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12 votes

Swap curve construction

I think your question can be split into two parts: (i) how to value a swap mathematically and (ii) how swaps actually work as a traded product. Part (i): As noob2 pointed out, "theoretically"...
Jan Stuller's user avatar
  • 6,118
10 votes
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SOFR Discount Curve Construction in Nov 2021

Fixed vs SOFR swaps for longer maturities are very liquid, since the interbank market trades these directly now, and these are the best instruments to construct the long end of the curve (2yr to 50yr)....
dm63's user avatar
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5 votes
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When we try to build curves, why we need fixings?

When pricing a swap with at least one floating leg referencing some index, if the fixing date of the index is before evaluation date, but the floating coupon period start date, end date, and payment ...
ir7's user avatar
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5 votes
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Swap curve construction

I think I understand the question, but maybe not. In USD market, the most liquid IR swaps have floating leg reset quarterly from 3Mo LIBOR. (The fixed leg is semi-annual. Ths will change when LIBOR is ...
Dimitri Vulis's user avatar
5 votes
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What curve are you shifting when you calculate DV01 for a swap?

Let's step back and look at the reason for making a DV01 calculation first before answering the question; The reason for making a DV01 calculation is to quantify what market movements has impact on ...
Fred's user avatar
  • 86
4 votes

Interpolation and extrapolation of Discount factors

Be careful with various naive smooth interpolations of discount factors that are easy to screw up and may lead to unrealistic rates between the nodes. But your choice depends on your planed usage. If ...
Dimitri Vulis's user avatar
3 votes
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Curve building dates overlapping impact on discount factor

There is no overlapping, the first instrument is tied to the LIBOR rate starting at $25/10/2019$, the second one is tied to the LIBOR Rate at $27/04/2020$. For the sake of clarity, let assume that ...
Canardini's user avatar
  • 553
3 votes

Dual discounted forward curve

Which currency are you looking at ? Say that your 1y swap would have yearly fixed payments vs 3M floating payments. Your 1.5y swap would probably have: a fixed payment 6m after effective date and ...
Bozothegrey's user avatar
3 votes

Current discount rate of Hull White One-Factor Monte Carlo Simulation

The average of simulated discount factors from the Hull-White model and market discount factor are the same in theory but very similar in the simulation due to numerical error. I draw one figure ...
sh lee's user avatar
  • 41
3 votes

Using Discount Rates and Zero rate curve from Bloomberg in Quantlib

You should be aware that Bloomberg doesn't have a yield curve. Bloomberg has market prices of the instruments to build a yield curve and the result will depend on the particular configuration for your ...
David Duarte's user avatar
  • 5,825
3 votes
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Constant continuous forward rate interpolation

Assume the (annualised, continuously compounded) forward rate between two nodes, say $t_{10}$ and $t_{12}$, is constant, say $ f_{10,12}$, then the discount factors of the two consecutive knots will ...
Magic is in the chain's user avatar
2 votes

Calculating the short rate from the discount curve

For simplicity, let's say that your time $0.003$ equals 1 day, and your second pillar (probably $0.083$ instead of $0.00833$) equals 1 week. What you do: Approximate the short rate with the 1-day ...
Kermittfrog's user avatar
  • 6,663
2 votes

How to Validate and Test a Discount curve (i.e. SOFR, LIBOR, ESTR)

A first step would obvisouly be to check if the curve you built replicates the input instruments. A second step might be to check the forwards to see if there is irregular behaviour around the curve ...
David Duarte's user avatar
  • 5,825
2 votes

Curve building dates overlapping impact on discount factor

Your rates do not overlap. You have a 6M (185/360) rate of 5%. And a forward rate agreement where the 5.2% rate starts at the end of your initial contract (4/27/20) for a period of 6M (183/360). ...
AlRacoon's user avatar
  • 6,612
2 votes

Discount factor

You have $\beta_1=\frac{1}{(1+r)^n}\frac{1}{(1+r)^\theta}$ and $\beta_2=\frac{1}{(1+r)^n}\frac{1}{(1+\theta r)}$. Both are equal when $\theta=1$. If you consider simple interest then go for $\...
Pandaaaaaaa's user avatar
2 votes

What curve are you shifting when you calculate DV01 for a swap?

