# 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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### Historical data on european corporate bonds [duplicate]

I am trying to run a factor analysis on European corporate bonds and I need historical data since mid - late 90s on : 1.bonds listed 2.spread 3.firm´s total debt at the time 4.Sector of firm 5....
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### $E_p(e^{-\int_j^k r(t)dt})=B(0,j)$

Consider $r(t)$ the spot rate of default-free interest where $B(t,T)$ represents the $T$-maturity zero-coupon bond price at time $t$. Also assume, we are taking the expectation under the risk-netural ...
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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 mean to ...
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### 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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### 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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### OIS Fixed Rate - how to calculate on trade booking?

I am trying to understand how the Fix rate on a OIS trade is calculated at trade initiation. I understand this process for a Fixed V LIBOR trade non collateralized ( discount and projection curve are ...
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### 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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### 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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### 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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### 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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### 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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### 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 XVA is on uncollaterized exposure, we should be using LIBOR discounting environment. Why don't we do that?
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Fixed rate bond pricing issue in Quantlib

I cannot retrieve the same price for a fixed bond using quantlib. ...