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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12
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1answer
2k 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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3answers
10k 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, ...
13
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3answers
26k 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 ...
1
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1answer
3k views

Setting input parameters for Nelson Siegel Svensson model

I am trying to determine the parameters for the Nelson Siegel Svensson model and am solving a Non-Linear Optimization problem to do this. I am trying to solve: $$ \min_\theta{\sum{(p_i - \hat p_i)^2}...
10
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2answers
24k views

Formula for forward price of bond

What is the formula for the forward price of a bond (assuming there are coupons in the interim period, and that the deal is collateralised) Please also prove it with an arbitrage cashflow scenario ...
1
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1answer
699 views

PDE for Pricing Interest Rate Derivatives

Suppose that interest rate $r(t)$ follows some short-rate models, say Vasicek, so that$dr = a(b-r) dt + \sigma dZ$, with constants $a,b,\sigma$. It is well known that the price of zero-coupon bond $...
4
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1answer
3k views

Zero-coupon bond price volatility with one factor Hull White interest rate model

I have been trying to understand the H&W model expression for zero coupon bond price volatilities: $\nu_B(t_0,t_M)=-\frac{\nu_r}{m}(1-e^{-m\tau_{0,M}})$, where $\nu_B(t_0,t_M)$ is zero coupon ...
3
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1answer
371 views

Yield to Maturity

For a bond with market price $P_t$ and fixed payments $c_n$, I'm told the yield to maturity is given by the solution $Y$ to the equation $P_t=\sum_{n=1}^N c_n e^{-Y(t_n-t)}$. Firstly, I'm not great ...
3
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1answer
290 views

Cap option on Libor

We denote discount factor $D(t),$ zero coupon bond $B(t,T),$ $E_t[X] = E[X|\mathcal{F}(t)]$ and $T$-forward measure $E_t^{T}[\ ]....
0
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1answer
482 views

What is the value/price of a bond paying floating rate

I am going through J.C.Hull for swaps. Where he says we can value a swap using bonds. Let $B_{fl}$: value of floating rate bond, $L$ notional principal. Why is $B_{fl} = L$ just after a payment ? What ...
11
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6answers
7k 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 ...
4
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1answer
18k 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 ...
7
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1answer
4k 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%. ...
5
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1answer
323 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
1k 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 ...
8
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1answer
1k 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 ...
3
votes
1answer
315 views

Yield of a Bond

If we have a coupon bearing Bond and want to calculate it's Yield then what is the standard practice to determine the ...
3
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1answer
524 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 ...
2
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1answer
3k views

Bond price in Ho-Lee Model

I know Ho-Lee model and want to extract the price at $t$, of a European call option with strike price $K$ and exercise date $T$, on an underlying $S$-bond, but I don't know what way should I choose: ...
2
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1answer
443 views

Boundary Condition for Convertible Bond under Two-factor Model Interest Rate

I want to find Boundary conditions for Convertible Bond under Two-factor Model Interest Rate.The portfolio contains stock where stochastic differential equation for the stock price is \begin{align} ...
2
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1answer
269 views

Pricing bonds of float coupon rate by stochastic interest rate

So I am not sure whether the following pricing of the bond is possible. Given the stochastic interest rate, one wants to price the bond with the floating coupon rate or the coupon rate being unknown. ...
2
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1answer
5k views

Pricing a zero with Vasicek model

I'm trying to understand bond pricing with the Vasicek interest rate model. I'm using McDonald's book for this purpose (not homework). Recall that Vasicek dynamics are \begin{equation*} \mathrm{d}...
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1answer
1k 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
17k views

Duration of a floating rate bond

It is known that the price $p_t$ of a floating rate bond can be calculated discounting $(L+k)$ the sum of the next coupon payment $k$ and the face value $L$ at the relevant risk-free rate. Hence, ...
8
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1answer
678 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+\...
6
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2answers
11k 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 ...
4
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2answers
628 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(...
3
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0answers
92 views

Optimized search for yield-to-worst of a callable bond

Suppose that I need to find the yield-to-worst of a callable bond, and that the option is American (call any time). The bond may have step-up coupons and/or non-constant call price (oprion strike). ...
3
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4answers
2k 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
3k 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
388 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 ...
2
votes
1answer
533 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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2answers
1k views

How does one calculate carry-roll-down theoretically assuming expectations of short-term rates are realised

I am not asking for an explanation that is hugely quantitative, but rather one that is more intuitive. I am aware that there are different assumptions that one could take when it comes to carry-roll-...
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2answers
1k views

Macaulay or modified duration in Python

i was wondering to ask, is there any function in pyhton, that calculates macaulay or modified duration, when time to maturity is not a whole number, for example time to maturity is 1514 days, and you ...
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1answer
3k views

Understanding how to calculate Accrued Interest of Bonds

When calculating the accrued Interest of Treasury Bonds, how does one set the settlement date? And, is it possible for certain bonds that there are no coupon payments before the settlement date and ...
1
vote
1answer
113 views

Building a Nelson-Siegel curve

I originally posted this on Mathematics, but was told my question is better suited here. I want to graph a yield curve with an extended version of the Nelson-Siegel-Svensson. I have the issue date, ...
1
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1answer
1k views

Calculating Accrued Interest of Bonds

I am trying to calculate the accrued interest for a set of Treasury Bonds. I am comparing the answer from the code below with that for the 1st Bond(row) over here. In the link the AI is ...
1
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1answer
215 views

Quantlib: How do I price a bond after having built a term structure

I below are my codes using QuantLib to build a term structure What I would like to do is use that to price any hypothetical bond lets say startdate : 8 Feb 2016 end date : 8 Feb 2021 coupons : 10% ...
1
vote
1answer
293 views

Correct Theoretical Discount Factors from Nelson-Siegel-Svensson?

I am calculating the theoretical discount factors associated with a bond that has 30 months to maturity from today with the parameters below obtained from here using the Nelson-Siegel-Svensson Model. ...
1
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0answers
295 views

Duration of a FRN in continuous time interest rate model

This question was inspired by my attempt to understand the duration of a floating rate note, or FRN for short. Several answers, like this, say the duration of a FRN is just time to next coupon payment....
0
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2answers
920 views

Legitimate input parameters for Nelson Siegel Svensson model

I had previously asked this question and have come to better understand the answer with regards to setting the input parameters for the Non-Linear Optimization problem that provides the NSS parameters....
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1answer
138 views

What is the connection between the federal funds rate and US government bonds

If the Federal Funds Rate changes, does that affect bond prices? How? Also, is there any connection between the Federal Funds Rate and the coupon payment on US bonds?(for those that have a coupon ...