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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14 views

Black-Derman-Toy model AND European-type bond call option

In a Black-Derman-Toy model in which Ω ={ ω1, ω2, ω3, ω4 }, the risk-neutral probability for each state ωi, i = 1, 2, 3, 4 is 1/4 . The spot rates in BDT model are given as follows. ω r1 r2 ...
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41 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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712 views

Issue with OLS Regression for Nelson Siegel Svensson parameters

I have been working on getting input parameters to the Non-Linear Optimization which gives the Nelson Siegel Svensson model parameters and am carrying out the OLS regression as described in this ...
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51 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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14 views

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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407 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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153 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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1answer
72 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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54 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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44 views

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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118 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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199 views

Bond PDE under an Affine Jump Diffusion model

Under the Jump extended Vasicek model, the dynamics of the short rate are as follow : $$dr_t=\kappa(\theta-r_t)dt+\sigma\sqrt{r_t}\,dW_t+d\left(\sum\limits_{i=1}^{N_t}\,J_i\right)$$ where $N_t$ ...
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51 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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1answer
71 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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29 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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1answer
2k 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
53 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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1answer
85 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
71 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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1answer
46 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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1answer
66 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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48 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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41 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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38 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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43 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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40 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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1answer
76 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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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
72 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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355 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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43 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
194 views

Observed market price for the August-Greece-paid bonds were the NPV of the bond or of an option?

The bonds which Greece has paid had been valued by market as junk once, just before their payment. Given that the observed market value is the net present value of the instrument, why were they so low?...
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43 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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4answers
3k views

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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1answer
86 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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1answer
52 views

What discount rates should I use to price municipal bond with unknown market price

I have a payoff structure but I do not know the price of bond. The bond is municipal. What discount rates should I take for each period in order to calculate its fair price?
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174 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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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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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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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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1answer
104 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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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

Calculation of Bond returns [closed]

Given that I have a portfolio of High yield bond with USD 50.
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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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107 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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63 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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1answer
91 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? ...