Questions tagged [bond]

A bond is a fixed-income instrument generating cash flows at some specific dates in the futures. These cash-flows depend on the interest rate of the bond, which can either be fixed or variable. It is a debt instrument acting as a loan made from the buyer to the seller.

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1answer
60 views

Cap price as bond options

I am currently struggling with model calibration of the Hull-White (or Vasicek) model to Caps and Floors. My main problem is that I am confused about the notation. In Brigo & Mercurio (2006, p. ...
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68 views

Calculating the Macaulay duration of a floating-rate bond

I am new to the pricing of bonds: Suppose that I would like to price a floating-rate bond with par value \$100, with maturity at $T$ years from now, paying coupons semi-annually. Suppose that $r_{n-...
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39 views

Expected Yield to Maturity & Default Risk Premium

For a corporate bond, which natuarally has a default risk, the expected yield to maturity (EYTM) is defined as the probability-weighted average of all possible yields. Hence, for a 10-year zero-...
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Is there any difference between “shorting a bond” and “selling a bond” concepts? [closed]

Shorting a bond means borrow it form other and sell. It seems to me that this operation is the same as just simply issue a bond. Am I right? If yes, then why do we use "shorting" terminology for bonds?...
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65 views

Nelson & Siegel model (Fixed Income Securities)

I am well aware of the basic model formula and for what it is used, theoretically speaking, however I cannot find any concrete, problem solving exercises. Soon, I will have to deal with this problem ...
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What is the most recent measure of the US Municipal Bond Market Size (Capitalization)?

$3.853 trillion in second quarter of 2018 according to Fed. Today?
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Are Muni REVENUE bonds secured or can the local gov. use the revenues for other purposes not paying the bond holders if its going bankrupt? [closed]

Municipal bonds are of two kinds: GO (General Obligation) Bonds or Revenue Bonds. My question on Revenue Bonds is: are the revenues from the specific project secured or can the local government use ...
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44 views

Derive the discount bond prices of the Vasicek model by the PDE approach

The question is shown above. Anyone can help me?
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61 views

treasury bond cash future net basis

In the cash bond and future basis trade, the net basis is like the option (quality option and time option) premium, right? So, it should be positive. Sometimes I see it went to negative, so does this ...
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24 views

What MIPS (Municipal Inflation Protected Securities) are out there besides the two DFA ones?

DFA has DMREX AND DCARX. Are there others? I'm specially looking for high quality, medium or long duration MIPS but a list of anything would help.
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41 views

Calculating bond forward rate/price

What's the difference these two methods on calculating the bond forward rate/price. First of all I'm assuming forward rate is the same as forward price in this context, if this assumption is false, ...
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38 views

Can a bond be denominated in another security?

Could a bond be issued that's denominated in securities like ETF shares or stock shares? Of course most people would not want to buy it, but is it possible? I know it's possible to short a security, ...
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124 views

Origin of the $-\frac{1}{P}$ in Macaulay Duration?

Changes in the yield curve affect the total return of a coupon bond instrument, hence I want to compare different bond instruments in how sensitive they are to $y$. Well, I just take the derivative, ...
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80 views

How are returns on Bond Funds (or ETFs) calculated?

For example, if we consider the fund "iShares Core U.S. Aggregate Bond ETF (AGG)", I am trying to figure out how the yearly/Monthly returns are being calculated. I extracted the historical NAV values ...
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54 views

If 10s20s steepener have equal DV01 weighting on each swap then why does convexity play a role in MtM

Receiver Swap 10yrs Notional: 1,000,000 DV01: +1,300 Tenor: 10yrs Rate: 4% Payer Swap 20yrs Notional: 500,000 DV01: -1,300 Tenor: 20yrs Rate: 5% Looking at this fictitious example, I want to ...
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How does the securities lending market work?

After doing some research, literature suggests that "most" securities lending happens over-the-counter (OTC) as opposed to securities trading which is mostly done through a centralized electronic ...
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75 views

Fastest way to calculate YTM from bond price

I would like to calculate YTM for every top of the book update on the 10-year note traded on Brokertec. There is no closed form solution so have to use a root finding method like Newton-Rhapson. It ...
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91 views

carry for a sovereign bond

For sovereign bond, I saw two carry calculations: one would be forward yield - spot yield, the other would be spot yield - repo rate. I would assume these 2 methods result in same or very close result....
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Bond strategy in rising rate environment

During a period of rising interest rates, it makes sense for investors to either swap out their longer term bonds for shorter ones, or simply invest in shorter maturity bonds in order to reduce ...
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52 views

How I can calculate index bond market

I know that some of the bonds on the market have been manipulated by investment funds. I could identify these bonds. I have classified similar bonds in terms of risk, maturity and Duration. I have ...
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45 views

EONIA capitalisé jour tr eur: can't find index data! Do you know what kind of index is?

