19 votes

What does instantaneous forward mean?

1. Observable instruments, spot rates, and forward rates First remember that something observable means that you can observe/find the rate in the market by looking at traded rate instruments or ...
Pontus Hultkrantz's user avatar
13 votes
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What does instantaneous forward mean?

Given a forward rate, for example: $ F(t, T, T+\delta)$ The instantaneous forward rate $f(t,T)$ fixed in $t$ is the limit when $\delta \rightarrow 0$ of your forward rate. If the relation between ...
Yassine Q.'s user avatar
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

Martingale measure and replicating portfolio in Risk Neutral Pricing of Defaultable Zero-Coupon Bonds

The risk-neutral probability measure is defined in terms of its numeraire. For the usual risk-neutral probability measure the numeraire is the bank account, $\beta(t)$. If we have a tradeable asset $X(...
mmencke's user avatar
  • 835
5 votes
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Difference between ED futures and ZCB

In general futures contracts are leverage instruments. They never require the investment of principal. They do however require margin: you need to fund your account at a futures exchange so that they ...
Attack68's user avatar
  • 9,929
5 votes

Estimating a Yield Curve in a country without Bond Stripping

You do not need zero rates to estimate a parametric model of the yield curve, such as Nelson-Siegel. Suppose for instance that you have a cross-section of bond prices. Then: For given parameters for ...
Enrico Schumann's user avatar
5 votes

Difference between FRA and a zero coupon swap

A forward rate agreement is an agreement to exchange a fixed for a floating rate over one period, with the payment being made at the start of the period. A zero coupon swap (with both legs paid at ...
Chris Taylor's user avatar
  • 5,901
4 votes
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Why is it desirable to receive fixed on a zero coupon swap, and undesirable to pay fixed on a zero coupon swap?

I notice you mention GBP. This effect is particularly apparent there since a large number of insurance, pension and asset management companies like to trade ZCS. They do this because the forward risk ...
Attack68's user avatar
  • 9,929
4 votes
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Value of a 30 year bond using the Yield curve

The value of the bond would be the first case, because you have to discount each cashflow with the relevant spot rate for that payment date. Although, because rates are normally expressed in annual ...
David Duarte's user avatar
  • 5,795
4 votes
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Strange Market Data YTM for a Zero Coupon Bond

This bond has a slightly different calculation logic to your average zero coupon bond. Denote $t$ the trade date, $t_0$ the issue date, $T$ the maturity date and $P$ the traded price. You'll first ...
oronimbus's user avatar
  • 1,901
4 votes
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Zero Coupon Bonds for Structured Products

You just subtract the price of the option from 100 (assuming the structured note is issued at par), giving the price of the zero coupon bond. Then, you calculate the yield of the zero coupon bond ...
dm63's user avatar
  • 16.9k
3 votes
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zero coupon bond pricing formula using Hull White

Under the Hull-White interest rate model, the short rate $r_t$ satisfies a risk-neutral SDE of the form \begin{align*} dr_t = (\theta(t)-a r_t)dt+ \sigma dW_t. \end{align*} The price at time $t$ of ...
Gordon's user avatar
  • 21.1k
3 votes

yield concept for a short maturity zero coupon bond

(1) corresponds to simple interest and (2) to compound interest. For instance, Canadian treasury bills are based on simple interest (see Broverman's book Mathematics of investment and credit).
Bjørn Kjos-Hanssen's user avatar
3 votes
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Coupon bond pricing problem with reinvestment

In part (a) use discount rate $e^.07 -1 = .072508181$ to get the right answer. For part (b) I am just giving you hint: Calculate bond price at the end of 1st year and 2nd year in the same way as ...
Neeraj's user avatar
  • 2,228
3 votes
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What techniques can be used to get the missing maturities from the CMT yields?

