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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How to calculate the unrealised profit on sinkable bond

How is calculate the unrealised profit on Sinkable Bond when 50% of the bond value already been paid? Is the following method correct: Unrealised P&L = ((Current.Position * Market.Price) - Cost....
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73 views

Issue on pricing bond using RQuantLib

trying to pricing a simple bond using RQuantLib, but cannot get the right values. For example, consider a bond with 2% annual coupon rate and flat interest rate of 3%, a 5 year maturity, and \$100 ...
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241 views

Bond Convexity: Relationship between discrete and continuous interest rate

The interest rate risk of a bond price $P$ is measured by its Duration: $$D=-\frac{\frac{dP}{P}}{dr}$$ However, the explicit formula for the Duration given a function $P$ is different if $r$ is ...
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112 views

HJM model, existence of arbitrage:

The Setup: Suppose I know the yield curve of a Bond satisfies: f (0, t) = 0.04 for t ≥ 0 and f (ω, 1, t) = 0.06, t ≥ 1, ω = ω 1 , 0.02, t ≥ 1, ω = ω 2 , where Ω = {ω 1 , ω 2 } with P[ω i ] > 0, i = 1,...
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116 views

Where can I find bonds time series?

I want to study dependence and correlation between bonds and CDS. I have already found a large CDS database of time series there: www.datagrapple.com I am looking for such a similar database (with an ...
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77 views

state space for affine yield curve

i would like to reproduce in R the working paper " Affine free arbitrage class of Nelson Siegel term structure". The authors considering the equation of nelson siegel plus an adjustment term(C(t,T)) ...
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179 views

RQuantLib FixedRateBondPriceByYield() Non-tradable error

How do I use FixedRateBondPriceByYield() function on maturity date that is earlier than today? I get "non tradable error" when applying on date older than today. <...
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56 views

Is there a limit to the number of Spot rates than can be calculated from Par Yields

I am just trying to calculate Spot Rates from Par yields. I find that the code below gives very similar spot rates for the data here, yet if I increase the size of the ...
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109 views

Please recommend a book regarding Monte Carlo simulation in OAS

I couldn't find a book that explains in details how to use Monte Carlo Simulation to generate a number of interest rate scenarios. And then based on the interest rate scenarios, how to calculate the ...
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27 views

Annuity Duration Based on Closed Derivative is half of Effective Duration?

I am analyzing an annuity with a stub. I calculate the effective duration as (P(-10bps) - P(+10bps))/(2*Principal * (.001)) I then take the derivative of the standard annuity formula discounted by ...
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301 views

Bond pricing with HJM simulation

I'm using Glasserman 3.16 and 3.17 algorithm to price bonds. The algorithms evaluates the forward rates and the discount factor $B(0,t_j)$. My question is: How can I price bonds in a future time? I ...
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59 views

Expectation hypothesis, expectation under which measure?

As I understand the expectation hypothesis says that the implied forward rate, can be used to predict future spot rates? If $r_{0,2}$ is the rate for a zero coupon bond maturing in two years, and the ...
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72 views

Can the duration of a floating rate bond with yield spread be negative?

Summary In my calculations below I find that the effective duration(not spread duration, but interest duration) of a floating rate bond with yield spread can become negative. Do you see if they are ...
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84 views

Duration of a floating rate bond with spread

I need to calculate the duration of a floating rate bond with spread. With zero spread the price of the bond is given by: $$p_\tau=(1+c_1)e^{-r(\tau_1) \cdot \tau_1}$$ so the duration is: $$-\frac{\...
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152 views

Why is the effective duration of a floating rate bond the time to the next payment?

I am wondering why the effective duration of a floating rate note is the time to the next payment. Effective duration is is defined as $$\frac{V_{-\Delta y}-V_{+\Delta y}}{2V_0\Delta y},$$ for a small ...
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79 views

Will modified duration and effective duration be the same for floating rate bonds with no option-elements?

Let $P(r_1)$ be the present value for a floating rate bond, with no option-elements, where $r_1$ is the interest rate to the first payment. Is it then correct that the modified duration is $$-\frac{\...
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26 views

How do I get the CUSIPs of all bonds issued by a company?

I know that I can get prices for particular bonds from FINRA (http://finra-markets.morningstar.com/BondCenter/Default.jsp) if I know the CUSIP. But what I want is a list of bonds for a particular ...
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42 views

Bond Change in Absolute or Relatively Percentage

Since most of the bonds prices are quoted in price, for example, bond price of 103 means 103% of the principal or face value (ex. $1000). Suppose a bond has modified duration of 4.62 years. If yield ...
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43 views

Hedging Bond portfolio with Futures

I am working on a risk department. Our portfolio contains mostly some long German bond 15y and we tend to hedge it through BUXL and BOBL via PCA but our 15y key rate duration is not properly covered. ...
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19 views

Fixed rate bond historical simulation

I am using the QuantLib library to determine the historical simulation prices of a fixed rate bond. The idea behind my simulation is to use the spot curve as driver of the bond price. Let $\{y^{j}(t)\...
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21 views

Bond agreggation

I'm working on an asset and liabilities model for life insurance as a school project, one of the inputs of the model is a bond portfolio, for the sake of optimization of computation speed (the model ...
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33 views

future hedge and risk of bond basis trading

I am reading some book about bond basis trading. Assume we have 1M TY CTD and we simultaneously short TY front contract. So we long the basis. The risk should be relatively small. But when I read ...
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32 views