To get EONIA capitalisé jour tr eur index returns (monthly returns from 01/2007 until the most recent) is challenging. First i googled the index name searching for the ISIN or the index provider ...
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56 views

Clarification on certain finance terms surrounding bonds

Whilst revising for my upcoming financial mathematics exam I've been struggling to get to grips with certain terms/ phrases used when studying Bonds. I am very new to Finance and get confused very ...
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Finding the redemption yield of a bond given a capital gains tax

Let's say a bond has a face value of £$100$ with semi-annual coupons at a rate of $3$% p.a which is redeemable at par in $10$ years. Assume an investor purchases the bond for £$92$ on the day it is ...
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75 views

Zero-coupon bond pricing equation derivation

I'm trying to understand how in Chawla's paper that I've linked below, how he obtains equation (2.5) for the zero coupon bond pricing equation? The equation is: $\frac{\partial B}{\partial t} + \...
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58 views

Interest rate equation from bond price?

If a zero coupon bond price at time $t$, with maturity $T$ ($t<T$), is denoted by $B(t;T) = B(T;T) e^{(-\int_{t}^{T} r(s) ds)}$ where $r(t)$ is a known interest rate. How does this transform ...
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How do I derive a blend of a 3Y future and 10Y future risk?

So I have a portfolio of Govt. bonds that I'm trying to hedge with futures. Let's take one of the bonds out of the portfolio as an example. In bloomberg, every bond and its future counterparts has a ...
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124 views

Pricing a government bond

I am reading the "Bond" article on investopedia on stumble on the way they price a government bond. Say that the interest rate at time $t=0$ is $r=10\%$. I buy a government bond with face value 1000\$...
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How is CPR (re-)calculated for fixed fully amortizing agency mortgage pass-throughs given prior partial prepayments by mortgagors in the pool?

Background: in the US, mortgagors are allowed to prepay any amount and in any arbitrary time during the lifetime of the mortgage, which leads to prepayment risk if this deviation differs from the ...
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State price deflator in the Vasicek model

I am trying to implement a simple bond pricing model using state price deflators in a Vasicek model. I am simulating paths of the processes $$\mathrm{d}r^{P} =\kappa^{P}(\theta^P - r^P(t))\mathrm{d}t ...
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96 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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103 views

Duration. Floating rate note

I don't understand why the duration of a floating rate note equal to the time to the next coupon payment? Please, look at my calculations. Here: P - is price at moment 0.
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50 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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70 views

Determining parent issuer from ISIN

What digits/letters of a bond's ISIN correspond to its parent company issuer? I have noticed that for many bonds, the first two digits stand for the country of issuance and oftentimes there is ...
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73 views

Simple Relation between Put Price and Zero Coupon Bond Price

Consider your standard European Put Option, with strike price $K$ and maturity $T$, and denote by $P_t(K,T)$ the price of this option at time $t$. Moreover, consider a standard Zero-Coupon bond with ...
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Matching the yield on a bond with the zeroRate on a curve in Quantlib

I am using QuantLib to generate a US Treasury curve from 1y, 3y, 5y, and 10y yield quotes. However, after building the curve and running zeroRate on it, it ...
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cashflow for floorlet option on 1 month Libor under Vasicek

I have to figure out the cashflow for a floorlet option written on 1 month Libor under Vasicek model by considering yield curve power series expression and bond pricing equation: Has anyone an idea ...
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Credit spread model

Let $c(t,T):=-\frac{1}{T-t}[\mathrm{ln}(P_1(t,T))-\mathrm{ln}(P_0(t,T))]$, with: $c$ measure of how a company is prone to fail; $P_0(t,T):=e^{-r(T-t)}$ price of no-defaultable bond. $P_1(t,T):=\...
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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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Equivalent of recovery rate

I'm trying to understand the functioning of "recovery of face-value" approach. Let $V_t$ the fair-value, that is the price that the holder of a defaultable bond must pay for hedging of default of ...
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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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81 views

Proof standard Brownian Motion under change of measure

Let's split the usual time horizon $[0,T]$ like $0=T_{0}<T_{1}<\dots<T_{n}=T$ and consider the bond price $P(t,T_{i})$ for $i=1,...,n$. We assume $$\frac{dP(t,T_{i})}{P(t,_{i})}=r_{t}dt+\xi_{...
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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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64 views

Proving that YTM > Current Yield on Discount Bond

I’m currently stuck in proving that for a discount bond: YTM > current yield, with: $$\text{current yield} = c \frac{100}{P}$$ with $P=100-d$ the price of the discounted bond and $c$ the coupon rate....
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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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46 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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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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1answer
61 views

Are pure PIK bonds' payoffs known from the start?

I am developer working in the financial field and I would like to understand what I'm doing. My latest work subject involves Payment In Kind bonds with coupons fully reinvested (e.g, no coupons ...
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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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simple question on bond futures pricing formula assuming continuous compounding

I'm reading a paper (Statistical arbitrage in the U.S. treasury futures market 2017), and have come across this derivation for the price of a bond future assuming interest payments and coupons ...
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What is a quick way to estimate the haircut on a collateral that is actively traded

If I have an traded asset like a bond with face value of 1 million, but currently trading at 0.9 million, can I simply say that the haircut, if I use this asset as a collateral for repo, is 1 - 0.9=0....