Questions tagged [fixed-income]

Securities which obligate the borrower/issuer to make payments on a fixed schedule. Fixed income securities include sovereign, corporate and municipal bonds, corporate loans, and securitized lending (e.g., ABS). "Fixed" refers only to the schedule of obligatory payments, not the amount, and may include inflation linked bonds, variable-interest rate notes, and the like.

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How to use swap rate bootstrapping to calculate fixed index rate

I have been provided with a table of rates and asked to use swap rate bootstrapping to calculate the fixed index rate for a 7 year loan. I'm struggling to get an intuition for what this actually means....
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Reasonable way to price swap under realized forwards assumption

I'm looking for a way to price swaps in QuantLib under the assumption of realized forwards, i.e. couple of weeks or months from today the yield curve would be the same as it is expected by the market. ...
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The price of liquidity

We are currently in the US Treasury roll period when investors are rolling from the previously issued notes and bonds into the currently issued notes and bonds, aka "Rolling from Off-The-Runs to ...
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Is it possible to simulate yield spreads for different bonds?

Let`s say I have different bonds from multiple issuers and I know the yield spreads for today. Is there a way to simulate those spreads for a future period like 1 month? I dont just want to simulate ...
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Treasury futures wild card option (Monte carlo simulation)

I recently joined a bulge bracket bank in New York City trading the long-end but mostly doing a lot of analysis until I get up to speed. I'm working on the Wildcard model which is going to be an ...
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Book recommendations for derivatives [duplicate]

I would like to ask you, if you could suggest me a good book regarding derivatives. Specifically, i would like a book which is more focused on how the derivatives are working and traded in practise ...
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Do you roll back the maturities and schedules when backtesting VaR for portfolios of bonds, options or future contracts?

I want to backtest VaR models which are applied to portfolios of products which have maturities (options and futures) and even schedules (bonds). I have a question which never came up when backtesting ...
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Bond value as a function of spread change and duration/maturity

I am trying to calculate the change of value in a universe of bonds given a series of shocks to the credit spread of each bond. As a constraint, the initial dataset only contains the spread change for ...
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Returns of an interest rate swap

I would like to calculate returns for a plain-vanilla (fixed-for-floating) interest rate swap. Consider, that I am long in USD 5-year swap rate, i.e. I'm holding a receiver swap for 5-year swap rate ...
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Model-Free Implied Volatility: Data of Expired Options and Bond Price

I am attempting to calculate Model-Free Implied Volatility for several equity indices (S&P500, NASDAQ100, CAC40, FTSE100, DJIA, EUROSTOXX50, NIKKEI225, NIFTY50). I wish to get historical data of ...
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Simple (?) question about expected bond returns

Newbie here. I should say upfront that I'm not a quant, just someone trying to broaden his knowledge of fixed income investing. I apologise in advance if I'm mangling some terminology. Imagine a ...
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How to calculate the yield of a perpetual bond that pays a floating coupon payment?

I know that perpetual bonds are becoming a rare phenomenon and that ones that pay a variable coupon are even rarer. However, I believe that there are such bonds out there, and I'm hoping that someone ...
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How to break down yield to maturity to different components?

Suppose we have the PV of a bond, as well as two separate streams of cash flows, say, $C_a$ and $C_b$ that make up the total annual cash flows $C$ (i.e. $C=C_a+C_b$). In other words, suppose we have, \...
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How can I optimize a Bond Portfolio in Practice?

I'd like to optimize a bond portfolio with different bond classes (government bonds, corporates, ...) and different ratings as well as maturities. Is this even possible to optimize such a portfolio? ...
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Interest rate risk of a bond as a function of the coupon

This SEC document claims that increasing the ocupon on a bond decreases the interest rate risk (bottom of page 3): And the Finra SIE exam states the same also. I cannot understand the logic behind ...
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Trying to learn to bootstrap with the Treasury Curve and can't seem to get a result that makes sense

I'm trying to learn to bootstrap and am taking some bonds from the Treasury curve: https://docs.google.com/spreadsheets/d/1vA7s4ZfFzGfTji_d9cLUid5rqyaugRrI0etCW_3Jb6w/edit?usp=sharing For some reason ...
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Calculate returns using Federal Reserve's constant maturity interest rate series (for 5, 10 and 30 years)

I am looking to replicate the results from a older research paper. To do that I need first to calculate the returns from Federal Reserve's daily constant maturity interest rate series. According to ...
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Jarrow and Turnbull (1997) Discrete time forward rate confusion

I'm reading Jarrow and Turnbull (1997). They defined $p(t,T)$ as the time $t$ price of a default free zero coupon bond paying a sure dollar at time $T$ where $0\le t \le T$ (in year). They also ...
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Is repo-ing out a bond the same as shorting the bond?

In fixed income, or in any other products for that matter, borrowing an asset is essentially shorting the asset. As a result, you would see hard-to-borrow names where the borrow rates are much higher ...
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Why is the formula for the 5y5y inflation swap forward on bloomberg 2*USSWIT10 Curncy-USSWIT5 Curncy

If USSWIT10 Curncy is the expected average inflation for ten years and the USSWIT5 Curncy is the expected average inflation for five years, I don't know why that formula would tell me what the ...
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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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UnivariateSpline Spline Interpolation behaving erratically

I am using univariate spline to interpolate betweeen a number of dots I have (in blue - it is a yield curve). The code is the following: ...
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Simple bond math calculation - Quantlib

I am reconciling a dirty price calculation using quantlib and I am having difficulty getting the same dirty price manually. I am confident it is used to the day count convention but I've tripled ...
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OIS Rate - How to get current OIS rate?

