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17

The OIS is not the secured (collateralised) lending rate. It represents the cost of repeated overnight unsecured lending over periods of up to two weeks (sometimes more). Because it is based on overnight lending, it is assumed to have a lower credit risk than longer term interbank loans based on say 1M, 2M or 3M Libor and this is what drivers the OIS-Libor ...


11

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: ...


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 ...


6

The OIS rate is the market rate that is most dependent on the Central Bank Deposit Rate (i use that as a broad term since it is called something slightly different across currencies but principle is the same). The transmission mechanism (that is of central concern to Central Banks) therefore impacts this rate more than any other with high correlation. OIS ...


4

You can leave it out during the bootstrap of the curve. In that context, the index is only used to ask for its conventions. Later, if you want to forecast index fixings, you can initialize a handle with the curve you bootstrapped and pass it to the index.


4

So you can get depo and swap rates from markit daily, at links like this: http://www.markit.com/news/InterestRates_<cncy>_<yyyymmdd>.zip i.e. http://www.markit.com/news/InterestRates_USD_20170105.zip and there's a spec for it here - though that's from 2009 so may be out of date, maybe you can find a more up to date one someone on their site, ...


4

No its not the Fed Funds Rate, or the Bank of England Base Rate or the ECB Refi Rate, it is the forecast, published OIS fixing index determined by the relevant authority in the currency. I.e in USD it is FFOIS, in GBP it is SONIA and in EUR it is EONIA. (Actually these names may in fact be transitioning to other in index definitions now, especially in EUR) ...


4

I see several problems that might explain those differences: The frequency of the fixed leg on a EONIA swap is Annual and not semi The deposit facility rate is not part of the EONIA curve. Use the Eonia rate. You are calculating rates with simple compounding and not annual compounding Here is an alternative implementation: tenors = [ '1D', '1W', '2W', '...


4

Given a initial discount bond $P^M(0, T)$ curve, the expression for $\theta(t)$ in the Hull White Short Rate model is a know result given by: $$ \theta(t) = \frac{1}{\kappa} \cdot f'(0, t) + f(0, t) + \frac{1}{2} \cdot \left( \frac{\sigma}{\kappa} \right)^2 \cdot \left( 1 - e^{-2 \kappa t} \right). $$ I have used a notation where the spot rate dynamics is ...


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

A curve is used to do calculations (e.g. discounting of cash flows) as of a given trade date. Bootstrapping a single curve for two different trade dates does not make sense. With the first set of data you should bootstrap an OIS curve for the 2017-02-09 trade date, with the second set of data you should bootstrap an OIS curve for the 2017-02-10 trade date.


3

As far as I know, it's a market convention. The two products, namely OIS swap (fixed vs floating) and Fed Fund Libor basis swap, are developed differently, so they follow different conventions. My only guess is that it's because of the difference in maturity and period: OIS swap is typically a single-period swap (i.e. zero coupon swap) on short-end (< 2 ...


3

The fixed leg of the OIS is an unsecured rate that is very close to Risk Free Rate (RFR) because of the combination of several reasons: it is akin to a money market term deposit rate swapped against overnight deposit rates, compounded geometrically over the swap lifespan, so a net expected present value at inception of zero (Feynman-Kac) should reflect ...


3

Secured and unsecured refers to lending. However OIS is a swap based on FF, not a loan. It is a different animal. So OIS is a derivative, or a bet, based on the average of future (unsecured) FF rates over a period.. For example my name is Noob Rademayer, I am not a bank so I can't lend or borrow FF in the interbank market, but I can bet on the rate at ...


3

Your method assumes you can borrow or lend at OIS in both currencies, but in practice you cannot. That's why there is a current basis swap market , where you lend at OIS in one currency versus borrowing at OIS + X in the other currency , where X is not zero. That is the missing piece of your calculation. Why, you may ask , is X not zero , as many ...


2

I agree with dm63 in that cross-currency swap (CCS) is essential for building FX forward curve. Let me add/correct two things: FX curve < 1 year can be backed out by FX forward contract. CCS is typically longer than 1 year, so you need it for the long-end of the FX curve. CCS swap is typically exchange of 3m USD LIBOR vs 3m FOREIGN LIBOR (or equivalent) +...


2

Not all overnight indexes were given a specific class. As a workaround, you can create an instance of the OvernightIndex class and pass it the relevant parameters (fixing calendar, day counter etc.). E.g., if there wasn't an EONIA class already, you could build an instance of it as: index = OvernightIndex("EONIA", 0, EURCurrency(), ...


