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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1answer
1k views

What equation will convert implied yield volatility to implied price volatility?

I am trying to figure out how to turn implied yield volatility of a short-term interest rate into implied price volatility. Is there an equation to do this? I have come across the equation for a ...
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1answer
101 views

Calculate forward discount factors and forward reference rate when discount factors are known

I am trying to learn how to value interest rate swap through portfolio of FRA's(forward rate agreement).But I have got stuck in calculation of floating leg. Here is the scenario as given below for ...
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378 views

Importance of z-spread in CDS-Bond Basis trading

Consider the following: A bond with a 9% coupon and a price of $98. Let's say the zero swap curve is flat at around 7% (e.g. the zero swap curve is high because we're at the end of a business cycle). ...
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71 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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1answer
52 views

How do Repo traders use OIS and Fed fund rates

I would like to know how do Repo traders use FED Fund rates and OIS to cover themselves. For example assuming the repo trader bought paper(borrwed paper/lent cash) in the 1 year. How do they cover ...
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75 views

Why did high yield corporate bond ETFs tank during the great recession

My apologies if this is not mathematical enough for this outlet. My understanding of the pricing of a bond ETF is that lowering interest rates drive the price up and increased risk of default drives ...
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1answer
9k views

Duration of a floating rate note

I have the following C# code for calculating the modified duration of fixed coupon bonds: ...
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1answer
53 views

What is Yield To Convention?

I know what gross redemption yield of a bond is. I am unaware of "Yield To Convention". It is a Bloomberg ticker code (multiple in fact) YLD_CNV_MID, YLD_CNV_ASK & YLD_CNV_BID The term "Last ...
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23 views

Framework for hedging fx and utilizing correlation between asset returns

Can anyone point me in a direction (research paper, books, ..) which developes a framework/strategy for hedging currency exposure for an international bond portfolio? This paper finds optimal ...
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1answer
40 views

Zero-coupon bond price under Rendleman-Bartter Model

let's say that I have simulated the interest rate using the Rendleman-Barttermodel, (which is not the best for rates I know) and then I want to simulate paths for the bond paying 1 at maturity: $$...
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28 views

Implied volatility of Treasury options

For practitioners, does the concept of implied volatility also apply to (European) Treasury Options (whose underlying is Treasury Futures contracts)? For the standard individual stock vanilla ...
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2answers
93 views

Roll Returns vs Total Returns

Very basic question I'm confused about : Is there a formula that relates total return of a bond as a function of yields and its roll down returns? I mean ignoring reinvestment risk, would the ...
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30 views

Collecting historical coupon data on sovereign generic bonds in Bloomberg

In the Bloomberg terminal, a generic bond (e.g. GGR >> Australia >> 5Y bond) has a coupon rate stated in the Security Description (DES). I have daily historical yield data for the generic bonds, and ...
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1answer
63 views

Treasury Futures Basis Trade - Funding enhancement

In a basis trade, if you short the Treasury futures and buy the underlying bond and hold it to maturity, is funding the only source of risk assuming there no CTD switches. You have locked in the ...
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45 views

Factor Loading with multiple exposures?

How do I decompose portfolio exposures when assets may have exposure to a few of my risk factors? For instance I have some sector and state specific risk factors. If I have a bond with exposure to ...
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41 views

Poisson distribution and counting process

Let $\begin{Bmatrix} N_t \end{Bmatrix}_{(t\in[0,T])}:=\mathbb{I}_{(\tau \leq T)}:=k, \forall t \in [\tau_{k}\leq \tau_{k+1})\sim \mathrm{Po}(\lambda_{t}:=\int_{0}^{t}\lambda_{s}ds<+\infty)$ a ...
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1answer
28 views

Add a country OAS to a government bond model? (modelling returns of the bond price)

when modelling the % returns on a government bond, I use a model like this: $$\Delta P_t / P_{t-1} = \sum_i KRD_i (-\Delta y_i)$$ Does it make sense at all to add the following "country oas" ...
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38 views

Wave Method and Implied Duration

I am pricing an MBS under three different rate scenarios: a base case, +5bps and -5bps I compute partial durations on the base case using the wave method (P. Hagan: Calculating Delta Risks and Hedges ...
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0answers
42 views

Pricing bond backed by collateral

I'm new to quantitative finance, and trying to derive an interest rate for a collateralized bond. Imagine there are two parties, Alice and Bob. Alice wants to lend $X$ units of an asset to Bob. The ...
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1answer
105 views

Fixed Income Portfolio Optimization

I'm trying to solve for a maximum sharpe ratio portfolio in the fixed income space. To do so, i use CVXPY in python. I use this Paper as reference. This is my "setup": ...
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2answers
114 views

Is there an inverse relationship between (future-spot) price and yield?

If the difference between futures and spot prices rises will the yield for the current bond increase as well?
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1answer
67 views

what are the underlying transactions for SOFR?

Recently I am reading about SOFR (Secured Overnight Financing Rate), which is projected to replace LIBOR to be the reference for risk-free rate in the market. But I still don't understand or imagine ...
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2answers
3k views

Pricing a fixed rate bond in Quantlib Python

I'm trying to implement a pricing model for fixed rate bonds with the code below. ...
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65 views

Valuation of Callable Bonds

Is there any way to price American Callable Bonds (those which can be called on any date before expiration) other than basic CRR interest rate trees, since they won't be accurate enough to give ...
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1answer
95 views

When to use which zero curves

I have a very basic question. Why are there many different zero curves for a given currency/market? For example, there are zero curves constructed using gov bonds, swaps, STIR futures, OIS, Inflation, ...
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2answers
96 views

Optimal investment mix of equity and debt in a single company, HY vs IG

What is the optimal mix of equity and debt that an investor should invest in a single company? If an investor invests in both the debt and equity of a company, they are in effect de-levering the ...
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2answers
130 views

Treasury futures cost of carry and P&L

I'm looking to understand the P&L implications of holding 2YR treasury futures. Assuming no movement in interest rates through to maturity (i.e., no capital gains or losses due to interest rate ...
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7answers
352 views

Investment Grade Bond vs Junk Bond, whose duration is larger?

