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
28 views

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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25 views

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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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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56 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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41 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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60 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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47 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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41 views

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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38 views

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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36 views

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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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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39 views

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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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
71 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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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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1answer
59 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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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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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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1answer
49 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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30 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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76 views

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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36 views

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....
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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 ...
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1answer
83 views

No-arbitrage and the sharpe ratio?

I'm reading a paper and it says that in a no-arbitrage market the sharpe ratio is the same for all bonds. I'm guessing that a difference in two bonds sharpe ratios would open the possibility of ...
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107 views

Definition of the field YAS_RISK for bonds on Bloomberg terminal

The Bloomberg terminal has the following definition for the field YAS_RISK (SP190): "Indicates the price sensitivity given shifts in interest rates." It does not specify, however, what currency is ...
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36 views

Finding B(t) in the Vasicek model relating to the bond equation, more specifcally from the initial condition

In the Vasicek model for derving bond prices, we have the ODE $$\frac{dB}{dt}=\gamma B-1$$ which gives rise to the general solution $$B(t)=C_1 e^{\gamma t}+C_2$$My problem is that we have the "initial"...
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100 views

Calculation of Bond returns [closed]

Given that I have a portfolio of High yield bond with USD 50.
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170 views

Pricing a callable bond

I have read the Lehman Brother's paper on OAS which I mostly understand, they outline how to find the OAS for a callable bond of which the formula is effectively (ignoring refinancing costs): Market ...
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71 views

Bond spreads - SQASW

I posted this question in the finance/economics arm but someone suggested this would be a more relevant place. I have attached a photo of a list of bond issuance's in Australia. Could someone please ...
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61 views

Duration and yield

I have some basic questions about mainly duration and yield. 1) Almost no-one defines what yield they are talking about when talking about duration and discount rate, I've seen some talk about ...
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38 views

How to convert a vector of bonds ZC Spreads into default spreads

If we consider a set of bonds issued by a given entity that are quoted on the market, one can get for each of those bonds a ZC spread on top of reference swap curve (say the bonds are in USD and so we ...
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89 views

Why is Plain-Vanilla Bond most common bond in the market? [closed]

I have very straigtforward question (in my perception): Is there any study/research/evidence that provides insights on the following question(s): Why is plain-vanilla most common bond in the market? ...
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1answer
151 views

Bond discounting conventions

during the preparation for my thesis, I've come across some strange discrepancies between literature and the information I've been taught. It comes down to the proper way of discounting cash-flows of ...
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67 views

Question on bond pricing [closed]

Excuse my naivete, but I have a simple bond math question. I was asked to calculate the duration for a 10 year bond at 12%, with a refinance at year 5 at par, and 20% amortization. I started by ...
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94 views

How can we compute the daily drop in gross basis?

Background The implied repo rate (IRR) is essentially the carry for going long basis (buying the deliverable bond and selling the futures contract). For this reason, it rises in value day-by-day as ...
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What are industry-standard terms for MBIS “situational bid”?

In the data feed from Municipal Bond Information Services there is a field called "situational bid", which is defined in their reference as "Bids on a security that is being offered for sale." If I ...
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2answers
100 views

Why use par-value weighted average when valuing portfolio of bonds?

I'm looking at a formula for valuing a portfolio of different bonds that sums the market value times the par value for each bond. Conceptually, why are the bond values weighted in this way by their ...
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176 views

Bond dynamics in Ho Lee model

The short rate in the Ho-Lee model is given by : $$dr_t=\left( \frac{df(0,t)}{dt} +\sigma^2t\right)dt + \sigma dW_t$$ I'm trying to find the bond dynamics given by : $$dP(t,T)/P(t,T)=r_tdt-\sigma(...
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2answers
57 views

Why is the yield return preferred to the price return for selecting hedges for bonds?

For evaluating a hedge for a bond, I noticed that we often look at the yield return correlation between the two instruments, instead of the price return. Why is that? To me, the price would make more ...
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1answer
62 views

Calculating value of bond

The bond has a facevalue of 40 and maturity of 20 years. It produces 0 coupon payments during the first 6 years but pays coupons of 2 annually during the last 14 years. The discount rate is 7%. The ...
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1answer
65 views

Markowitz portfolio risk with PV01 instead of variance

As the PV01 ($= dpdy \times notional$) of a bond is a measure of its risk, as well as its price return variance, could we measure the risk of a bonds portfolio with the Markovitz portfolio variance ...
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Monte Carlo VAR with differente asset classes

I have found a very useful post regarding the use of Monte Carlo simulaton to obtain portfolio Value at risk, based on Cholesky decomposition, random variates, etc. This post I'm talking about is: Is ...
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2answers
79 views

Why do constant maturity bonds account for modified duration?

One can create a constant maturity treasury (CMT) by building a zero coupon discount curve and generating constant maturity bonds from that curve. This allows one to look further back than is possible ...
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64 views

Bond is maturing in 10.25 years, YTM calculation

Bond is maturing in 10.25 years and has an annual coupon rate 4.15% paid semiannually and price 92-12+ I need to calculate yield to maturity Ok so I know that 92-12+ is basically 92 + 12/32 + 1/64 =...
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89 views

Bond Overall Return vs Yield to Maturity

I've been working on what I had hoped to be a simple model demonstrating that a bond "returns" its yield-to-maturity over its life. However, whatever data I use, I end up with a return that is a ...
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1answer
43 views

Question regarding coupons for government bonds

I was looking at government bonds/treasuries and I wondered if my line of thinking is correct: 1) In general, how is the coupon set? I found out that usually they are auctioned for (a bit) less than ...
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2answers
158 views

Why does the YTM equal the coupon rate at par?

I know the YTM of a coupon bond is the interest rate $i$ which verifies $ P =\frac{C}{(1+i)} + \frac{C}{(1+i)^2} + ...+ \frac{C}{(1+i)^n} + \frac{F}{(1+i)^n} $ where $P$ is price, $C$ is the coupon ...
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299 views

How does one price the market value and estimate the fair value of a bond futures roll?

Consider the current situation: we are entering December, meaning that the December futures are being rolled into the March futures (i.e. traders are selling their holdings of December futures ...
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Bond Index Return from Yield Curve Data [duplicate]

I am trying to compare fund returns with benchmark returns. I have some yield curve data (some of them calculated by Bloomberg) but not bond price or return data. Is there any way to get bond returns ...