Interest rate swap

General description An interest rate swap's (IRS's) effective description is a derivative contract, agreed between two counterparties, which specifies the nature of an exchange of payments benchmarked against an interest rate index. The most common IRS is a fixed for floating swap, whereby one party will make payments to the other based on an initially agreed fixed rate of interest, to receive back payments based on a floating interest rate index. Each of these series of payments is termed a "leg", so a typical IRS has both a fixed and a floating leg. The floating index is commonly an Secured Overnight Financing Rate (SOFR) To completely determine any IRS a number of parameters must be specified for each leg: • the notional principal amount (or varying notional schedule); • the start and end dates, value-, trade- and settlement dates, and date scheduling (date rolling); • the fixed rate (i.e. "swap rate", sometimes quoted as a "swap spread" over a benchmark); • the chosen floating interest rate index tenor; • the day count conventions for interest calculations. Each currency has its own standard market conventions regarding the frequency of payments, the day count conventions and the end-of-month rule. Extended description As OTC instruments, interest rate swaps (IRSs) can be customised in a number of ways and can be structured to meet the specific needs of the counterparties. For example: payment dates could be irregular, the notional of the swap could be amortized over time, reset dates (or fixing dates) of the floating rate could be irregular, mandatory break clauses may be inserted into the contract, etc. A common form of customisation is often present in new issue swaps where the fixed leg cashflows are designed to replicate those cashflows received as the coupons on a purchased bond. The interbank market, however, only has a few standardised types. There is no consensus on the scope of naming convention for different types of IRS. Even a wide description of IRS contracts only includes those whose legs are denominated in the same currency. It is generally accepted that swaps of similar nature whose legs are denominated in different currencies are called cross currency basis swaps. Swaps which are determined on a floating rate index in one currency but whose payments are denominated in another currency are called Quantos. In traditional interest rate derivative terminology an IRS is a fixed leg versus floating leg derivative contract referencing an IBOR as the floating leg. If the floating leg is redefined to be an overnight index, such as EONIA, SONIA, FFOIS, etc. then this type of swap is generally referred to as an overnight indexed swap (OIS). Some financial literature may classify OISs as a subset of IRSs and other literature may recognise a distinct separation. Fixed leg versus fixed leg swaps are rare, and generally constitute a form of specialised loan agreement. Float leg versus float leg swaps are much more common. These are typically termed (single currency) basis swaps (SBSs). The legs on SBSs will necessarily be different interest indexes, such as 1M LIBOR, 3M LIBOR, 6M LIBOR, SONIA, etc. The pricing of these swaps requires a spread often quoted in basis points to be added to one of the floating legs in order to satisfy value equivalence. Uses Interest rate swaps are used to hedge against or speculate on changes in interest rates. They are also used to manage cashflows by converting floating to fixed interest payments, or vice versa. Interest rate swaps are also used speculatively by hedge funds or other investors who expect a change in interest rates or the relationships between them. Traditionally, fixed income investors who expected rates to fall would purchase cash bonds, whose value increased as rates fell. Today, investors with a similar view could enter a floating-for-fixed interest rate swap; as rates fall, investors would pay a lower floating rate in exchange for the same fixed rate. Interest rate swaps are also popular for the arbitrage opportunities they provide. Varying levels of creditworthiness means that there is often a positive quality spread differential that allows both parties to benefit from an interest rate swap. The interest rate swap market in USD is closely linked to the Eurodollar futures market which trades among others at the Chicago Mercantile Exchange. ==Valuation and pricing==

IRSs are bespoke financial products whose customisation can include changes to payment dates, notional changes (such as those in amortised IRSs), accrual period adjustment and calculation convention changes (such as a day count convention of 30/360E to ACT/360 or ACT/365). A vanilla IRS is the term used for standardised IRSs. Typically these will have none of the above customisations, and instead exhibit constant notional throughout, implied payment and accrual dates and benchmark calculation conventions by currency. Regarding the curve build, see: the rate over the same period (the most liquid tenor in that market), and the IRSs are in turn discounted on the OIS curve, the problem entails a nonlinear system, where all curve points are solved at once, and specialized iterative methods are usually employed (see further following). The forecast-curves for other tenors can be solved in a "second stage", bootstrap-style, with discounting on the now-solved OIS curve. A CSA could allow for collateral, and hence interest payments on that collateral, in any currency. To accommodate this, banks include in their curve-set a USD discount-curve to be used for discounting trades which have USD collateral; this curve is sometimes called the (Dollar) "basis-curve". It is built by solving for observed (mark-to-market) cross-currency swap rates, where the local is swapped for USD LIBOR with USD collateral as underpin. The latest, pre-solved USD-LIBOR-curve is therefore an (external) element of the curve-set, and the basis-curve is then solved in the "third stage". Each currency's curve-set will thus include a local-currency discount-curve and its USD discounting basis-curve. As required, a third-currency discount curve — i.e. for local trades collateralized in a currency other than local or USD (or any other combination) — can then be constructed from the local-currency basis-curve and third-currency basis-curve, combined via an arbitrage relationship known here as "FX Forward Invariance". Various approaches to solving curves are possible. Modern methods tend to employ global optimizers with complete flexibility in the parameters that are solved relative to the calibrating instruments used to tune them. These optimizers will seek to minimize some objective function - here matching the observed instrument values - and this assumes that some interpolation mode has been configured for the curves; the approach ultimately employed may be a modification of Newton's method. Maturities corresponding to input instruments are referred to as "pillar points"; often, these are solved directly, while other spot rates are interpolated. (Then, once solved, all that need be stored are the pillar point rates and the interpolation rule.) Starting in 2021, LIBOR is being phased out, with replacements including other "market reference rates" (MRRs) such as SOFR and TONAR. (These MRRs are based on secured overnight funding transactions). With the coexistence of "old" and "new" rates in the market, multi-curve and OIS curve "management" is necessary, with changes required to incorporate new discounting and compounding conventions, while the underlying logic is unaffected; see. -->The complexities of modern curvesets mean that there may not be discount factors available for a specific index curve. These curves are known as 'forecast only' curves and only contain the information of a forecast index rate for any future date. Some designs constructed with a discount based methodology mean forecast -IBOR index rates are implied by the discount factors inherent to that curve: :r_j = \frac{1}{d_j} \left ( \frac{x_{j-1}}{x_j} - 1 \right ) where x_{i-1} and x_{i} are the start and end discount factors associated with the relevant forward curve of a particular index in a given currency. To price the mid-market or par rate, S of an IRS (defined by the value of fixed rate R that gives a net PV of zero), the above formula is re-arranged to: :S = \frac{\sum_{j=1}^{n_2}r_j d_j v_j}{ \sum_{i=1}^{n_1} d_i v_i} In the event old methodologies are applied the discount factors v_k can be replaced with the self discounted values x_k and the above reduces to: :S = \frac{x_0 - x_{n_2}}{ \sum_{i=1}^{n_1} d_i x_i} In both cases, the PV of a general swap can be expressed exactly with the following intuitive formula:P_\text{IRS} = N(R-S)A where A is the so-called Annuity factor A = \sum_{i=1}^{n_1} d_i v_i (or A = \sum_{i=1}^{n_1} d_i x_i for self-discounting). This shows that the PV of an IRS is roughly linear in the swap par rate (though small non-linearities arise from the co-dependency of the swap rate with the discount factors in the Annuity sum). ==Risks==