The CMT yields published by the Fed/US Treasury are par yields calculated using a cubic spline model. In other words, these are the yields to maturity as well as coupon rates on bonds whose theoretic ...
Helin's user avatar
  • 11.6k
3 votes

Quantlib: convert par swap rates to zero rates back and forth

Maybe you should start with a simple example, because you have so many moving parts that it's hard to figure out where the difference is. Most likely some different convention between your helpers and ...
David Duarte's user avatar
  • 5,795
3 votes
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Zero Rates for Deposits using Quantlib Python

I just changed the last part of your code and removed the bonds as they don't affect the first rates. The problem is that your zero rates have 2 extra days in relation to your deposits. You can change ...
David Duarte's user avatar
  • 5,795
2 votes
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How to show that the exponential Vasicek model is not an affine term-structure model?

Here is a general proof for all parameters in an open domain. $$dr = adt+bdW:=r\big(k(\theta-x)+\frac12\sigma^2\big)dt+\sigma rdW.$$ Let $$u(r(s),s):=e^{-\int_t^sr}B(r(s),s,T)=:\phi(s) B.$$ Then $$u(...
Hans's user avatar
  • 2,766
2 votes

When estimating P/L through greeks based on zero rate curves, does it contain time (theta) PNL?

Yes. The time p/l can be found by leaving all the inputs the same and allowing a day to pass. I prefer not to call it theta - that term is used to describe the time decay of options.
dm63's user avatar
  • 16.9k
2 votes

Can we derive 5 year zero coupon interest rate by using 1, 2 and 3 year zero coupon interest rate?

Who knows what the 5 year zero coupon rate is in that case, there could be an event 4.5 years out that will have serious interest rate implications that we don't know about. The only thing you can do ...
user2183336's user avatar
2 votes
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Vasicek Model, zero coupon bond question

Let $P(t,T)$ denote the time $t$ price of a zero-coupon bond (with unit face value) maturing at time $T$. Firstly, recall that for every $s\leq t$, we have \begin{align*} r_t = r_s e^{-\kappa(t-s)}+\...
Kevin's user avatar
  • 15.7k
2 votes
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How to calculate zero-coupon curve for Italian BTPs?

Many countries issue sovereign debt denominated in EUR. The common (but not universal) methodology is to treat only German sovereign debt as credit risk free, and all other countries as credit-risky. ...
Dimitri Vulis's user avatar
2 votes
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How to calculate the discount factors for two deposits in an interest rate curve

I found the answer after extensive digging in this forum, particularly what gave me the answer was the following post How does bloomberg calculate the discount rate from EUR estr curve? [closed]. Thus,...
Xiarpedia's user avatar
  • 137
2 votes

Rationale for issuing zero coupon bonds

The rationale is that the bond issuer gets capital upfront with no periodic payment required. So depending on the use of the proceeds, it may be more beneficial to receive a lower amount upfront in ...
D Stanley's user avatar
  • 1,321
2 votes
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Rationale for issuing zero coupon bonds

The stripping does not affect the present value (to a first approximation), if the firm issued a 1 million coupon bond, and it was stripped, the value received from selling the coupon-strip plus the ...
nbbo2's user avatar
  • 11.1k
2 votes

How does Bloomberg use the OIS curve to get the zero rates?

If you take screenshots, it helps if you do not cut off the important parts - or at least mention where the screenshot is from. Usually, ICVS is where one would ...
AKdemy's user avatar
  • 9,029
2 votes
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QuantLib: How to price or construct a zero coupon swap using Quantlib

I am running QuantLib version 1.30 and it works for me. Here is the code I compiled to investigate as unfortunately yours did not work for me ...
Xiarpedia's user avatar
  • 137
2 votes

Stochastic representation of a zero-coupon bond

$B(t, T)$ (and in general conditional expectations of random variables, under the usual conditions) are not deterministic but $F(t)$ measurable. $r(t)$ here is also $F(t)$ measurable. One intuitive ...
Rylan's user avatar
  • 410
1 vote

Zero-coupon Loan Investment

Safest would be FRA to lock the interest rates. Thanks
Srinivasan J's user avatar
1 vote

Proving that YTM > Current Yield on Discount Bond

I think this proof works: Denote the annual yield of a bond as follows: $$ y(-Price, Annual Coupon Amount, Redemption Amount). $$ Then for example, $y(-100, C , 100) = C$ Which simply says that ...
dm63's user avatar
  • 16.9k

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