Question about financial mathematics, meeting a claim

I have a question regarding exercise 12, chapter 1 of "A course in Financial Calculus" by Alison Etheridge. It is as follows: "Suppose that the value of a certain stock at time $T$ is a random ...
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36 views

Pricing 5Y US treasury day count convention

I am trying to price a simple 5Y US T Bill. The pricing should be fairly straightforward, however my result is still off by a significant amoaunt. I think the daycount fraction is incorrect, but I am ...
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40 views

$E_p(e^{-\int_j^k r(t)dt})=B(0,j)$

Consider $r(t)$ the spot rate of default-free interest where $B(t,T)$ represents the $T$-maturity zero-coupon bond price at time $t$. Also assume, we are taking the expectation under the risk-netural ...
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49 views

Arbitrage argument with bonds

Let $B(t,T)$ denote the cost at time t of a risk-free 1 euro bond, at time T. Assume that the interest rate is a deterministic function. Show that the absence of arbitrage requires that: $ B(0,1) B(1,...
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35 views

Fixed income management problem

First of all, hope everyone is safe and sound. I would like to describe the following scenario and my thinking Welcome any comments on my thought process!!! 3 swaps outstanding Pay fixed 100mln, ...
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34 views

US Treasury: given YTM, calculate price

According to https://www.marketwatch.com/investing/bond/tmubmusd10y At the end of 3/13/2020, the 10 Year Note (maturing 2/15/2030, coupon rate 1.5%) has: yield = 0.981% price = 104 9/32 Assuming a ...
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25 views

Formula for bond after-tax total return?

I'm interested in calculating the after tax total return on a fixed coupon bond. In Fabozzi's "Fixed Income Mathematics", 4th ed, p. 149, a formula for "after-tax coupon income interest on interest" ...
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1answer
85 views

Discount margin on FRN - widening but bond price increasing?

Why would a bonds discount margin widen but its price increase? Shouldn't the price be falling when margins are widening? Looking at the bond pricing formula, if the price is higher doesn't the rate ...
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28 views

Hedging with a different underlying - bond options case

I'm working on government-bond options pricing (Black-Scholes world, nothing fancy). In EUR, that's pretty much a "non market" in the sense that there's pretty much no quotes, so no implied vols, no ...
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98 views

Is callable bond pricing available in Quantlib XL?

I am able to find documentation for pricing callable bonds in Quantlib Python or C++, however, I am struggling to locate it for Quantlib XL. Is there a way to price callable fixed-rate bonds in ...
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73 views

Quantlib for Amortizing securitized loans with option for prepayment

I have not had much experience with QuantLib, but from a brief look through the docs it doesn't necessarily seem suited to my task. Consider a mortgage backed loan. There are various options on ...
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45 views

How to proof the formula to be martingale under ITO process?

How can implies that is a martingale when using the defaultable bond price?
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76 views

Bond arbitrage in practice

If we have the following term structure for riskless bonds: \begin{array} {|c|c|} \hline \text{Maturity} & \text{\$1 Zero-Bond price}\\ \hline \text{0 years} & \$ 1.00 \\ \hline \text{1 years}...
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97 views

Calculating bond prices from constant maturity yield

Goal: turn a constant maturity yield time series into bond prices. The federal reserve has great data series including this one. This is a time series of historical treasury bond yields and I need to ...
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96 views

Getting Bond Price Data

I am on my thesis about Hull-White model and I need the bond price to calibrate the parameters. How can I get historical bond price data instead of historical bond yield data?
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161 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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48 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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60 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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159 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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106 views

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

I have a payoff structure but I do not know the price of the 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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40 views

Bond Data on UK corporate

I have got data from FRED on Moody's Seasoned Aaa Corporate Bond Yield. Does anyone know where I can get such UK data on this? If not, would using exchange rates and the interest rate parity theorem ...
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626 views

Yield to maturity as discount rate

Assume that face value of a bond is equal to 1000. The coupon rate is 3% and yield to maturity is 4%.How can we correlate coupon rate and YTM in order to explain the state of current bond price. (...
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42 views

Cash flow of longevity Bonds

For a longevity Bond, how is the cash flow and how can I replicate it? I am confused with the cash flow. An Investor pays a principal and receive coupon payment depends on the longevity of certain ...
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1k views

bond price formula in excel

I inherited a excel spreadsheet that has the following code to price a bond given coupon and current yield ...
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69 views

Which bond corresponds to which curve?

Bond X has a coupon Bond Y is a zero-coupon bond (Maturity 2 years) Bond Z is a zero-coupon bond (Maturity 10 years) The following graph is given: X-axis: yield curve, Y-axis: price Question: Which ...
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101 views

How to prove following order?

Consider a consol bond, i.e. a bond which will forever pay one unit of cash at $t = 1, 2, . . ..$ Suppose that the market yield $ y$ is constant for all maturities. (a) Compute the price, at $t = 0$, ...
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66 views

Is there an open architecture API or excel solution for calculating and adjusting bond pricing?

Is there an open architecture API for calculating and adjusting bond prices? I am looking to adjust bond pricing on OAS or adjusted spreads to various indices and need a tool to process large amounts ...
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263 views

This is the dirty price or clean price

A one year bond of principle 100, coupon 6% with half year paying and yield 11%. Suppose the beginning day of bond is 1.1 and today is 3.1, then I want to ask that, the price $$c = \dfrac{3}{e^{0.11 *...