16 votes
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Deriving Interest Rates

There are two parts to your question and I'd like to answer them separately. Curve Construction On a daily basis, you can observe prices on a large variety of instruments, whose prices are driven by ...
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  • 10.9k
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"...
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  • 4,941
8 votes
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Why are multiple custom curves (swap) built for one desk?

Chapter 1: Goldilocks is ousted by the bears Once upon a time, the banks used a fixing called LIBOR as a measure of the risk-free interest rate. Then the big hairy crisis came along and ate all our ...
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  • 3,589
8 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)....
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6 votes
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Curve Euribor - Euribor 3M

It is incorrect to use 1m euribor or O/N euribor in a 6m Euribor forward curve. You should only use instruments based on 6M euribor, such as 1x7 FRA, 6x12 FRA or swaps v 6m Euribor, as you have done ...
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  • 304
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 ...
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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 ...
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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 ...
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3 votes

Deriving Interest Rates

I don't think they are implying that future interest rates are predictable. They may be speaking of implied forward rates as predictors of future rates or, generally, of the yield curve as an ...
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  • 3,240
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 ...
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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 ...
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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 ...
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3 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 ...
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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 $\...
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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 ...
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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: $$1 + d_i s_i = \prod_{j=1}^{n(i)}(1+ d_j r_j) \; , \quad \text{where} \quad d_i = \sum_{j=0}^{n(i)} d_j \;.$$ ...
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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 ...
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  • 5,603
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 ...
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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.
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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). ...
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  • 5,010
2 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 ...
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  • 5,285
2 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 ...
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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 ...
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  • 5,285
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 ...
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  • 5,333
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 ...
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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, ...
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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.
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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 ...
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  • 7,997
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 ...
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  • 372
1 vote
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Linear interpolation Discount factors

I don't recommend linear interpolation of DFs and the swap rates you are applying this to are either against 12M libor which is illiquid or you are not accounting for Quarterly or Semi-Annual floating ...
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