# Tag Info

## Hot answers tagged ois-discounting

12

It comes down to the definition of LIBOR: London Interbank Offer Rate -> Every business day, a panel of large banks are asked by the BBA[*] (British Bankers Association) at what rate they would lend cash (unsecured) in a certain currency to another bank of that panel for a certain maturity, and that for a range of currencies and maturities. e.g. Currency: ...

11

There are two parts to this question: 1) Is OIS a good risk-free proxy? and 2) Why is OIS used to discount cash flows of derivatives. First, overnight indexed swaps, in the US, are indexed to the Fed funds effective rate, which in turn tracks the Fed funds target rate. The Fed Fund target rate is directly set by the Federal Reserve, while the Fed Funds ...

9

Collateral posted in currency XYZ is remunerated at $\text{OIS}_{\text{XYZ}}$, which translates, using the XYZUSD basis, into a synthetic USD rate $\text{OIS}_{\text{USD}}^{\text{XYZ}} = \text{OIS}_{\text{USD}} + \text{basis}_{\text{XYZUSD}}$. If you post collateral you want to choose the currency XYZ that has the highest equivalent synthetic USD rate, and ...

9

I reproduce the Ametrano-Bianchetti paper on dual-curve bootstrapping in Python with QuantLib in a chapter of the QuantLib Python Cookbook. (Note: I'm not sure what the etiquette is about plugging one's own for-sale book. Moderators, please let me know if that's out of line.) That includes both OIS and LIBOR bootstrapping with different tenors, and it's ...

8

The market is using SOFR discounting for all sorts of quotations already (not FF). For example, swaption vol is quoted with SOFR discounting, CME and LCH moved to SOFR PAI and discounting on Oct. 16 2020 on new AND legacy swaps. For EUR cleared, major CCPs did this since July 27 2020. The market switched to discounting with the relevant RFR rates on the ...

7

The problem here is that your market is not arbitrage-free: JPY OIS = 10% per day, flat USD OIS = 0% per day, flat USDJPY spot = 100 USDJPY Forward for tomorrow = 100 A quick sense check is that, if you have an interest rate differential, you cannot have the FX forward equal to the spot FX. I would take advantage of the arbitrage as follows: I ...

7

OIS Discounting: First note that we already discount using USD OIS rates, but these would be OIS rates constructed from USD OIS Swaps linked to the Effective Federal Funds Rate (EFFR). In other words, the floating rate of the OIS swap would be based on the EFFR rate, whilst the fixed leg would be the normal fixed leg we are used to seeing in swaps. So the ...

6

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 in your second example. The actual 6m euribor fixing itself can be thought of as a 0x6 FRA out of spot. Before the financial crisis basis between different ...

6

"CSA discounting" does not give you a lot of information: it just means the collateralisation of the trade follows the rules agreed upon between both parties in the Credit Support Annex. But you don't know what those rules are so you would not necessarily be discounting your transaction's cashflows at OIS. I have heard people use "CSA discounting" ...

5

The ois curves were (and still are) primarily build from adding together (a) interest rate swap rates and (b) Fed Funds/Libor basis swaps. For example, if 10yr swaps are 2.0%, and 10yr fF/libor is -35bp, the 10yr ois is 1.65%. The basis swaps have been liquid for decades, so this calculation has always been possible. However, participants didn't ...

4

An OIS, or Overnight Index Swap, is an interest rate swap whose floating leg payments are calculated as a geometric average of the daily fixings of some underlying O/N or T/N index (these indices are generally volume-weighted averages of reported daily transactions). The annualized floating leg rate is defined as  c_T^{float} = \frac{\prod^{s+T}_{t=s}{(1+...

4

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 profile of a ZCS more accurately reflects the increasing notional of their portfolio and avoids them having to deal with interim coupon payments. They almost ...

4

It's done in 2 steps: 1) First you bootstrap OIS curve independently from Libor curve, get OIS discount factors 2) Then use these to bootstrap Libor curve (using OIS discount factors instead of Libor ones,Libor used for projections only)

4

SOFR was never meant to take USD LIBOR's role, as USD LIBOR reflects unsecured funding (and is credit sensitive). An index like BSBY, on the other hand, can. BoA just started issuing FRNs linked to it. A BSBY-SOFR basis swap was also struck a month ago.

3

Collateralised means that when the IRS is negatively valued (i.e. a liability) for one of the counterparties then they post collateral to the other respective counterparty (i.e. the asset holder) to protect them against default of the liability owner. Collateral comes in many forms. The 'gold standard' is cash remunerated at the OIS rate, but it could be ...

