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Market Expectations Trough Derivative Instruments Stefano Caprioli

Market Expectations Trough Derivative Instruments Stefano Caprioli. 2nd Lesson Euribor Crisis through EONIA Discounting. Overview : OIS Discounting as standardized market convention in order to take into account liquidity , credit and counterparty risk

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Market Expectations Trough Derivative Instruments Stefano Caprioli

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  1. Market ExpectationsTrough Derivative InstrumentsStefano Caprioli 2nd Lesson Euribor Crisisthrough EONIA Discounting

  2. Overview: • OIS Discountingasstandardized market convention in orderto take into account liquidity, credit and counterpartyrisk • Implications on Collateral Management • Implications on Derivatives World • OIS-LIBOR Spread as Key Risk Indicator

  3. Since the financial crisis, a whole host of new issues and complications have arisen surrounding the previously uncomplicated area of valuing simple derivative instruments. Liquidity and credit risk, and basis risk volatility which arose in interest rate markets during the crisis has meant that Libor rates are no longer appropriate for derivative discounting. New discounting methods have had to be developed to deal with these issues. There are further difficulties stemming from how collateral impacts upon the trade, and issues such as collateral optionality are now sources of much debate in the trading community.

  4. WhatisCollateral Management? Collateral management is the method of granting, verifying, and giving advice on collateral transactions in order to reduce credit risk in unsecured financial transactions. The fundamental idea of collateral management is very simple, that is cash or securities are passed from one counterparty to another as security for a credit exposure. The form of collateral is agreed before initiation of the contract. Collateral agreements are often bilateral. Collateral has to be returned or posted in the opposite direction when exposure decreases. Collateral management has many different functions. One of these functions is credit enhancement, in which a borrower is able to receive more affordable borrowing rates. Aspects of portfolio risk, risk management, capital adequacy, regulatory compliance and operational risk and asset-liability management are also included in many collateral management situations.

  5. DearCounterparty, We wouldliketoadviseyouthat XXXXX willmoveto OIS curve fordiscountingpurposes, withreferencestoitsderivativescollateralizedexposure. ChangewillbeeffectiveMonday, 6. StartingTuesday, 7, allmargincallswillbecalculated and managedaccordingly. OurSalesForceisavailableforanyfurther information youmayrequire. WithKindRegards XXX Collateral Management Desk

  6. OIS reflects “real” conditions better than Libor Rate since the underlying index for OIS is based on traded rates rather than a poll.

  7. When Banks CDS went to 200 bps, Market Operators started to distinguish between OIS and Libor.

  8. Fast topicsoverview: • LIBOR is the rate at whichanindividualContributorPanelBankcouldborrowfunds, wereitto do so byaskingfor and thenacceptinginterbankoffers in reasonable market size just priorto 11:00 [am] London time. • In the early 1980s, in ordertoensurecontinuedgrowth in the trading ofnumerousnewinstrumentssuchas interest rate swaps and currencyoptions, therearose the pressing needtoestabilish a uniform benchmark indexagainstwhichtheseinstrumentscouldbereferenced. LIBOR isnot a traded rate, bit rather the outcomeof a pollofbankrates.

  9. An overnight indexed swap (OIS) is an interest rate swap where the periodic floating rate of the swap is equal to the geometric average of an overnight index (i.e., a published interest rate which is also called Overnight Rate or EONIA) over every day of the payment period. The index is typically an interest rate considered less risky than the corresponding interbank rate (LIBOR). OIS rates (or, in particular, the difference or "spread" between LIBOR and OIS rates) are an important measure of risk and liquidity in the money market. A higher spread (high Libor) is typically interpreted as indication of a decreased willingness to lend by major banks, while a lower spread indicates higher liquidity in the market. As such, the spread can be viewed as indication of banks' perception of the creditworthiness of other financial institutions and the general availability of funds for lending purposes.

  10. Another New Market Feature in OrdertoMinimizeCreditRisk • A lotofinstruments are “forward premium”: theypaid on the delivery date and not the spot date. This convention wasintroduced in October 2009 by the interbankoptions market asan alternative to the spot premium. As a resultof the recentcrisisitbecomes more likelythatanoption seller may default. Accordingly, especiallyfor long termoptions, the forward premium convention reduces the risk. In addition, anotheradvantageisthatallcashflows are exchanged on one date (on the delivery).

  11. OIS as Risk free Curve and Forward Premium tominimizeCredit and Counterparty Risk Market Source:Reuters

  12. OIS as Risk free Curve and Forward Premium tominimizeCredit and Counterparty Risk Market Source:Reuters

  13. Two Curves and Fx Framework: Academic Approach In the double–curve case, no arbitrage requires the existence at any time t0 ≤ t ≤ T of a spot and a forward exchange rate between equivalent amounts of money in the two curves such that Where the subscripts f and d stand for forecasting and discounting. Cd(t) is any cash flow (amount of money) at time t in units of discount curve and Cf(t) is the corresponding cash flow at time t (the corresponding amount of money) in units of forecasting curve. Xfd(t,T) -> xfd(t,T) for t->T Remember also that, having a single curve, xfd(0)=1 Note that’s the same Foreign Structure in order to build a non arbitrage free framework whereas d stays for domestic, f for foreign and x is the spot rate.

