4. OTC Derivatives and Counterparty Credit Risk Mitigation: The OIS Discounting Framework

Unlike the credit risk generated by a loan, where the probability of loss is unilateral, insofar as it is held by the issuing bank, counterparty risk as a rule creates a risk of potential bilateral loss. In fact, the market value of the transaction can be positive or negative for both counterparties and the risk is manifested in the one where the value is positive in the case of insolvency (Basel 2). In addition, Basel 3 has predicted a specific capital requirement for the risk of changes in fair value of OTC derivative positions.

According to Article 4, Paragraph 13: the counterparties perform the compensation of the derivative contracts belonging to a class of OTC derivatives if these simultaneously satisfy two characteristics: (1) Their conclusion occurred in one of these ways: (a) Between two financial counterparties; (b) Between a financial counterparty and a non-financial counterparty; (c) Between two non-financial counterparties; (d) Between a financial counterparty or a non-financial one and a subject of a third country, which if located in Europe would be subject to the clearing obligation; (e) Between two subjects in one or more third countries, which if located in Europe would be subject to the clearing obligation. (2) There are entered into or novated: (a) starting from the effective date of the clearing (b) starting from the effective date of the clearing referred to in Article 5, paragraph 1, Regulation (EU) number 648/2012 – EMIR (European Market Infrastructure Regulation), http://​ec.​europa.​eu/​finance/​financial-markets/​derivatives/​index_​en.​htm.

Regulation (EU) number 648/2012 – EMIR (European Market Infrastructure Regulation), http://​ec.​europa.​eu/​finance/​financial-markets/​derivatives/​index_​en.​htm.

To determine the value of the margins to be collected from clearing members, the central counterparties should use models and parameters that take into account the risk of the products cleared. These models are subject to validation by the supervisory authority.

Official Journal of the European Union, Legislative Acts, EU Regulation number 648/2012 of the European Parliament and of the Council of 04 July 2012, Title II, Article 11, page 22.

Represented by the mid-market value at the time of the default adjusted for the bid-offer spreads charged to the counterparty that has not failed which will have to pay in order to substitute the contract that has been terminated early.

BCBS (2011), International regulatory framework for banks, http://​www.​bis.​org/​bcbs/​basel3.​htm.

The so-called wrong-way risk, namely the increase in exposure when the credit quality of the counterparty decreases.

The retrospective assessment of exposure to counterparty risk.

Vecchiato W., Virguti E., Rischio di controparte, derivati e Credit Value Adjustment: strategie e metodi di gestione, Bancaria number 5/2013, page 49.

Official Journal of the European Union, Directive 2013/36/EU of the European Parliament and the Council of 26 June 2013, Title IV, Articles 381 to 385, pages 224–228.

In order to approve bilateral compensation agreements to reduce the exposure value (pursuant to Article 296 and 297 of CRR), the bank must meet the following requirements:

Often reference is made to the probability of default of the issuers published by the external rating agencies.

OIS (Overnight Index Swaps) are also swaps, where at maturity, one party will pay an amount based on a daily geometric accrual of an index and will receive the OIS rate for the period. The daily accrual rates for OIS are typically based on overnight central bank rates. In a EUR OIS, the daily accrual is based on Eonia, while for a GBP OIS it is Sonia.

The consideration of each yield curve for the determination of the mark to model of the single product is derived according to the maturity of the variable rate to which the derivative is indexed.

From the application point of view, the new multicurve framework based on OIS discounting implies that the procedure to determine the OIS zero curve is similar to that used to determine the Euribor/swap zero curve in a discounting Euribor system, while the new technique concerns the method of determining the forwarding curves: namely the set of forward rate curves useful to enhance the cash flow of the derivatives whose tenor of reference rate is consistent with that of the quotations from which the derivatives are obtained.

In this regard and in brief, there are considered a number of swap prices relating to a set of interest rate swaps traded in the market, each having a notional amount equal to N and a different deadline.

Using the matrix representation, for each of the interest rate swap considered the value of the fixed part is obtained as:

\( \left|\begin{array}{ccccc}N{c}_1+N& 0& 0& \dots & 0\\ {}N{c}_2& N{c}_2+N& 0& \dots & 0\\ {}N{c}_3& N{c}_3& N{c}_3+N& \dots & 0\\ {}\dots & \dots & \dots & \dots & \dots \\ {}N{c}_j& N{c}_j& N{c}_j+N& \dots & N{c}_j+N\end{array}\right| \)

where the generic discount factor v _j is valued on the basis of a zero coupon j-esimo obtained from the OIS zero curve. As is known, at the time of negotiation of each interest rate swap the value of the fixed part must be equal to that of the variable part for which we have:

\( \left|\begin{array}{ccccc}N{v}_1& 0& 0& \dots & 0\\ {}N{v}_1& N{v}_2& 0& \dots & 0\\ {}N{v}_1& N{v}_2& N{v}_3& \dots & 0\\ {}\dots & \dots & \dots & \dots & 0\\ {}N{v}_1& N{v}_2& N{v}_3& \dots & N{v}_j\end{array}\right|\times \left|\begin{array}{c}{a}_1\\ {}a\\ {}{a}_3\\ {}\dots \\ {}{a}_j\end{array}\right|=\left|\begin{array}{c}{P}_1-N{v}_1\\ {}{P}_2-N{v}_2\\ {}{P}_3-N{v}_3\\ {}\dots \\ {}{P}_j-N{v}_j\end{array}\right| \)

where the generic term a _j represents the forward rate necessary to enhance the j-esimo cash flow of the variable part of the swap, determined by solving the j-esime relations that tie the value of the variable part to that of the fixed part of the interest rate swaps traded on the market.

The presence of negative interest rates also requires a shift in pricing interest rate options from a valuation framework type lognormal (Black model) to a framework normal (Bachelier model); the Black model assigns probabilities equal to zero to the fact that interest rates can take zero or negative values.

The structure of the curve is composed of three segments: the first refers to the money market quotations, the second to FRA market and the last to interest-rate swaps against Euribor.