3

An uncollateralized swap transaction should be valued at its own funding rate, which in practice means the bank unsecured funding rate, for instance approximated as 3M Libor. Alternatively use the OIS curve for the base valuation and mark the difference between 3M Libor discounting and OIS discounting as FVA.

3

There are many resources describing how to build a trinomial tree for the Hull & White model (for instance http://www-2.rotman.utoronto.ca/~hull/downloadablepublications/TreeBuilding.pdf), and finite differences schemes are popular as well. These apply to the single curve case. To deal with the multi curve case while keeping everything 1 factor, the ...

3

I believe that Eonia can still be used for discounting derivatives after 2020. Article: https://www.risk.net/derivatives/5848051/esma-eonia-can-be-used-in-csas-after-2020 If it becomes illiquid, counterparties can repaper csa's to Ester. That will cause an economic effect if there is a non zero Eonia/Ester basis.

3

Modern curve building methodologies, certainly implemented in top tier fixed income trading houses, use a simultaneous non-linear solver to construct all curves at once. Essentially the procedure is: a) define a set of instruments whose prices are known and will be calibrated (arbitrarily different in different currencies but of sufficient coverage to ...

3

OIS discounting is a subset of CSA discounting... technically they are not the same thing. CSA actually stands for Credit Support Annex, which is an Annex to your ISDA agreement with your trading counterpart that governs how your derivative trade is collaterallized (or not). Without the CSA agreement, the trade will get priced at the highest level of ...

3

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 another fixed payment 18m after effective date regular quarterly floating payments Your curve was built with 1y and 2y swaps, nothing in the middle ? Then yes, ...

3

First of all, it seems that you are solely concerned about the Funding Valuation Adjustment (FVA) here, and not CVA; Sovereigns have credit risk which should also be valued here given they would not be posting any collateral as mitigant when the market moves in your favour. But let's focus on FVA: It is important to think about FVA (and all other VAs also) ...

3

you have a missing element in your data - you need to take into account xccy basis. when you do so, then you would get the same valuation in both methods. the key is to remember that since your payoff of 100JPY is collateralised in usd, it effectively needs to be thought of as if your payoff is cash settled in usd.

3

To expand on Marcino's correct appraisal of the matter: arbitrage was introduced with the 4 pieces of market data. i.e. JPY OIS = 10% per day, flat USD OIS = 0% per day, flat USDJPY spot = 100 USDJPY Forward for tomorrow = 100 are not consistent with no-arbitrage. Discounting is driven by how the trade is funded. e.g. if there is a collateral agreement ...

3

To trade a swap counterparties must have an ISDA Master Agreement drawn up and signed between themselves. If collateral is to be exchanged that agreement will also contain a section called a CSA: a Credit Support Annex. That documentation defines the types of collateral available to post as the liability holder: and the banks choice of discount curve will ...

3

A plethora of instruments, a menagerie of curves Different instruments are traded in different ways, and relate to a collection of curves. Floating rate instruments depend on some index in order to calculate the cashflows, and so trading instruments which depend on different indices is implicitly trading the expectations of those indices in the future. Fed ...

3

For both cleared and OTC swaps you need to post margin. If you are delivering cash then you will receive OIS in generally in either case. As OTC trades are bespoke you might have a different agreement with your particular counterparty - but that would be unusual. The main advantage of a central clearer is the recycling of margin. If I receive 5y from ...

3

I try to keep your enumerated structure yet address the points you edited into the question: (i) I only know of USD OIS referencing the EFFR and the SOFR (ii) My perception is that EFFR als float leg reference is far more liquid at the moment (compare the traded volumes, e.g. https://apps.newyorkfed.org/markets/autorates/fed%20funds vs. https://www.cmegroup....

3

See 'Collateral Posting and Choice of Collateral Currency' (Theorem 1, in particular) and 'A Note on Construction of Multiple Swap Curves with and without collateral' by Fujii et. al., and also 'Cooking with Collateral' by Piterbarg (the basics of unsecured and collateralized cases for forward contracts in general are covered in Piterbarg's paper 'Funding ...

3

OIS is overnight index swap: fixed float swap with floating rate based on some overnight rate Traditionally (some examples): EONIA (EUR) Fed Funds (USD) RFR: New Risk free rates (secured overnight funding rate): ESTA (EUR) SOFR (USD) In terms of what these curves look like: Reference is the underlying OIS. The curve uses instruments (Futures, Swaps) to ...

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