The short answer is that there's no consensus. A popular method is to shock each input instrument by 1 bp (i.e., change the futures rate by 1bp, the swap rates by 1bp, OIS rates by 1bp, etc.), rebuild ...
Helin's user avatar
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2 votes
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OIS Discount Factor Bootstrapping - Do we assume simple interest?

An OIS interest rate swap rate with annual-annual freq is determined under one year by: $$1 + d_i s_i = \prod_{j=1}^{n(i)}(1+ d_j r_j) \; , \quad \text{where} \quad d_i = \sum_{j=0}^{n(i)} d_j \;.$$ ...
Attack68's user avatar
  • 10.5k
2 votes

Characteristics of a Discount Curve

By no arbitrage, market participants need to agree on the values of the discount factor, even if they are using different conventions (day count, compounding period) to convert the discount factor ...
Chris Taylor's user avatar
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2 votes

How to use USD OIS discounting for local currency uncollateralised swaps?

Suppose you wanted to value a 5Y EUR IRS with a USD cash collateralised curve this is the broad process: Get the 5Y EUR 3M / OIS basis, say this is 10bps: This establishes the discounting basis in ...
Attack68's user avatar
  • 10.5k
2 votes

Discount Factors to Zero Rates

Equation 2 gives the annual zero rate for all tenors. In practice, people sometimes quote rates f less than one year using Equation 1, but in general , equation 2 is used.
dm63's user avatar
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2 votes
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Discount factors curve shapes

If the input data is correct and there aren't any calculation errors, then the discount curve should be decreasing (just like your second chart). Using a no-arbitrage argument, Hagan & West (2007) ...
oronimbus's user avatar
  • 1,896
2 votes

Quantlib interpolated zero rates not as expected

Found the answer eventually by manual calculation. Even if the zero curve is an annual 365F compounded curve, Quantlib works in continuous terms. Therefore the dates between the pillar dates use ...
Douglas Gagiano's user avatar
2 votes

swap curve calibration with interpolation using newton-like method

You cannot solve for 4 degrees of freedom with two fixed parameters. That is an underspecified curve and it will (even though solvable, with infinite solutions) lead to chaotic behaviour within your ...
Attack68's user avatar
  • 10.5k
1 vote

Swaps curve building with Deposit, FRAs & Swaps

You can find examples in the open source QuantLib library easily enough, that can be found here: https://www.quantlib.org/ For the book reference I think a good example of a modern text is: https://...
BrownianBread's user avatar
1 vote

Basis Swap Dual Curve Calibration

Actually it is not just the long end of the swap curve it is any part of the curve that needs some form of basis swaps to be calibrated. A set of curves in any currency usually encompasses the ...
Attack68's user avatar
  • 10.5k
1 vote

Curve building for a swap

Try Howard Corb's book ["Interest Rate Swaps and Other Derivatives", Columbia Business School Publishing, 2012]. And your 2y rate looks odd which should be intuitively obvious - simple arithmetic ...
user42108's user avatar
  • 2,262
1 vote

Correct Discount Curve for Exchange Traded (Centrally Cleared) Products

if you are asking how CME collateral is discounted, then you have two considerations: What does the CME give you on your USD cash? That's simple, it's OIS. You don't get the interest immediately, ...
JoshK's user avatar
  • 2,613
1 vote
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Correct Discount Curve for Exchange Traded (Centrally Cleared) Products

This question Setting the r in put-call parity? shows the details are subtle and nuanced, but the answer is to use the rate paid on the collateral or margin.
Jared's user avatar
  • 745
1 vote

Convexity in interest rate curve bootstrapping

Generally speaking there are more inputs that are required to precisely specify the multicurve structure, and they are potentially more important. For example consider constructing a EUR interest ...
Attack68's user avatar
  • 10.5k
1 vote

Bootstrap discounted cash flow

It's difficult to see your screenshot. But I think you should just follow some real examples online instead of having people find out what's wrong on your side. This is an excel example, go play with ...
Hui's user avatar
  • 402

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