I'm using the following link to find all fixed income rates, but unable to get current OIS rates (Fixed vs Float)? https://www.wsj.com/market-data/bonds How to get current OIS rates?
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Convert spreads to prices for bonds via duration

I have the price of a bond and would like to convert it to spreads. Is this possible by just having dollar duration? Secondly, if I just care about the relative spreads of multiple bonds, is it enough ...
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Between these bonds, how to find out which is one pricey (Higher valuation) and cheap (Lower valuation)?

Trying to understand, how to find out which of these bonds are cheap and which are expensive? The current spot rate is 8.167%. How do I go about finding the cheap vs expensive bonds especially when ...
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Finding Asset-backed Security Prospectuses in EDGAR

Currently, I'm trying to find prospectus on more esoteric types of asset-backed securities, such as those backed by various equipment so I that I can learn about how to model/structure such types of ...
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Bootstrapping when cashflows are irregular

EDIT: this question was previously closed because it was 'assumed that it should be common knowledge'. I advise you to READ THE QUESTION PROPERLY and you will find out is is NOT common knowledge at ...
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Unexpected Inflation and Asset Allocation

If asset allocation decisions were made prior to the news of unanticipated inflation, how should asset allocators incorporate the fact the inflation is now 5% higher than the 2% inflation target? It ...
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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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sofr/sonia/estr floating rate notes

I wonder if there is an agreed market convention on a discount margin formula for the new style frn's with overnight-compounded rates paid in arrears i.e. sofr/sonia/estr/etc frn's? This question is ...
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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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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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Applying Differential Evolution to the Nelson Siegel Model in Python

I am trying to create a zero curve from a series of government bonds by minimizing the differences in the dirty prices. The problem is that there is something wrong with my differential evolution ...
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How do you calculate pull to par effect on z-spread?

Currently bonds are widening almost across all maturities and sectors. I'm looking at some senior bonds with maturities of less than 1 year, that have widened more than 100bps. This happened even ...
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Returns of interest rate swap

I would like to calculate returns for a plain-vanilla (fixed-for-floating) interest rate swap. Consider, that I am long in USD 5-year swap rate, i.e. I'm holding a receiver swap for 5-year swap rate ...
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0 answers
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Using linear regression to determine RV opportunities in yield curves

Hi all, I've been looking at potential trade ideas, trying to get an understanding of how to use linear regression to determine RV opportunities within swaps. Does anyone understanding how to ...
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Differential vs. derivative in the Vasicek model [closed]

Can anyone help me in understanding how we get the line I have marked with a red arrow? I guess I have trouble in understanding the difference between differentials and derivatives, i.e. what is the ...
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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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How am I supposed to understand the following statement on the convexity adjusted rate

Given, a numéraire $(N(t))_{0\leq t \leq T}$ and an index $(X(t))_{0\leq t\leq T}$ that is a $\mathbb Q^{N}$-martingale, we consider the natural payoff $V_{N}(T)$, where it pays $$V_{N}(T):=X(T)N(T) \...
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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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Finding the distribution of $I(T_{1},T_{n})$ under an appropriate measure if the forwards are lognormal? [duplicate]

My question follows beneath the "lengthy" setting I describe: Given a tenor discretization $0 = T_{0}< ... < T_{n} =T$, and under the assumption that under $\mathbb P$, for all $i = 1,....
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If any zero coupon bond $P(T)$ can be chosen as a numéraire, then why can the rolling bond for any time discretization be chosen as numéraire

Let us consider some finite time horizon $[0,T]$, and we assume that $P(t)$, the zero coupon bond maturing in $t$ for any $t\in [0,T]$ can be chosen as a numéraire, i.e. such that the numéraire-...
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"The five year swap has the same dv01 as a par five year treasury bond" Why?

Am reading a book where the author gives an example of someone buying a 5 year par 4.65% treasury and someone else entering an 5 year interest rate swap agreeing to receive 5.75%. The treasury yield ...
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Back testing fixed income for bond portfolio management

When doing back test trying to replicate a paper, how do you handle bonds that are maturing in an index? Say I was trying to create a strategy, how do I account for bonds that mature in terms of ...
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How to determine the fair value of "off-the-run" U.S. Treasury securities

In the U.S. Treasury securities market, there are seven (7) "on-the-run" coupon-bearing issues: 2 year 3 year 5 year 7 year 10 year 20 year 30 year I believe the Fed uses a monotone convex ...
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Systematic Pricing and Trading of Municipal Bonds by P. Kolm

does anyone have the pdf for this article? It was available on SSRN a few weeks ago but not anymore, I'd really appreciate it if someone could share it. Thanks
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Incorporating Accrued Interest to price fixed income callable bonds in short rate models

I am using the DerivaGem software provided by Hull & White (available at DerivaGem 4.00a) in Options, Futures & Other Derivatives. I am attempting to back propagate a bond to obtain the ...
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Why are there so many money market yield measurements? (MMY, BEY, BDY) Are all of them really used?

I have heard teachers online explain that since these measures do not account for compounding they are "naive" and are "rough estimates" since they have such a short maturity that ...
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