26 votes
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Formula for forward price of bond

Amazingly, there are several different methods for computing bond forward price – the underlying ideas are the same (forward price = spot price - carry), but the computational details differ a bit ...
Helin's user avatar
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18 votes
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What are some of the best textbooks on Fixed Income securities?

If I were to recommend one, it would be: Bruce Tuckman's Fixed Income Securities. This is by far my absolute favorite. It is extremely well written and discusses complex concepts in very easy-to-...
Helin's user avatar
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13 votes
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Simple QuantLib Bond Math

To begin with, as Student T suggested, you can check that the cashflows are those you expect: ...
Luigi Ballabio's user avatar
11 votes
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Callable bonds with very short call period. Purpose?

It's because of a bank regulation called the Liquidity Coverage Ratio. This says that if you have liabilities of less than 30 days, you have to hold liquid assets against it. To avoid that , you ...
dm63's user avatar
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10 votes
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Do we use the Nelson-Siegel model to calculate the yield curve?

In the beginning, we had a plot of yields of individual bonds against time to maturity, the crudest form of "yield curve." Years later, people began hand-drawing a smoothed line through these yields ...
Helin's user avatar
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9 votes
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Bond curve fitting, practical question

Let's define the problem as follows: Given a set of $N$ bonds, we wish to create a discount curve, composed of $M$ degrees of freedom, so as to minimize the weighted price errors: $$ \min_{m_1...m_M} \...
Helin's user avatar
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8 votes
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Do price approximations lead to arbitrage opportunities?

No. The dirty price is the market's estimate of fair value for the bond. The clean price is just a quoting convention (so that the price doesn't jump when you pass over a coupon date). The market ...
Chris Taylor's user avatar
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8 votes

Fastest way to calculate YTM from bond price

I faced this problem trying to price bund yields from Bloomberg ticks. I found the fastest method was to price three static yields from three static prices and determine a quadratic function for those ...
Attack68's user avatar
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7 votes
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What happens to accrued interest and coupon payment if coupon date is weekend?

For the vast majority of bonds, as other commenters have pointed out, coupon sizes are generally not affected by bad days (i.e., holidays and weekends), so for a bond with semi-annual coupon payments, ...
Helin's user avatar
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7 votes
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BUS/252 accrual - why 252?

Business days are all weekdays excluding holidays under the respective settlement calendar. The "252 business days per year" rule of thumb is quite common not only in Brazil - see e.g. here. The ...
LocalVolatility's user avatar
7 votes
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Why does the YTM equal the coupon rate at par?

Let $P$ denote the dirty price, $F$ the face value and $i$ the YTM. Using the geometric sum we get \begin{align} P &= \sum_{j=1}^n \frac{C}{{(1+i)}^j} + \frac{F}{(1+i)^n}\\ &= C\frac{1-\...
Andrew's user avatar
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7 votes
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reason behind bond yield diverge for bonds with the same maturity during 2008 crisis

Just to elaborate on the comments above to include some visuals. As you pointed out, the high coupon, seasoned 10.625s traded at a steep discount. The first chart below shows the yield spread against ...
Helin's user avatar
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7 votes

How to compute par yield from zero rate curve?

For simplicity, let us assume continuously compounded zero rates and periodically compounded par yields. If you have to work with continuous rates, you may adapt the formulas accordingly. Using the ...
Kermittfrog's user avatar
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7 votes
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Construct a zero coupon bond

(Assuming that the two coupon bonds have exactly the same schedules, and that you're settling when the accrueds are 0.) Consider a portfolio consisting of \$7 long 3% bond and $3 short 7% bond. This ...
Dimitri Vulis's user avatar
7 votes

Bond curve fitting, practical question

@Helin provided a great answer for the specific question. I would note that when curve building your framework always falls under one of three regimes: Completely specified: the number of degrees of ...
Attack68's user avatar
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6 votes

question regarding carry & roll of a bond

Carry and roll-down are two different measures. The carry is the PNL resulting from holding a position. However, even if you don't finance the bond in repo, you can still measure your carry as the ...
Riccardo's user avatar
6 votes
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question regarding carry & roll of a bond

The formula you quote (forward minus spot) is the yield carry for a financed position. The problem is that different people use the word carry to mean different things. The most commonly used ...
Helin's user avatar
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6 votes
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Pricing foreign currency bonds - which approach is more theoretically "sound"?

