Hot answers tagged

19

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 ...


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: ...


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 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 ...


5

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', '...


5

RFR (risk free rate) is the current acronym ISDA, central banks and regulators are pursuing to signify and politicise the transition from IBOR, which has been dogged by rigging scandals. OIS (overnight index swap) is the acronym that has been associated with an unsecured overnight interbank cash lending rate fixing (OIS fixing) (with different calculation ...


5

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

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

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 ...


4

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 ...


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 ...


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

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

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

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) +...


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

Unfortunately, I cannot provide a definite answer. In the major currencies, the risk free rate working groups (US:ARRC, UK:RFRWG and the EU:RFRWG) try to promote new standards for the cash and derivatives markets. Further, there exist recommendations from various industry bodies how to incorporate (lagged) SONIA/SOFR(/ESTR) in new contracts. As an example, ...


3

I believe that this recent paper by Andrei Lyashenko and Fabio Mercurio is going to help you! For me it was completely amazing. It seems that we can just extend the Libor Market Model in a "simple" manner to cope with the new RFR because we can define an extended numeraire $P(t, T)$ for $t > T$ that recovers Ibor-like properties, such as the ...


3

I would use SONIA. That's the official RFR for the UK. See this BoE link: https://www.bankofengland.co.uk/markets/transition-to-sterling-risk-free-rates-from-libor


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 ...


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

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 $...


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

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 ...


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

By definition, the overnight rate is the rate at which banks lend to each other overnight. Overnight index swaps (OIS) allow banks to 'lock in' the cost of funding overnight for a specific term. They exchange a predetermined OIS rate for a payoff equal to the growth of the notional amount of money lent at the overnight rate for a specific term. The overnight ...


Only top voted, non community-wiki answers of a minimum length are eligible