to price a bond?
Say that some corporation has a long position in a fixed rate bond. To turn this into a float-rate asset, they take a fixed paying position in a fixed/float swap. If we are given the par swap curve, ...
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PCA on portfolio depending on multiple time series
There is extensive documentation about PCA on specific time series (for example the UK yield curve). When you have a portfolio which only depends on the change of the UK yield curve then a PCA on the ...
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How do you construct a zero coupon curve from the current market yield curve?
If I was to take the current market yield to maturity and tenor for all bonds for a particular issuer how can I convert this curve into a zero-coupon curve?
For example if we were to get the yield and ...
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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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Data on historical, cross-country nominal yield curves
Various central banks publish their fitted nominal yield curve estimates: the Fed, BOE, SNB, BOC, ECB (cf: Bundesbank), RBA, Russia, RBI.
(I couldn't find for BOJ; Brazil; BOK; or PBOC. Links for ...
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IR risk sensitivity to curve instruments
I need to understand if the 2 approaches are equivalent:
assume I am constructing a yield curve with N instruments. I would like to compute IR delta for a product using this curve. One approach is to ...
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Principal Component Analysis for attributing yield curve changes
I have calculated the Principal components using daily yield curve changes. After calculating these components, i noticed that 98% of the return can be attributed to the first 3 components.
How do i ...
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Cross currency basis swaps to build interest rate curves
I was speaking with someone in the market the other day who complained that: "...we always have difficultly building the front end of the curve". He then went on to say that he builds ...
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Building a yield curve out of YTM's with different coupon periodicities
I want to graph a yield curve using the yield to maturity of my bonds. However, my coupon rates have different periodicities. Financial Mathematics for Actuaries by Wai-Sum Chan Yiu-Kuen Tse give the ...
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Building a Nelson-Siegel curve
I originally posted this on Mathematics, but was told my question is better suited here.
I want to graph a yield curve with an extended version of the Nelson-Siegel-Svensson. I have the issue date, ...
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Why do we have daily series of T-bill yields?
I understand that each week the US Treasury issues new T-bills at different maturities (1-month, 3-months, 1-year, etc). As far as I understand, this issuance happens every Tuesday. After the auction, ...
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Advice for automating swap curve construction
Let me start by assuming a simple single curve framework, whereby we take input instruments (mm,fra,futures,swaps etc) and strip out a discount-factor curve. Modern implementations of this are usually ...
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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 ...
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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 ...
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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 ...
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How to minimize Nelson-Siegel parametric form
Problem
I am given the following function to minimize (w.r.t. $\theta$)
$$f= \sum_{k=1}^5 \Big [ \sum_{i=1}^{N_k} CF_{k, i} \cdot e^{-r(t_{k, i}, \theta)\cdot t_{k, i}} - P_k^* \Big]^2$$
where $\...
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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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which market instruments are used to strip the SOFR curve under 1 year?
which instruments are used to strip the SOFR curve for the short term of the curve(below 1 y) ?
there are no swaps with maturity under 1 year, right?
thanks
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Yield curve steepening/flattening using different duration treasury futures (TUT Spread) and volatility
Yield curve steepening: long 2 contracts 2 year (2 contracts due to contract size), short 1 contract 10 year
Vice versa for flattening.
If the 2 year note has a expected volatility of 2% per contract (...
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How to resampling the risk of a specific tenor on a interest rate curve without replace the instrument?
For example, suppose we have an interest rate curve bootstrapped from multiple instruments, at the short end, we used eurodollar future (up to 2Y), at the longer end, we used interest rate swap (3Y to ...
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What's the difference between short rate and the bootstrapped interest rate?
This thing confused me for a long time, since we can a have a curve (e.g. LIBOR 3M) bootstrapped from the market quotes of instruments (e.g. FRA, SWAP), and we can get the spot rates and also the ...
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Generating a PAR curve from Bond Price Inputs
I am a brand new user to QuantLib and I am running it in Python.
I am attempting to generate a PAR yield curve from time to maturity and price input as shown here
'time to maturity': ['30-03-2020','...
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Constructing a USD LIBOR curve
USD_LIBOR rates are only published up to 12 months.
how would you approach constructing the curve to at least a 30-year tenor, to price for example an interest rate swap.
I have heard that swaps can ...
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How to value a long term interest rate swap if the floating leg is USD-LIBOR
To value an IRS, you require a spot/zero curve. If I am correct this zero curve will be the USD-LIBOR curve. However, if you have e.g. a 10-year swap that you are trying to value 2 months into the ...
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Zero Rates for Deposits using Quantlib Python
I have used QuantLib Python to construct a zero curve from deposits and bonds.
Below are my codes:
...
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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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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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Calculating the short rate from the discount curve
I'm currently looking at some code that implements the Hull-White model. As one of the inputs, the code accepts a table of discount factors at various dates.
Time in Years
Discount Factor
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0.003
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Interpolation of Zero rate curve
I have the zero rates at certain time nodes, say 3-month, 5-month, 8-month,...,2-yr,... Now I want to interpolate the curve so that the implied one-month forward rates are piecewise linear. That is, ...
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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 ...
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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 ...
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How to Validate and Test a Discount curve (i.e. SOFR, LIBOR, ESTR)
Let's say an Interest Rate/Discount Curve (SOFR, ESTR, LIBOR or any other) is bootstrapped using the standard inputs and market quotes for Cash, Futures, Bonds/Swaps. What are the metrics to be looked ...
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Can you use the Svensson model to fit a smoothed curve for yields on coupon paying bonds rather than spot rates?
i've been struggling to find an answer to this question online, I know most applications of the model are used on zero (aka spot) rates. But could you use yields from a sovereign yield curve (i.e ...
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Estimating VaR of bond due to changes in the US yield curve
I am attempting estimate the 99% 10-day VaR of an investment grade bond due to changes in the US yield curve. The data provided is the daily prices of the bond over time. In addition I have the Daily ...
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Repricing SOFR Quotes and Non-Zero NPV
I generated/calibrated a SOFR Curve using Quantlib Python and would like to know why when repricing the swaps have non-zero NPVs. Appreciate any assistance. Thank you.
Parameters
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How do I hedge yield spread?
We'd like to offer a product in which a notional amount $(N)$ is given, and the underlying is spread $(s)$ defined as, say, 30Y yield minus 10Y yield (both from treasury YTM yield curve). At the end ...
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Why can a two-factor interest rate model not be used to value a coupon bearing bond as the sum of options on ZCBs
I am currently reading some notes which state that
For one-factor models, the value of a European option on a coupon bond can be calculated as the sum of European options on zero-coupon bonds (ZCBs). ...
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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 ...
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Regressing changes in yield/yield curve
If I'm regressing changes in individual points along a yield curve and measures of changes in level/slope/curvature of that yield curve against the returns of some random variable then do I want to ...
