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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Fixed Income ETF Portfolio Risk

The classic Markowitz risk is $$f=\boldsymbol{x}^{T} \Sigma \boldsymbol{x}$$ Now say I have a duration vector $\boldsymbol{d}$ for my assets; and also correlation (of say change of yield) matrix $\...
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Show that a zero-coupon bond discounted by a bond with mautrity $T$ is a martingale under the $T$-Forward measure

Here's the exact question: Show that for any $s>0$, $\frac{P(t,s)}{P(t,T)}$ is a $Q^T$-martingale. Here's my attempt: Let $t^\prime < t$. First consider the case $s>T$. \begin{aligned} \...
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Normalizing with Sum of Zero-Coupon Bond Prices

Suppose you are receiving a payment $K$ at time $t_m$. Let $p(0,t_i)$ be the maturity-$t_i$ zero-coupon bond price at $t=0$. If we consider a discrete time $\{0,...,t_m\}$, what would it to ...
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38 views

Zero Curve from a par curve curve QuantLib

I'm trying to understand why pricing a par bond with zero curve, contracted from par bonds themselves doesn't give me par. (Based on examples here) ...
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42 views

Interpolation for discount curve building QuantLib for bonds

I'm trying to figure out how to build a discount curve to price bonds from spot rates using some advance interpolation methods like PiecewiseLogCubicDiscount. I know I can build this curve with ...
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28 views

How to model the different returns of agents with different information information

For a seminar, I would like to graphically represent the returns made by agents of different information standpoints. In other words, say I have a market tuple $(\Omega, \mathbb{F}, P,S)$ where $S$ is ...
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62 views

Difference between Price and Value in Forward and Futures

Consider forward and futures contract on a zero-coupon bond. Denote the time $t$ forward (contract) price on a $T_2$-maturity zero-coupon bond with delivery date $T_1$ as $F(t,T_1:T_2).$ Similarly, ...
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62 views

Zero-coupon Bond Price, Yield, and Forward Rate

Consider a discrete-time trading economy with varying maturities of zero-coupon bond. Let $p(t,T)$ be the time $t$ price of a zero-coupon bond maturing at $T$. Similarly, let the time $t$ yield on a ...
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Handling illiquid bonds in a fixed income index

I am trying to create a fixed-income index for my country's bond market. Among other things, I am interested in extracting the weighted average (by market cap) yield to maturity. In order to do this, ...
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Duration of forward starting swap

For a spot starting interest rate swap, the duration is calculated as the duration of the fixed rate leg less the duration of the floating leg. Each of these calculations is akin to calculating the ...
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116 views

Calculating YTM for a floating rate bond

I am trying to understand how YTM's are calculated for floating rate notes. I have had a go at calculating it and I am always a few bps off for every FRN I try to calculate. Does anyone have any ideas ...
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70 views

Rebalancing Bond Indexes

I am trying to make an index for the bond market in my country, which will be modified daily. For simplicity, suppose that I only have three bonds. Additionally, suppose that I am interested in ...
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Treasury Bond Futures - last delivery date

When futures stop trading 7 business days before the last delivery date and assume there's no end of month option, what is the benefit for the short futures to hold their basis positions from the last ...
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43 views

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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Discounting for XVA

I was thinking that since CVA is on uncollaterized exposure, we should be using USD-0/LIBOR discounting environment. But I observed that the industry uses CSA discounting for CVA/uFVA computation. Am ...
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57 views

Does it make sense to adjust a bond spread for price/coupon effects?

I have come across the practice, in the wild, of bond OAS being adjusted for the price of a bond. The idea expressed to me was something like the following. A $\$90$ corporate bond with a 10 yr ...
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43 views

Quantlib - Duration of a Floating Rate Bond with Spread

I've used Luigi Ballabio's workaround to calculate the duration/modified duration of a floating rate bond (which you can find here: https://www.youtube.com/watch?v=r_1wSd0hnN4). However, if I add a ...
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70 views

Quant valuation of a credit card debt (or flexible loan)

What would you say is the generally accepted quantitative method of valuing an individual credit card, or flexible loan? Is the method very changeable if that were a pool of such loans? Suppose the ...
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Implied/Realised Vol ratio for negative rates?

I'm trying to calculate the implied vs realised vol ratio for different swaptions across major currencies. This works fine for the likes of USD and GBP as rates are positive. However I'm struggling ...
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93 views

Basic arbitrage exercise

In the exercise we are given, possible contracts to buy/sell and possibility to take credits / make deposits money with current market rates. We are asked if its possible to make profit at time T=0 ...
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77 views

Forward Contract Price on Zero Coupon Bond

I'm trying to calculate the forward contract on a zero coupon bond where the forward contract matures at t=4. The zero coupon bond matures at t=10 and has a face value of 100. The price of that bond ...
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40 views

Is callable bond pricing available in Quantlib XL?

I am able to find documentation for pricing callable bonds in Quantlib Python or C++, however, I am struggling to locate it for Quantlib XL. Is there a way to price callable fixed-rate bonds in ...
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39 views

How are the notionals on proceeds-weighted bond butterflies calculated?

Most LDI (Liability-Driven Investment) accounts construct bond butterfly (fly) trades by weighting them according to proceeds. This creates two constraints: The fly is duration-neutral (the usual ...
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Quantlib for Amortizing securitized loans with option for prepayment

I have not had much experience with QuantLib, but from a brief look through the docs it doesn't necessarily seem suited to my task. Consider a mortgage backed loan. There are various options on ...
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82 views

The similarity between a bond's quoted bid price and its clean price?

