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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The PDE of an Interest Rate Swap - ImplicitFinite Difference Method
Context:
I'm stuggling to implement an implicit finite difference scheme on an Interest Rate Swap (IRS) with a single factor short rate model:
I was following the textbook(Daniel J. Duffy - Finite ...
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Bond forward arbitrage relationships
I am trying to see if the following statement is true or not and I would really appreciate your help.
The statement is as follows:
$\forall $ Tradable Asset $V(t)$,
$$ E[\frac{P(t,T_{i})P(T_{i},T_{i+1}...
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Understanding the Effective Duration and Convexity from Yield Book across MBS coupon stack
Yield Book, based on the 8/10 close, shows that the Effective Duration on 2.5s are greater than 3s and so on as we go up the stack. But with the PMMS at 4.99% on 8/10, I don't see how Eff. Duration, ...
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Negative Accrued for treasury bonds?
I am looking at some spreadsheets that show the US treasury bonds have some negative accrued. Why would that be the case? Shouldn't bond accruals always be positive?
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How does Bloomberg bootstrap CASH Instruments?
Given the following datas :
If we do the bootstrap methodology for CASH Instrument we gotta :
Calculate the DF associated to the Market Quoted Rate (2.91157). For the 3M Fixing we have :
T = 0.26115.
...
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ML/AI in fixed income vs equity
From my perception of learning different ML/AI applications to finance I found there are lots of them in equity and not as many in fixed income. I wonder if the markets are different in some ways and ...
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Calculate Bond Price knowing Z-Spread
From my point of view, to calculate the price of a bond, we just need to add the discounted cash flows.
The discount factor calculation is as follows:
In my theory knowing the z-spread of a bond I ...
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Munk (2011) exercise 3.6
I'm trying to solve the exercise in Munk (2011). The exercise reads:
"Find the dynamics of the process: $\xi^{\lambda}_{t} = \exp\left\{-\int^{t}_{0} \lambda_{s} dz_{s} - \frac{1}{2}\int^{t}_{0} \...
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Why do bonds with a shorter next call dates have shorter extension risk?
I was reading a research article and I'm not really understanding why. Is it to do with the option premium being priced in at the beginning?
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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/...
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Convert UST Yield Curve to Spot Curve (Zero Coupon) using bootstrapping
Having the following UST Active Curve :
Tenor
Tenor ticker
bid_yield
Coupon
1M
912796XM Govt
1.891
0
2M
912796XV Govt
2.225
0
3M
912796V6 Govt
2.52
0
6M
912796XS Govt
3.026
0
1Y
912796XQ Govt
3....
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Is there a word or phrase with similar meaning to bond yield, but meaning yield on the actual price paid for a bond some time ago?
This is what I am looking for:
(coupon amount) / (the amount that I actually paid for the bond some time ago)
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Treasury Bond Clean Price - Quantlib
The clean price of the Treasury 10 year bond on 6/30/22 is 98.8046 according to Bloomberg. The settlement day for treasury bonds is 1 day. I think this still means the clean price of bond is 98.8046 ...
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Tree Pricing FRN Implementation
When pricing a bond via a short rate model on a tree, it seems natural to include intermediate time steps in addition to those corresponding to cashflow dates (i.e. for bonds with American style ...
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How to construct portfolio from monthly strategy that unwinds one year later?
In Rebonato and Hatano, The Economic Origin of Treasury Excess Returns: A Cycles and Trend Explanation (May 23, 2018) SSRN, there's a monthly long/short strategy that is only unwound after 1 yr.
So ...
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Z spread for callable bond
I see many definitions online for z spread with formulas written for a bond, how do they change if the bond is callable? Or is z spread calculated to maturity in this case?
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ML/DS in fixed income asset management
I am new to the topic but I would like to read papers/books/anything interesting to learn more how ML and data science is used in buy side Fixed income Asset management firms. Factor investing/signals/...
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Ten Year Note Futures Implied Repo Rate calculation from CME Understanding Treasury Futures Document
I am trying to determine how CME calculated their Implied Repo Rates in table 3 on the penultimate page of the Understanding Treasury Futures Document:
https://www.cmegroup.com/education/files/...
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How to scale t-bond yield movements on a chart to visualize its relative impact to the pricing of other assets?
How does one scale the 10yr yield on a chart to visualize its relative impact to asset valuations? I.e., so that the risk-free rate moving from 1->2% shows as a much larger movement than 11->12%....
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Can a Bond have FX Delta Risk?
Given we know the
Notional
Trade Price
Currency in which the Bond Pays Coupons
FX Rate from Bond Currency to USD
Trying to understand if a Bond can have FX Delta Risk and how it should be computed?
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Economics of buying a dollar roll
This is a basic question. But I wanted to understand how a TBA short (buying the dollar roll) is economically short an MBS? For example, if an investor believes a specific coupon is rich, they could ...
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Comparing TBA and Spec OAS
For a specific coupon, if TBA TOAS is greater than a Specs TOAS, does that imply that the Specs are trading too rich to TBAs (given liquidity risk, payup risk, etc)? I realize relative value ...
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Why do some TIPS bonds have credit spread < 0 [duplicate]
If we look at the yield spreads on Bloomberg of some TIPS bonds, we see they have credit spread < 0 (i.e. their yield is even lower than their benchmark treasury bonds)
Why is that the case. ...
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Macaulay Duration - Liability matching
Can someone provide a detailed example to prove the following statement:
"When the investment horizon is equal to the Macaulay duration of the bond, coupon reinvestment risk offsets price risk.&...
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Bid/Mid/Ask credit spreads
I have seen in different terminals that credit spreads of a corporate bond (spread,Gspread,Ispread) can been calculated for different sides (ie Bid Mid,Ask Gspread).
I wanted to ask if these spreads ...
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MBS Index replication month-end flows
Several investors track indices to gain exposure to specific asset classes. And these indices may be re-balanced on a monthly basis, based on market-cap etc which generates month-end flows from ...
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Why did Ginnie Mae MBS Net issuance decrease significantly in 2020-2021?
Net Issuance of Agency MBS can be thought of as driven by Existing Home Sales, New Home Sales, Cash out Refis, Amortization and Non-Agency MBS runoff. Based on this definition of net issuance, is ...
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MBS Dollar roll mechanics
Had a few questions on MBS Dollar rolls:
How are dollar rolls affected by Interest rate Volatility?
Does the OAS of underlying pools matter to dollar rolls, and if so, how do they affect it?
Does the ...
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Interest Rate Volatility for Binomial Trees
Does anybody know where I can get the data or calculate interest rate volatility for modelling callable and putable bonds in binomial trees. I have swap curves data. Does any sources like Bloomberg ...
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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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