  14. Two Curves and Fx Framework Considering the “spread ratio” between Fwds (d and f) we have: So we obtain the following relation: BAfd (t, T1, T2) =(Pd (t, T1)Xfd (t, T1) − Pd (t, T2)Xfd (t, T2))/[Xfd(t, T2) (Pd (t, T1) − Pd (t, T2))] Assuming the driftless lognormal martingale for Ff (t,T1,T2) we have: d Ff (t,T1,T2)= Ff (t,T1,T2)σf(t)dWf Under Pf(t,T2) Numeraire. We knowthat, under Pd(t,T2) Numeraire, Xfd(t,T2) moves according to a martingala: d Xfd (t, T2)= Xfd (t, T2) σX(t)dWx Withρdt=dWxdWf So, in ordertocalculateexpectations under “discountingnumeraire”, wemustadd a drift, so wehave: d Ff (t,T1,T2)= μf(t)dt+Ff (t,T1,T2)σf(t)dWf Withμf(t)=-σf(t) σx(t) ρ

  15. We thusobtain the followingexpressions: Where QAfd is the multiplicative adjustment you have to take into account. Market Standard is to assume ρ=0, so wehaveQafd=1 and you just need of a strip of σfthat match market Cap/FlorPrices.

  16. Example: Interest Rate Cap for Market Pratictioners

  17. Let L(t,T, ) be the ForwardLIBOR at time t for the accrualperiod [T,T+ ]. • Isexpressed in termsoffractionsof a year. • A capletis a calloption on L(t,T, ): After 2008 crisis we have P(t,T+ ) derivedby OIS Curve, while L(t,T, ) isobserved on the Market or derivedbyLibor Curve. Market pratictionerscallLiborderivedcurves “ForecastingCurves” and OIS derived Curve discounting Curve. We usedifferent market quotes in ordertobuilddifferentforecastingcurves: forinstancewehave EUR 6M Forecasting Curve that’s basedonly on 6 monthstenorinstruments, EUR 3M on 3 monthstenorinstruments and so on.

  18. Using Black Model we have (for Cap): Anotherimportantchangeis the Forward Premium convention: dealers start toexchangepaymentflows at eachcapletexpiry in ordertominimizeLostGiven Default embeddedinto the Cap or Floor.

  19. New market conventionshavealso impact on Banking Profit and Lossessince, movingfrom Euribor to OIS discounting curve, yourealize a PresentValuevariation on your Book. It’s interestingto note howimpliedvolatilitieschangetheirlevelsaccordingtodiscounting curve youchoice, so Brokers are forcedto show premiumsalsoformarketslikeCap & Floor or Swaptionswhere, before 2008, theypubblishedonlyvolatilities. DiffFlatVol Eur Disc - FlatVol OIS Disc on Cap & Floor Euribor 6M

  20. Swap Rates

  21. We can maintain the same notation in order to deal with Double Curve Swap Rates, moving in the same manner: Where the Annuity is:

  22. If we choice Af(t,S) as numeraire we have: Where vf is the Volatility and dWf is a Brownian Motion. We have: That’s a non arbitrage condition on Annuities.

  23. We can define a “Swap Forward Exchange Rate” Yfd(t,S) such that: Yfd(t,S) is a martingale under “Discounting Curve Annuity”, so we have:

  24. Again we make a change of numeraire in order to obtain forecasting Swap Rate dynamic under discounting swap measure: We thus obtain the following expressions: Also in this case market pratictioners moved to QAfd=1 in order to semplify pricing activities.

  25. Interest Derivatives continue to “bet” on Euribor butyouhaveto discount with OIS Curve: youhavetousetwocurves: • Forecasting Curve (Euribor Based) • Discounting Curve (OIS Based) Market Source:Reuters

  26. Interest Derivatives continue to “bet” on Euribor butyouhaveto discount with OIS Curve: youhavetousetwocurves: Market Source:Reuters

  27. OIS as Risk free Curve and Forward Premium tominimizeCredit and Counterparty Risk Market Source:Reuters

  28. CONCLUSIONS • We showed two remarkable market standards in order to minimize credit, liquidity and counterparty risks for interest rate derivatives: • Collateral Management by OIS Discount Curve • Forward Premiums • OIS Discounting determines a new way to price IR Derivatives, since we must add new assumptions on drift you have moving from one to two curves. • The key is to understand if it’s better a centralized clearing house or a “one-to-one” collateralized agree both for risk management and front office purposes or, on other hands, both for regulators and market operators.

  29. “Clearing houses around the world generally performed well in the highly stressed financial environment of the recent crisis. However, we should not take for granted that we will be as lucky in the future. Past crises, including the financial panic of 1907 and the 1987 stock market crash, led to significant reforms and improvements in clearing and settlement that paid off in subsequent periods of financial stress. Given the growing interdependencies among clearing houses, along with the new mandates for central clearing, now is a good time to reflect on the lessons of the recent crisis and consider whether further improvements are possible.” 2011-US Federal Reserve Chairman Ben Bernanke

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