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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11
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1answer
1k views

Pricing Treasury futures

I've recently learned that at the delivery of Treasury futures the short side can decide which of the $n$ Treasury bonds (with relevant maturities) to deliver. If the short side chooses to deliver the ...
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1answer
315 views

Why can CDS indices be used as a bond market index?

I don't understand why the iTraxx indices family, which are credit default swap indices, are in practice often used to gauge the bond market. How are CDS prices related to bonds prices? And what other ...
9
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1answer
688 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 ...
8
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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 ...
8
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1answer
9k views

Calculating instantaneous forward rate from zero-coupon yield curve

I have a big dataset containing zero-coupon bond yields with different relative maturities. I fix a time horizon on my dataset and I want to calculate instantaneous forward rate. I'm going to write ...
8
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1answer
529 views

Use of Girsanov's theorem in bond pricing

Assume that we want to calculate the time $t=0$ price of a bond: $B(0,T) = E_P[\exp(-\int_0^T r_s ds)]$, where $r$ is the interest rate following the SDE $dr_t=k(\theta-r_t)dt+\sigma dB_t=b(r_t)dt+\...
8
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2answers
16k views

question regarding carry & roll of a bond

I have a simple (and might be a dumb) question regarding the calculation of a bond's carry. If someone doesn't take into account cost of financing (e.g. the repo rate) then the bond's approximate ...
8
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1answer
379 views

Integral-differential equation for forward rates

I am struggling in this question: Let $P(t,T)$ denote the price of a zero-coupon bond (with marturity at time $T$) at time $t \in [0,T]$. As usual, at time $t$ for maturity $T$, the forward rate is ...
7
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1answer
4k views

Pricing a FixedRateBond in Quantlib: yield vs TermStructure

I am trying to price a simple U.S. treasury in QuantLib, using two methods. The first method calls FixedRatebond.dirtyPrice(...), passing in a YTM and other parameters. The second method involves ...
7
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7answers
352 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 ...
7
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2answers
434 views

How can we have negative probabilities in finance? Can we have negative payments in bonds? If not, how else can we have negative probabilities?

In Half of a Coin: Negative Probabilities, the author mentions bond duration. Suppose we have payments at times $t = 1,2,...,n$ denoted respectively by $R_1, R_2, ..., R_n$ and the discount factor is ...
7
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1answer
478 views

Wrong discount factors when finding Nelson Siegel Svensson model parameters

I am trying to determine the parameters for the Nelson Siegel Svensson model and am solving a Non- Linear Optimization problem to do this. Some of the code I have written is below and this is where my ...
7
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0answers
83 views

Predicting bond auction result. Should I train separate models for different maturity in face of Data deficiency?

Problem Statement Trying to predict how bond auction result ( in terms of yield ) is different from its forecast (the when-issued yield ). More info:http://www.mortgagenewsdaily.com/mortgage_rates/...
6
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1answer
192 views

Arbitrage with freshly issued bonds

I recently heard someone mention an arbitrage strategy involving selling freshly issued bonds and buying the "old batch" as it has shown that the liquidity in the fresh batch motivates/drives up these ...
6
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1answer
665 views

Definition of gearings, spreads and curve in RQuantLib's Floating Rate Bond function

Consider the RQuantLib package function FloatingRateBond(). This takes as inputs gearings ...
6
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1answer
279 views

Callable bonds with very short call period. Purpose?

Looking at a portfolio of bonds, I've come across a large number of callable bonds with relatively long maturities (20 to 30 years) but very short call windows. In other words, the first and only call ...
6
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2answers
7k views

What happens to accrued interest and coupon payment if coupon date is weekend?

Say a 5% bond using 30/360 convention, 2 coupons per year. Last coupon payment was on 2016-04-01. Now 2016-10-01 is weekend and the coupon is paid on 2016-10-03. Is this coupon 2.5 or slightly more ...
6
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2answers
6k views

How to calculate US treasury total return from yield?

I'm struggling to understand the meaning of US treasury total return. What is easily available to get is yield data. Yield can be directly translated to the bond price at that time. In other words, ...
5
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2answers
8k views

Can the duration of a bond be greater than Time to Maturity

In the case of a vanilla bond I know that the duration will be less than the time to maturity. But I am observing that for a non-vanilla bond, the duration is greater than time to maturity. Can ...
5
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1answer
79 views

yield concept for a short maturity zero coupon bond

I am trying to clarify what is the more relevant and appropriate quantity for a discount security / zero-coupon bond, that is defined by a face value, FV, a present value, PV and a time to maturity, t,...
5
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1answer
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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1answer
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Why does a barbell portfolio have higher convexity than a bullet porfolio

I cannot quite understood absolutely why a barbell portfolio has higher convexity than a bullet porfolio. I can easily understand how the parallel line represents duration but I cannot see what the ...
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2answers
628 views

What is the hedging underlying of MBS

I am working on hedging agency MBSs using treasury bonds. So my question raise as which treasury bond should more likely be a hedging underlying of a MBS. What is the matching criteria usually for MBS ...
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2answers
1k views

BUS/252 accrual - why 252?

I've recently found out about the BUS/252 accrual method used in Brazil, where, to calculate how much of the yearly accrual falls on a given period by calculating the number of business days during ...
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3answers
2k views

Default Probability Implied in Bond Prices?

