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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75 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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273 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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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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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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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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118 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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141 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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77 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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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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Bootstrapping The Spot Yield Curve

I have some questions regarding the bootstrapping technique for constructing the spot yield curve. Assume that I want to fit the spot yield curve for U.S Treasury securities and I observe the prices ...
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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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325 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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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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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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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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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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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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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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Free swaps/swaptions data

I would like to play around a bit with some yield curve models. I am looking for a way to get a hold of free swaps/swaptions data. Obviously, the quality does not have to be super good, I am merely ...
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Nelson Siegel Model calculation of the zero bound price at time zero that expires in 2 years

I am somewhat stuck and not sure how to proceed, so any help would be appreciated. I got the Nelson Siegel model with all parameters for the real data. The curve that is produced is yield vs maturity. ...
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Construct the midsection of the yield curve from Eurodollar futures prices

As detailed in this section of the Wikipedia page on the Yield Curve, we can construct the yield curve from the money market as follows: The LIBOR rates give us the short end of the curve (t < 3m) ...
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315 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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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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203 views

R Yield Curve: Nelson Siegel Fitting

I'm trying to fit a yield curve using Nelson Siegel through the R Yield Curve package. However, the Nelson.Siegel() function only takes two inputs of yield and ...
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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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Quantifying the difference between 2 Foward Curves

I'd like to quantify the difference between 2 Foward Curves. In particular, I'd like to get a single metric which represents the magnitude of change between curve A and curve B. I'd like to plot this ...
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How to find OIS discounting factors from OIS swap rates. Please explain with example

Suppose I have the following OIS Swap rates: 1 year OIS Swap: 0.36% 2 year OIS Swap: 0.37% 3 year OIS Swap: 0.38% 4 year OIS Swap: 0.40% From these, how do I get the OIS Discounting factors for ...
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Comparing curve fits

I am experimenting with building a forward curve. I have a piece of code which constructs my prototype curve. I've got a curve sample which was constructed manually and I use it as the baseline - the &...
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Relationship Between Yield Curve and STRIP Prices

Suppose at different maturities (e.g., 1 year from now, 2 years from now, 3 years from now, etc.), the price of a STRIP security is consistently decreasing as the maturity increases all else held ...
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Quantlib Yield Curve given spot and forward rate

Is it possible to create a yield curve, given the spot rate and the forward rate?
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Meaning/importance of “yields” (bonds) [closed]

After reading many articles on bond yields (yield-to-maturity) I'm still not getting what they are used for by investors. I understand the math behind its evaluation, but, say, what exactly I can tell ...
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862 views

Swap curve construction

I am new to this area so my question might be basic to many but please answer. For valuing interest rate swaps how will we define which curve to take, like sometimes we use usd 3m curve, or usd 3mv 6m ...
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I am looking to bootstrap a USD and GBP yield curve: what are some of the futures and swaps I can use that are findable on Bloomberg?

Getting overnight-to-12 month LIBOR on Bloomberg is easy. Had difficulty finding GBP futures (range of maturities) on Bloomberg. Any tips (both USD and GBP)? Swaps (maturities all the way to 30 years) ...
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261 views

Creating yield curve from exchange-listed products only?

For use in subset of my thesis, I’ve been given some exchange market data for several exchange-listed products, including Eurodollar rate futures as well US treasury futures and Fed Funds futures. I ...
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719 views

How to compute par yield from zero rate curve?

How does one calculate the below two-year par yield given the zero rate curve: Assume the following two-year zero rate curve, with continuous compounding: ...
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101 views

How to optimise Fixed Income portfolio (Yieldbook) based on YTM, duration, rating and exchange rate

I have a fixed income portfolio built up in the Yieldbook and BBG Port. However due to some bad performance of my portfolio compared to the benchmark I would like to build up an optimisation which ...
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Which curve is better to approximate bond yields (python)

I would like to approximate bond yields in python. But the question arose which curve describes this better? ...
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Choosing which interest rate model to go with?

I've been assigned with the task of modelling zero rate curve. I did it with two models: Vasicek and CIR. Looking at the two curves produced, I can see that one is closer to the observed curve than ...
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373 views

Bootstrap with QuantLib: Fair Swap or zero NPV

In all brevity What is the termination condition used in QuantLib's curve bootstrapping? Can I modify this setup to my needs, e.g. can I tune this to a higher accuracy? Background When bootstrapping ...
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5k views

Dual Curve Bootstrapping - When to OIS discount?

I am a new quant and I am trying to understand some of the specifics of dual curve bootstrapping. For concreteness, suppose I want to build a Libor forward curve. From what I understand OIS ...
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198 views

How to do simultaneous dual curve bootstrapping?

I wish to understand how dual curve bootstrapping is done? Lets say we want to bootstrap FF OIS curve and Libor 3 month fwd curve simultaneously. Lets also assume we don't LIBOR-OIS basis swap rates ...
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What is Dual Curve Bootstrapping? And how to do it, with an example?

I am starting to explore this area. My ultimate aim is to build a 3 month LIBOR forward curve. 1) I wish to know what exactly 'Dual Curve Bootstrapping' is (If someone could explain it in clear ...
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Value of a 30 year bond using the Yield curve

If I buy a $1 30 year bond with 4% coupon payment, would my cash flow be: $$ V^{30}(t) = \frac{$1 \times0.04}{1 + R(t, 1)} + \frac{$1 \times0.04}{1 + R(t, 2)} + \cdots + \frac{$1 + $1 \times0.04}{1 + ...
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daycount of the yield curve

Complete characterization of an interest rate requires a few elements: day count compounding frequency the rate itself start date and end date That said, I notice that day counts are never displayed ...
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yield curve basics

Suppose we observe the following term structure (of annualised spot rates): 0-3 Months $\rightarrow$ 4.0%. 0-6 Months $\rightarrow$ 4.2%. 0-9 Months $\rightarrow$ 4.4%. Question1) How can we ...
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Risk-Neutral covariance matrix of arbitrage-free Nelson Siegel

For my thesis on a Bayesian sampling routine for a modification on arbitrage-free Nelson-Siegel I came across an equation that involves a matrix exponential within an integral, i.e. $\int_{0}^{\Delta ...
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USD MultiCurve Calibration - IOER vs. OIS/Fed Funds

I'm building out a calibrated USD MultiCurve set, focusing on Fed Funds & 3M LIBOR for the purpose of trading in Fed Funds Futures and Eurodollar Futures (for now ...). I had always assumed that ...
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In the curve building process, why do we need funding curve and projected curve and what are they exactly in current industry? [duplicate]

I am a newbie to fixed income quant side and I am trying to understand in the curve building process, why do we need funding curve and projected curve and what are they exactly in current industry? ...

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