Is the Best Quoted Bid Price the same as the Clean Price for bonds? I understand that the Clean Price is the Dirty Price less Accrued Interests, however, I am a bit confused of why the Bid Price = ...
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66 views

Bonds are traded and settled at clean price or Dirty price? [closed]

Are Bonds are traded and settled at clean price or Dirty price ?
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217 views

Libor to SOFR transition Yield Curve Construction

With the imminent transition from LIBOR to SOFR next year, what are the data points practitioners are using to the yield curve? Also, since LIBOR implicitly took into account credit risk of the ...
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89 views

Repo risk - how the desk operate

I am trying to understand how repo traders are being measured(pnl/risk). I understand the amount of repo that can be done is limited by regulation but want to dig deeper on how the performance is ...
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42 views

How key rate durations are calculated

I just had a question regarding how key rate durations are calculated in practise. I Know it involves changing the key rates and calculating new bond prices. But how are these new bond prices ...
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169 views

Treasury Futures Wild Card

I am looking at some empirical methods to model the Treasury Futures wild card. I was looking through some sell side reports and found this statement. "Wildcard fair BNOC is the net basis under ...
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1answer
77 views

Is this regression suitable for fixed income products (negative interest rates)?

I am currently looking at a regression which tries to model EWMA volatility in the presence of negative interest rates. The regression is as follows and uses absolute return instead of relative in ...
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43 views

Compute value of $\mathbb{E}(B_3)$

I wonder would anybody tell me how to calculate $\mathbb{E}(B_3)$ Assuming that $\int_0^{t}r_s\,ds\sim N(0.03t,0.25t)$, then is ===== I have similar problem solved: Assuming that $\int_0^t r_s ds \...
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342 views

Calculating the Discount Margin for a FRN

I am working with a programming case where there are two methods of calculating YTM / discount margin for bonds and FRNs. Both methods use an iterative approach to find a rate / spread that ...
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65 views

Calculating bond prices from constant maturity yield

Goal: turn a constant maturity yield time series into bond prices. The federal reserve has great data series including this one. This is a time series of historical treasury bond yields and I need to ...
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Fed repo operations - Balance sheet constraints

There's been a lot of discussions regarding end-of-year balance sheet constraints as dealers wind down their repo activity. However, the Fed is engaged in open market repo operations in overnight and ...
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zero-coupon bond and forward rate

My understanding, in a discrete-time setting, the relationship between a zero-coupon bond price and forward rates is: $$p(t,T)=\frac{1}{\Pi_{j=1}^{T-1}f(t,j)}.$$ where $p(t,T)$ represents the price ...
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42 views

Bond whose amortization scheme initiates at a later time in its life?

Is there any type of bond whose amortization initiates at a later time in its life? For example the first year we observe interest-only payments and after year 1 there initiates an amortization ...
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115 views

Payoff of Forward Contract

Consider the following notation: $P(T_j,T_2)$ is the price of a zero-coupon bond at $T_j$ with maturity $T_2$. $F(t,T_h,T_2)$ is the price of a forward contract at time $t$ on the above $T_2$-...
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59 views

Futures vs Forward (Last Delivery or Last Trading Day)

For all contracts except the 2-year and 5-year, the last trading day is 7 business days before the end of the contract month. If we assume there is no optionality, isn't there a mismatch in carry. ...
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What is the price of a bond that settles on its coupon date?

Let's say I have a bond that pays on coupon on 10/03. I buy this bond on 10/01 with settlement on 10/03. Who gets the coupon ? Does it depend if it's paid in the morning, in the afternoon, before/...
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126 views

Hedging the duration and convexity of a bond portfolio

I'm trying to work through this homework question, but not sure how to approach it. You recently took over as the manager of a bond portfolio. Your total assets under management – all consisting of ...
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69 views

Cox-Ingersoll-Ross Zero Bond Put Option

according to Brigo & Mercurio (2006): But how is the Zero bond Put of the CIR model? I couldn't find any information about that. Thanks in advance. Regards Chris
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112 views

Hedging a trade for PCA component neutrality

Suppose I am given a set of financial instruments, e.g. {1Y, 2Y, ..., 30Y} interest rate swaps or {Barclays, Lloyds, .. } FTSE100 companies. It doesn't matter which so let's go with IRS. I have ...
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138 views

Is my thinking on futures implied repo correct?

I am building analytics for futures and have a theoretical understanding. If implied repo > actual repo then I can short futures and go long the security and finance it in repo. ON my Bloomberg ...
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71 views

Floating Loan Valuation and Par Value

Why is it true that the value of a floating rate loan is equal to its par value at payment dates? How can one show this mathematically? I want to understand this both conceptually and mathematically.
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How do you find a company average quality of income ratio?

Do you divide the weight average number of shares outstanding basic and diluted/by the net income? Or just add the current year and prior year quality of income ratio divide by two?
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54 views

Treasury auction trading strategy (tails vs stop throughs)

All Treasury auctions stopped through this week across the 2, 5, and 7 year auctions. People are saying that dealers lost because dealers typically short then when-issued bond and cover at the ...
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319 views

Best topics to begin Quantitative Finance Research/Programming

I have a background in mathematics (Functional Analysis and Probability Theory) and am looking to acquaint myself with research in quantitative finance, particularly with a programming component. ...
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Question regarding loan tape data when thinking about providing credit facility to bank

I have few questions regarding loan tape data such as this one: Data Say that I as a fund want to provide a credit facility to this bank and am given this loan tape data. (1) What observations / ...
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31 views

Hedged portfolio dynamics under T-forward measure

I'm looking to find the hedging PDE for a multi-currency derivative $u(F_d, F_f, X,t, T)$ under the T-forward measure, using the delta-hedging argument (F - forward rate, X - forward FX rate). ...

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