Say I am trying to find the probability of default on JP Morgan implied by the price of their fixed income assets. Can this be done? Are there any pitfalls to this approach? I have heard of this ...
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4answers
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What happens when bond price is less than the recovery rate

I am simulating various price path of bonds, and one issue that came up is the recovery rate. When a bond defaults, the amount you get back recovery rate * principle. This creates a problem if the ...
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2answers
451 views

Why is the duration of a bond important?

I know what duration measures, but now in the age of computers why is it useful? If the yield changes, we could just simply plug the new yield into a program, or excel or something like that, and ...
4
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1answer
2k views

Simple QuantLib Bond Math

I am new to QuantLib and am trying to get it to replicate some simple bond math. Suppose we have a 5-year bond with annual coupon payments of \$5 and face value of \$100, and interest rate of 4%. ...
4
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3answers
2k views

How do I determine the maturity date from a T-bill's CUSIP?

Is there a way to determine a government bill's or bond's maturity date by looking at its CUSIP? For example, the CUSIP for US T-Bills with a maturity of 12/1/11 is 9127953V1. As you probably know, ...
4
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2answers
380 views

How do I price $P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$?

Derive the pricing formula $$P(t)=P(t,T_{n})+\sum_{i=1}^{n}[P(t,T_{i-1})-P(t,T_{i})]$$directly, by constructing a self-financing portfolio which replicates the cash flow of the floating rate bond. $P(...
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1answer
17k views

Conversion factor for bonds

Hull defines the conversion factor for a bond as the "quoted price the bond would have per dollar of principal on the first day of the delivery month on the assumption that the interest rate for all ...
4
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1answer
503 views

Yield for valuation of illiquid corporate bond

I am trying to value a illiquid corporate bond issued at a discount to face value by a privately held company in India. The corporate bond is a sinkable bond (amortizing principle) with coupon rate of ...
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3answers
228 views

Positive VaR when calculation on Total Return Indexes?

I recently saw a VaR calculation, and I was wondering whether that calculation made sense. Here the details: 1. Construction of a total return bond portfolio index. By total return I mean that the ...
4
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1answer
1k 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 ...
4
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3answers
2k views

YTM and current yield

Which of the following statements is correct? a. If a bond’s yield to maturity exceeds its coupon rate, the bond’s current yield must also exceed its coupon rate. b. If a bond’s yield to maturity ...
4
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2answers
252 views

Compare the IRRs of two bonds

Say i have two 3 year bonds, which pay an annual coupon of 8% (1st bond) and 10% (2nd bond) respectively. Also, let's assume, that the spot curve is the same for both bonds. Other things equal, how ...
4
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0answers
260 views

RQuantLib: any difference between FixedRateBond() and FixedRateBondPriceByYield() with flat term structure?

Please, consider the following functions from RQuantLib package: FixedRateBond() ...
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4answers
1k views

Yield of a risky bond

When working with risky bonds, i.e. corporate bonds, what is usually defined as the yield of such a bond? Is it the yield calculated as if the bond was riskless, or is it calculated by properly taking ...
3
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2answers
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?
3
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1answer
244 views

How can I interpret US treasury?

I try to understand US treasury in the bond markets provided by bloomberg: In this webpage, I have a few questions, for instance taking 12month-Bill: (1) What is the maturity date? I find that it ...
3
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2answers
4k views

How to calculate the daily carry on a bond future?

I have been calculating daily carry on a normal bond as the difference in yields from one day to the next (roll down basically), interpolating the yield on one day, and interpolating it for the ...
3
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1answer
99 views

Custom Bond Index Construction

Let's say there are about 100 illiquid EM bonds. I would like to construct a Price Index of these bonds to see the overall performance of these instruments. I have their issue volume ...
3
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1answer
88 views

Bond yield to maturity vs current interest yield

How close is yield to maturity usually to current interest yield? Can I use yield to maturity to approximate current interest yield of a bond index? I am trying to calculate bond index price returns ...
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3answers
3k views

Why is G spread bigger than Z spread theoretically?

I am checking a few bonds on the YAS page on Bloomberg and I can see that G is higher than Z spread (this applies to bonds with optionality and bullet, too). As Z is stripped from reinvestment risk, ...
3
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1answer
170 views

Bond price under Poissonian model of interest rate

Working through an exercise in interest rate modelling and I have the following setup: $r_t = r_0 + \delta N_t$ where $\delta > 0$ and $\lambda > 0$ is the intensity of the Poisson pricess $N_t$...
3
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1answer
3k views

Cost of Carry Bear Flattener

I was reading a report last week that “the carry on a 2s5s gilt curve flattener is negative to the tune of 10bp over 6 months” and I realised I have little understanding of this concept and how ...
3
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1answer
166 views

Bond SDE under its own forward measure

I am trying to write the SDE for a forward bond, $dP(t,T_1,T_2)$, under the $T_1$-Forward measure, $Q_{T_1}$. I can easily do this by: Writing the equation of $dP(t,T_1)$ and $dP(t,T_2)$ under the ...
3
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4answers
159 views

Intuitively, why does liquidity premium contribute to bond yield?

According to the Wikipedia, "The upwards-curving component of the interest yield can be explained by the liquidity premium... Liquidity risk premiums are recommended to be used with longer term ...
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1answer
2k views

Pricing a bond contract from the yield curve

When giving a particular class in financial mathematics for a student I saw a problem in a list of exercises that says: How to calculate the price at 15 December 2010 of a bond paying a coupon of 11....
3
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1answer
262 views

Concise way of learning Bond & IR models

What is the most concise way to learn about bond and interest rate models from the book Mathematical Models of Financial Derivatives by Yue-Kuen Kwok? I have studied Oksendals Stochastic Differential ...