In #2, you can use FX forwards to convert your JPY cashflows to USD but it is more common in practice to use a cross-currency swap for this purpose. Indeed, the advantage of the latter is that it ...
Marcino's user avatar
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6 votes
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Custom Bond Index Construction

As @noob2 pointed out, a Laspeyeres type index is the way to go, so I'll focus on other parts of your question. Nearly all bond indices are rule-based and rebalanced monthly. At the end of each month,...
Helin's user avatar
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6 votes
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A very simple question about convexity of a bond

The chart you posted does not give a correct visual representaion of convexity . Convexity is not $\frac{\partial^2 P}{\partial y^2}$ but $\frac{1}{P}\frac{\partial^2 P}{\partial y^2}$. So you have to ...
nbbo2's user avatar
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6 votes
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YTM of "very-seasoned" bond issues

There is a liquidity premium between on-the-run treasury issues and off-the-run issues with similar characteristics. This is why when building a yield curve, typically on-the-run issues are used to ...
Helin's user avatar
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6 votes
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If I have the present value of an amortizing bond's cashflows, how do I figure out price?

Bullet bond prices are quoted as a percentage of face value (par). For most amortizing bonds that have already amortized part of the initial principal (face value), the price is a percentage of the ...
Dimitri Vulis's user avatar
6 votes
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Are risk-free-rate bonds and cash fungible?

First of all your statement is not quite correct. If you receive cash as collateral, you have to pay me interest at whatever rate we have agreed to (probably Fed Funds). If you receive bonds as ...
dm63's user avatar
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6 votes
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Parameters in Nelson-Siegel model and Nelson-Siegel-Svensson model

The Nelson-Siegel model has four parameters: $\beta_0$, $\beta_1$, $\beta_2$, and $\lambda$. These parameters have the following restrictions: $\beta_0$, $\beta_1$ and $\beta_2$ can be any real ...
Hans-Peter Schrei's user avatar
6 votes

Does the rolling of bond payments from non-business days to the next or previous business day affect the calculation of accrued interest and YTM?

It all depends on the individual bond/loan. Read the bond prospectus. Fixed $C\%$ per year, coupon frequency $n$, usually means exactly $C/n$ regular coupons. The daycounting convention is used if the ...
Dimitri Vulis's user avatar
5 votes

How to calculate US treasury total return from yield?

Assume you have the time series of 10-year Treasury constant-maturity yield $\{y_t\}$ from FRED (here), you can calculate the total return $R_t$ from $t$ to $t+\Delta t$ as following. Define $$ \text{...
Steve Lihn's user avatar
5 votes

Investment Grade Bond vs Junk Bond, whose duration is larger?

There are different measures and interpretations of duration. One, as has been pointed out already, has a formula weighting coupons and final contractual cashflow. Other definitions of duration take a ...
horseless's user avatar
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5 votes
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Default Probability Implied in Bond Prices?

Assume : $R$ a recovery rate, a continuous payment a flat intensity $\lambda$ i.e $$\mathbb{P}(\tau>t)=e^{-\lambda t}$$ a flat discount rate $r$ With bonds prices Assuming JPM bond pays a coupon ...
M. Jeunesse's user avatar
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5 votes

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

The answer is NO, with very few exceptions There might be bonds with negative coupon(s), and the Bloomberg search even finds some, but there are plenty of reasons why negative coupons are impractical....
vanguard2k's user avatar
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5 votes
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How to Compute Dates for Bond

To compute the cash flow dates you need to know the maturity date, the tenor, the payment frequency, the business day convention and the holiday calendar. The cash flow dates step backward from the ...
Chris Taylor's user avatar
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