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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32 views

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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23 views

Nelson Siegel Model - Backing out zero rate from Quantlib

I copied and pasted the example code from the quantlib python docs (https://quantlib-python-docs.readthedocs.io/en/latest/termstructures.html). From this, I am trying extract the parameters from the ...
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130 views

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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74 views

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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25 views

Treasury STRIP quotes

I'm looking for market price data on US Treasury STRIPS, but I can't find quotes anywhere. Would anyone happen to know a source for this?
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Standardize YTM's of coupon bonds with different coupon frequencies

In Financial Mathematics for Actuaries by Wai-Sum Chan and Yiu-Kuen Tse, the following formula is given for a $n$-year annual coupon bond with transaction price $P$ where the yield to maturity is $i_Y$...
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34 views

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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1answer
115 views

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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2answers
97 views

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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1answer
93 views

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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79 views

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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28 views

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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119 views

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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192 views

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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37 views

Hull-White model for yield curve prediction

I am using the Hull-White model (extended version of Vasicek) to predict Canadian zero-coupon bond yield curves. Most of the time the model does a pretty good job of fitting the real curve in terms of ...
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85 views

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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QuantLib C++: Extract RateHelpers from PiecewiseYieldCurve

Is there any way to extract RateHelpers that are used to build the PiecewiseYieldCurve in QuantLib? More specifically, I would like to know whether there is a way to obtain the instruments that are ...
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1answer
65 views

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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49 views

How the swap curve moves if fed fund rate decrease?

I am currently reading the book "Interest Rate Swap and other Derivatives by Howard Corb", in Chapter 8.2 Curve Trades, it mentioned: "Investors believes Fed is going to lowering the ...
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1answer
51 views

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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1answer
70 views

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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89 views

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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78 views

What is the correct way to build a full swaps curve using discount factor interpolation?

I want to keep this as high-level as possible so that the rest can be figured out, but we will use DF log-cubic interpolation. (Convert rates curve to discount factor curve, interpolate this using log-...
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112 views

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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1answer
120 views

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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167 views

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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58 views

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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1answer
84 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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175 views

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 0 1 0.003 ...
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1answer
146 views

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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73 views

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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75 views

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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65 views

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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38 views

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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171 views

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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83 views

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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1answer
96 views

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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2answers
239 views

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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225 views

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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1answer
49 views

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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60 views

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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114 views

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 ...
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2answers
365 views

QuantLib Python: how to calculate the npv of irregular cashflows?

I am trying to learn QuantLib for Python but I must say I am banging my head against the documentation (I also bought Ballabio's python cookbook) - maybe it's me, but even finding the most basic ...
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56 views

Hypothetical yield for a government perpetuity

I understand that with interpolation or bootstrapping one can determine spot rates given other spot rates, however how would you go about establishing what a hypothetical perpetual bond issued by, say,...
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219 views

How does the term premium of the 10y20y Treasury forward rate relate to the 30y rate?

I'm reading recent research on Treasuries and to paraphrase, it says that long term 10y20y Treasury forward rates now have a positive term premium over the long run nominal funds rate (neutral rate). ...
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1k views

How does one calculate carry-roll-down theoretically assuming expectations of short-term rates are realised

I am not asking for an explanation that is hugely quantitative, but rather one that is more intuitive. I am aware that there are different assumptions that one could take when it comes to carry-roll-...
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1answer
160 views

Calculate zero recovery discount curve from bond yields and cds prices?

Clarifying the below: Given the prices of bonds that are not trading in distress as yet (so yields are meaningful), and data on the CDS spreads, I’ve been looking for some approaches for estimating a ...
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3answers
508 views

Why does the coupon effect mean that higher yields do not necessarily mean that a bond is more attractive?

In Tuckman, it says "The fact that fairly priced bonds of the same maturity but different coupons have different yields-to-maturity is called the coupon effect. The implication of this effect is ...
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104 views

Negative Carry when Yield Curve is Downward Sloping

I am currently reading "The Treasury Bond Basis", and have a question regarding negative carry. The book states that the carry of a vanilla treasury bond will be negative when the yield ...

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