Just wondering how to calculate duration when take credit risk into consideration. I think if duration is calculated as weighted average of cashflow time, and weights are calculated using present ...
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26 views

Retrieve SYC from Par yields

Currently studying about fixed income and the construction of the Spot yield curve, but I do not know whether my intuition is right. Suppose we have a firm that has traded Bond for different ...
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2answers
82 views

CDS, default probability and bond price

When we calculate the implied default probabilities from CDS, can we use that information to price bonds? I am getting familiar with Fixed Income. I saw textbooks using implied default probabilities ...
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0answers
35 views

Determine same issuer from a list of ISINs?

I have a list of ISINs for all the securities that make up a fixed-income fund. Is it possible to tell from this which securities are from the same issuer? I have securities of which I know they are ...
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42 views

Extracting Risk Neutral Default Probabilities using Option Adjusted Bond Prices

I am currently in a project trying to quantify default risk premia for US Corporate Bonds. The data I have consists of bond prices, and other information (i.e. YTM, OAS, Effective Duration, Maturity ...
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1answer
134 views

stress testing zero coupon yield curve

i'm currently trying to stress test the zero coupon yield curve using daily observations from 2003 to 2019. Each Zero coupon yield curve originate from an actuarial curve with 37 tenors that range ...
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38 views

Calculating historical volatility and returns from bond yield

I am interested to calculate the historical volatility and returns from a time series of US 3m T-bill yield (see screenshot below), for portfolio optimization. I am not too sure how to bridge the idea ...
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What are some of the best textbooks on Fixed Income securities?

I'm looking for something that might be considered the 'Bible' of fixed income. Ideally it would contain everything from the basics of PV and discounting cash flows all the way up to some of the most ...
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27 views

Floating coupon rate based on sales?

Just a quick question, can a floating coupon rate be tied to SPV daily revenue? My client want to issue an ABS bond, and its coupon would be (0 + 2% of the daily sales) Would it be admissible? or ...
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0answers
36 views

How to apply multiplicative price seasonality to bond prices in quantlib?

Can someone please give a brief or any link which explains how to apply multiplicative price seasonality to inflation linked bonds in Quantlib using python modules. Have gone through most of the ...
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1answer
69 views

Calendar roll terminology (buy vs sell)

I am trying to get the direction/terminology correct in futures calendar trading. Let's say I have two calendar futures contract where the prices are 100 and 102 reflecting the front and back ...
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1answer
93 views

Cross currency basis swap for bonds

Running a cross currency swap on a GBP issued 2.75% 7yr bond (i.e a bullet), with funding in USD so need to determine the equivalent in USD. The GBP bond trades at circa 180bps over the Gilt. ...
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0answers
29 views

Perpetual bond valuation between coupon dates

According to this Derive Perpetual Bond Price , I learned how to derive the formula of perpetual bond. However, I still have some questions. Firstly, do I need to change the formula when valuing the ...
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2answers
1k views

Derive Perpetual Bond Price

It is known that a perpetual bond with coupon $c$ has price $$P=\frac{c}{r}$$ How do you get to this price? Is $r$ stated in discrete or continuous compounding?
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1answer
72 views

Treasury Futures Wild Card Option equation

I am confused about the equation on page 13 (upper right) from the CME: https://www.cmegroup.com/education/files/treasury-futures-basis-spreads.pdf The equation calculates the move in the CTD that ...
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0answers
44 views

Negative vega on IR swaptions mid curve

Why do IR bermudan options have negative vega on midcurve? Does it have something to do with mean reversion and a way of lower the price vs market prices?
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2answers
125 views

Choosing a proxy for asset credit event correlations

I'm interested in modeling the joint likelihood for rating changes and default events across a portfolio of bonds. To estimate the correlation between these assets, I can use a third-party factor ...
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2answers
291 views

Floating rate note value approximation

I was hoping somebody can assist me with a query. Would it be a valid approach to revalue a frn with a discount margin from a comparable bond as par minus the difference between the quoted margin and ...
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2answers
536 views

Bond fund's roll and carry

This is a question about modelling the returns of a bond index. Understand there's quite a bit about the roll and carry of an individual bond, but what about a bond index. Roll I would calculate the ...
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1answer
69 views

Why are KRDs calculated by shifting the par curve?

When we compute Key Rate Duration, why is the par curve the right curve to shift instead of the spot curve?
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1answer
55 views

CDS Credit Default Swap PnL

I estimate daily pnl on a CDS position using the spread change times the CS01. However I would like to estimate the PnL for a longer trade that has gone from a 5Y CDS to a 4Y with associated coupon ...
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2answers
67 views

Possible first rate cut by Fed - spot vs forwards

This may be my first rate cut since I joined the industry. I've only see rate hikes and I've been reading through literature from back in 2007 when the Fed last cut rates to get a general feel for how ...
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1answer
101 views

Fair price of a coupon paying bond

Consider a coupon paying bond with a maturity of $3$ years, that pays coupon annually. Let $c$ be the coupon rate (percentage) and let $F$ be the face value. This means that the holder of the bond ...