2

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 the local (EUR) currency. Now get the 5Y EUR/USD Cross-currency basis, say this is EUR 3M-IBOR - 40bps: This establishes your link to dollars. Now get the 5Y ...


2

A corporate that has an ISDA master agreement to trade Interest Rate Rwaps (IRSs) with a bank will undoubtedly be capable of also trading Overnight Indexed Swaps (OISs), as will any type of counterparty for that matter. A corporate whose loan is tied to floating LIBOR will hedge using an IRS to convert to fixed. Hedging with an OIS would introduce ...


2

When you say the Black Scholes formula for currency options, I assume you are referring to the Garman-Kohlhagen formula described here. Note that this formula is based on the interest rate differential $r_d - r_f$, which essentially captures the forward premium. An even more explicit way to see this is to use the Black Model described here. Using this ...


2

Depends on which OIS you are referring to. For EUR OIS Swaps, the EONIA Swap rate is calculated via the usual compounding formula (notice that in the example below, the rate $r_i$ is updated every night): Example is shown here: For USD OIS Swaps, the link to Investopedia that you shared is correct: it is pretty much the same formula as for the EUR swap ...


2

I think a little clarity is needed here. A swap means exchanging A for B. Swaps trade on anything and everything. You can trade IOS/BBA Muni swaps, you can trade a swap linked to the gold forward levels versus Euribor 9 month fixings. Whatever you want. You have a mistake above. OIS swaps are not OIS vs Libor. Generally, when someone trades an ...


1

iii) The OpenGamma piece on IRS market conventions might help. https://quant.opengamma.io/Interest-Rate-Instruments-and-Market-Conventions.pdf [EDIT or USSO2 BGN Curncy DES, for e.g., which provides details on the conventions for each leg] iv) Yes, SOFR/FF basis swaps trade OTC. Or you can trade SOFR futures vs. Fed Funds futures.


1

It's difficult to repo more than 3 months. Essentially a bank would be locking up their balance sheet over this time period which is difficult in this post crisis regulatory environment. So traders use OIS which is relatively more liquid to lock in financing by paying fixed on term OIS for example. That's why repo trades at a positive spread to OIS, while ...


1

To construct a PiecewiseLogCubicDiscount object with a fixed reference date, please use the following constructor: PiecewiseLogCubicDiscount(reference_date, helpers, day_counter, ...) Taking your example: eonia_curve = PiecewiseLogCubicDiscount(Date(15, December, 2012), helpers, Actual365Fixed()) eonia_curve.referenceDate() # result: Date(15,12,2012) How ...


1

An OIS interest rate swap rate with annual-annual freq is determined under one year by: $$1 + d_i s_i = \prod_{j=1}^{n(i)}(1+ d_j r_j) \; , \quad \text{where} \quad d_i = \sum_{j=0}^{n(i)} d_j \;.$$ Each $r_j$ is a forecast overnight OIS rate which as you can see are compounded in the floating side. Therefore a discount factor in the future, for maturity $...


1

I think I've found the answer in another forum (which fits my initial intuition). So just to share: FRA-OIS is traded via swap. So if you think the spread would widen you pay on the swap. So you would pay OIS + Spread and receive Libor. https://www.wallstreetoasis.com/forums/tech-questions-on-eurodollar-and-fed-funds-futures-hedging


1

Suppose the currency is EUR. Taking liberty with conventions, to give you the picture, the floating leg of an OIS swap of maturity $n$ years ("$n$Y") pays every year the compounded OIS rate on all business days on the past year period whereas its fixed leg pays every year a fixed rate $K$. Now the given OIS swap rate quoted on the market is the $K$ such that ...


1

CME (as of now) also publishes it. Folder: ftp://ftp.cmegroup.com/irs/ file name: irs_close_quotes_OISUSD_YYYYMMDD.csv, e.g. 20200717 CURVE_NAME,TENOR,RATE USD LIBOR-OIS DISCOUNT CURVE,2 Years,0.0033500000 USD LIBOR-OIS DISCOUNT CURVE,3 Years,0.2200000000 USD LIBOR-OIS DISCOUNT CURVE,5 Years,0.2212830000 USD LIBOR-OIS DISCOUNT CURVE,10 Years,0.2172810000 ...


1

Fed funds futures are nearly sufficient. You need to know the precise way in which Fed Fund futures are calculated for settlement purposes - e.g. that it is an arithmetic average of the fed funds fixings where a fixing is weighted by the number of days between the fix and the next fix (i.e. a Friday fix will be weighted 3 times if there is no holiday on ...


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