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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Different risk neutral measure
I don't understand in the following example how there can be a single risk neutral measure.
The risk free asset price $B$ at time $t = 1$ is $1+R$.
An other asset $S$ at time $t=1$ can take two values:...
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Factor model bond futures
I was reading the Lehman Brother Multifactor Futures Model and there are a few things I don't understand in the way they implement their model.
Firstly, they look at the fitted yields. When they look ...
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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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How do i change face value of a Zero Coupon Bond in Python rateslib?
I'm currently trying to calculate the effective annual YTM of a Zero Coupon Bond with the following data:
Issue date: 2024/07/01
Maturity date: 2024/09/30
Settlement date (also date of valuation): ...
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Accrued interest need day counts, but day count conventions return year fractions [closed]
As far as I understand, the formula for accrued interest is $acc = couponInterest\cdot \frac{accruedDays}{couponDays}$.
But that fraction: $\frac{accruedDays}{couponDays}$, depends on the day count ...
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Asset swap spread components
Assume that an investor holds a bond and enters into an asset swap with a bank in which the investor pays the fixed coupon and receives Libor + spread
and the following data: 10y bond price 103, bond ...
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IRS Swaps market
I would like to understand who are the major actors in the IRS Swap market and what's the major reason of the volume traded for a certain tenor.
I am not able to find any of this information that ...
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Are there closed formulas for non-callable defaultable floating rates in a reduced form models?
currently, I am evaluating for my company the possibility to price defaultable bonds with stochastic default intensity. Precisely, I am considering using the G2++ model where one factor is the ...
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Short bond convexity
Assuming you need to pick a bond to short. Is it better a bond with large or small convexity (all other things being equal)?
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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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How to value 3mo SOFR Spreads one year out, 2yr out
How does one value a 3mo spread spread in the far out future from present if fomc meeting schedule is only published for one year, and even with fomc's dot plot, it just shows the median expectation ...
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Modified Duration vs. Real-World Bond Price and Yield Changes
We know that modified duration at time $t$ of a bond with maturity $n$ is defined as:
$$
D_{nt} = - \frac{1}{P_{nt}} \frac{\partial{P_{nt}}}{\partial y_{nt}}
$$
And the definition of a derivative is:
$...
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Swap/Bond basis: Bond rates "too high" or swap rates "too low"?
I suppose this question is more of a discussion piece than a question per se, so I apologize in advance.
I've long been fascinated by the large negative basis between government bonds and swaps. These ...
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How do I calculate yield and trading margin of an Australian Dollar floating rate note?
I am trying to calculate the yield and trading margin on an AUD FRN in a robust manner. I am hoping someone can help with a few details.
I am forecasting cash flows and solving for the discount rate ...
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CS01 implied Var calculation
is there any straightforward way to roughly calculate the daily var from the CS01. Mostly from the corporate bond position. thanks,
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Dealing with day counts that span a weekend
Consider the following security:
CUSIP: 3130A3GE8
Federal Home Loan Bank
Maturity: 2024-12-13
Coupon: 2.75 % (CPN)
Previous Coupon Date: 2019-06-13
Today is ...
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Compute I-spread from ASW-spread (or vice versa)
The I-spread ("mid swap spread" or yield-yield spread) is a standlone measure of credit risk, a security against matched maturity vanilla swap rate. Consider a package in which the investor receives ...
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Discount margin on FRN - widening but bond price increasing?
Why would a bonds discount margin widen but its price increase? Shouldn't the price be falling when margins are widening?
Looking at the bond pricing formula, if the price is higher doesn't the rate ...
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Simple arbitrage pricing of bond option
This is Tuckman fixed income security textbook. The text here is trying to price a 990 six month call on a six month zero bond. When we replicate the portfolio, where is the F_.5 coming from?
My ...
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GBP OIS Curve - Zero Rate Curve Calculation in Quantlib
I am new to Quantlib and I am looking to create a Zero Rate Curve from GBP OIS to then use to calculate the present value of fixed rate bonds.
I have Looked at the documentation:
https://quantlib-...
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Modified duration in multi-currency portfolio
I was thinking about how to figure aut duration for portfolio of bonds denominated in different currencies… I would like to compare sensitivity of portfolio to shift of yield with competitive ...
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Calculating swap rolldown using the RatesLib Python Library
The code I am using is below, pulling in swap curves from BBG and then using RatesLib to price the swaps.
...
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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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What is the Italian BTP yield calculation in last period?
I chose this example becuase it highlight two aspects I can't reverse engineer and can't find any official source documentation.
BTP: IT0005518128: 1/Nov/2022 -> 1/May/2033 at 4.4%.
If this bond is ...
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Product Control Fixed Income - Interview Question
This was asked to me in my product control interview. What factors contribute to the daily pnl of a bond, if you exclude daily carry, price change and interest rate change? There would still be a pnl, ...
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Interview question on interest rate spread trade
Consider this interview question:
Tell me how you'd construct a risk neutral cross country trade on the 2 year �� 10 year interest rate spread in Germany and the U.S.
What does "risk neutral" mean ...
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Rates Curve 'Realising' vs 'Rolling'
Just saw an exchange on X and would appreciate if anyone could try their hand at going into a bit more detail (and even maybe using an example) to breakdown the conceptual difference of rates curves '...