Interest rate swaps expose traders and institutions to various categories of financial risk: Funding risks because the value of the swap might deviate to become so negative that it is unaffordable and cannot be funded. Credit risks because the respective counterparty, for whom the value of the swap is positive, will be concerned about the opposing counterparty defaulting on its obligations. Collateralised interest rate swaps, on the other hand, expose the users to collateral risks: here, depending upon the terms of the CSA, the type of posted collateral that is permitted might become more or less expensive due to other extraneous market movements. Credit and funding risks still exist for collateralised trades but to a much lesser extent. Regardless, due to regulations set out in the Basel III Regulatory Frameworks, trading interest rate derivatives commands a capital usage. The consequence of this is that, dependent upon their specific nature, interest rate swaps may be capital intensive; with the latter, also, sensitive to market movements. Capital risks are thus another concern for users, and Banks typically calculate a credit valuation adjustment, CVA - as well as XVA for other risks - which then incorporate these risks into the instrument value. Debt security traders, daily mark to market their swap positions so as to "visualize their inventory" (see valuation control). As required, they will attempt to hedge, both to protect value and to reduce volatility. Since the cash flows of component swaps offset each other, traders will implement this hedging on a net basis for entire books. Here, the trader would typically hedge her interest rate risk through offsetting Treasuries (either spot or futures). For credit risks – which will not typically offset – traders estimate: The other risks must be managed systematically, sometimes involving group treasury. These processes will all rely on well-designed numerical risk models: both to measure and forecast the (overall) change in value, and to suggest reliable offsetting benchmark trades which may be used to mitigate risks. Note, however, (and re P&L Attribution) that the multi-curve framework adds complexity in that (individual) positions are (potentially) affected by numerous instruments not obviously related. ==Quotation and market-making==

ICE Swap rate ICE Swap rate replaced the rate formerly known as ISDAFIX in 2015. Swap Rate benchmark rates are calculated using eligible prices and volumes for specified interest rate derivative products. The prices are provided by trading venues in accordance with a “Waterfall” Methodology. The first level of the Waterfall (“Level 1”) uses eligible, executable prices and volumes provided by regulated, electronic, trading venues. Multiple, randomised snapshots of market data are taken during a short window before calculation. This enhances the benchmark's robustness and reliability by protecting against attempted manipulation and temporary aberrations in the underlying market. Market-making The market-making of IRSs is an involved process involving multiple tasks; curve construction with reference to interbank markets, individual derivative contract pricing, risk management of credit, cash and capital. The cross disciplines required include quantitative analysis and mathematical expertise, disciplined and organized approach towards profits and losses, and coherent psychological and subjective assessment of financial market information and price-taker analysis. The time sensitive nature of markets also creates a pressurized environment. Many tools and techniques have been designed to improve efficiency of market-making in a drive to efficiency and consistency. By January 1989 the Commission obtained legal opinions from two Queen's Counsel. Although they did not agree, the commission preferred the opinion that it was ultra vires for councils to engage in interest rate swaps (ie. that they had no lawful power to do so). Moreover, interest rates had increased from 8% to 15%. The auditor and the commission then went to court and had the contracts declared void (appeals all the way up to the House of Lords failed in Hazell v Hammersmith and Fulham LBC); the five banks involved lost millions of pounds. Many other local authorities had been engaging in interest rate swaps in the 1980s. This resulted in several cases in which the banks generally lost their claims for compound interest on debts to councils, finalised in Westdeutsche Landesbank Girozentrale v Islington London Borough Council. Banks did, however, recover some funds where the derivatives were "in the money" for the Councils (ie, an asset showing a profit for the council, which it now had to return to the bank, not a debt). The controversy surrounding interest rate swaps reached a peak in the UK during the 2008 financial crisis where banks sold unsuitable interest rate hedging products on a large scale to SMEs. The practice has been widely criticised by the media and Parliament. --> ==See also==