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Treasury zero coupon curve for discounting two bonds but OAS different on Bloomberg
Using zero coupon Treasury curve, I discounted a 10% coupon bond. Using the same curve, I discounted a 5% coupon bond. Both these bonds have the same maturity. Since I discount both these bonds using ...
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Proving that Convexity approx. equals Duration squared but something goes wrong?
I am trying to derive a formula for bond convexity that I saw in a textbook which states that
$$\text{convexity} = \frac{\text{Macaulay duration}^2 + \text{Macaulay duration} + \text{dispersion}}{(1+\...
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Estimating the price of an illiquid 5y bond futures contract
Say I know the price of 10y Gilt futures, 10y Treasury futures, 5y Treasury futures, and GBPUSD futures.
I am asked to produce a quote on 5y Gilt futures using only this data. What is a sensible ...
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Parallel shift in spot yield curve moves the IRR of a bond portfolio in the same direction: Analytical Proof
I am trying to prove that a parallel shift in the spot yield curve will as its effect have the IRR of a bond portfolio move in the same direction and by the same amount.
I have tested this on few ...
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Misunderstanding of 'day counts' and accrued interest
I'm totally new to the fixed income world.
My goal with this question is to gain an understanding how interest is accrued day-by-day for a particular instrument. This will obviously be done by an app ...
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Interest rate swaps - if i expect rates to be cut later than market expectations, what swap can I put on?
If I think market expectations are too dovish and I expect rates to stay high for longer i.e. rate cuts by X central bank to happen in September for example (as opposed to whats priced in, e.g. May), ...
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Different CLOB for ONTR securities
I was trying to find the list of all the CLOB for on-the-run UST.
I know the following: BrokerTec, TradeWeb which both have different CLOB for ONTR UST.
I think Virtu Financial also has one, but I am ...
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What discount rates should I use to price a municipal bond with unknown market price?
I have a payoff structure but I do not know the price of the bond. The bond is municipal. What discount rates should I take for each period in order to calculate its fair price?
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What's the rate of return on a mortgage?
I'm trying to understand mortgages from first principles, from the perspective of a borrower.
Let $S_t$ be the price of the asset bought with the loan at time $t$ (i.e. house). Let $\alpha$ be the ...
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How would one calculate yield to first call for a debt security which is currently and always callable?
If an asset manager has multiple extended warehouse lines outstanding and each one is currently callable (some with penalties, some without), is it simply the case that a ‘to first call’ performance ...
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What are the assumption in the DTS paper
In the original Duration Times Spread paper from Arik Ben Dor
, Lev Dynkin, Jay Hyman
, Patrick Houweling
, Erik van Leeuwen and Olaf Penninga
, the authors define a change in spread as follows:
...
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Market Data UST
There a lot of new market data providers for retail algo traders.
For example the famous one for option is Theta Data Net and for Equities it is Polygon IO. You basically get all the greek/price data ...
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Bond Basis (non CTD)
I had a query regarding the trading of non CTD (but deliverable) basis. Obviously someone can buy non CTD basis (buy cash / sell bond future), with the hopes this widens, clearly I would not want to ...
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Recommended Setup for QuantLib-Python AmortizingFloatingRateBond
I am trying to model a term loan in QuantLib-Python that makes quarterly interest payments at CME Term SOFR 3M + 10bps + 525bps paid in arrears with a 2 business ...
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Get bonds data in python [duplicate]
Anyone knows a way of getting trustworthy bonds data in python? I know that for stock there is yfinance package but it doesnt include bonds.
Thx
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Why is accrued interest prorated linearly?
Cashflows from coupons and principal are discounted using the YTM to get PV of the bond in dirty price.
as shown here in this question
Misunderstanding of 'day counts' and accrued interest
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Relative Value and Z-spreads
I wanted to understand how I can use Z-spreads in the context of gov bond RV.
I understand how to compute Z-spreads although I am having some trouble interpreting the meaning. I am solving for the ...
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Is the "$\textit{theoretical}$" $DV01$ of a bond an accurate estimate?
Dollar duration $DV01$ is defined as negative of the price of the bond wrt yield:
$$DV01 = - \frac{\partial P}{\partial y}.$$
As we know that $P = \sum_{t=1}^{n} \frac{CF_{t}}{(1+y)^{t}}$, then
$$DV01 ...
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Calculating spread on a par rate curve given bond’s coupon and yield
In Tuckman and Serrat’s Fixed Income Securities, they give an example of a bond and state its coupon and yield.
They also provide an HQM par rate curve and quote the bond’s spread to this curve.
How ...
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Securities lending vs repo transactions
I have recently started on a repo/SBL trading desk and I am struggling to understand some theory. Normally, in a secured hard-to-borrow secured transaction, I pledge general collateral, receive the ...
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How do you interpret this data about corporate bonds? [closed]
If I have a corporate bond portfolio that has the following relative to the benchmark (this was given to me as interview question):
Given an initial portfolio with the following statistics (as of ...
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impact of bond futures conversion factor on calendar spread trading
i have a quick question about conversion factor and his implication in calendar bonds roll trading.
I go short on a calendar roll (short front+long back) which has the same cheapest to deliver.
The ...
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Setting up QuantLib to get correct yield for bond with long first payment period
I am dealing with fixed rate bonds. There is one particular bond, 34659UAC0, that caught my eye. This bond has a first coupon period of a whopping 5 years, followed by regular periods of 6 months. My ...
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