LIBOR vs. OIS: The Derivatives Discounting Dilemma

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1 LIBOR vs. OIS: The Derivatives Discounting Dilemma John Hull PRMIA May

2 Agenda OIS and LIBOR CVA and DVA The Main Result Potential Sources of Confusion FVA and DVA See John Hull and Alan White: LIBOR vs OIS: The Derivatives Discounting Dilemma, 2

3 Risk-neutral Valuation Project market variables in a risk-neutral world and discount expected payoff at the risk-free rate Risk-free rate defines the expected growth rates of market variables in a risk-neutral world and is used for discounting We focus on the rate that should be used for discounting 3

4 The Risk-Free Rate Many academics like to assume that the Treasury rate is the risk-free rate Pre-crisis practitioners assumed that a riskfree zero curve can be calculated from LIBOR rates, Eurodollar futures, and swap rates Post-crisis most banks have started to use OIS rates for discounting collateralized transactions and LIBOR/swap rates for discounting non-collateralized transactions 4

5 Why the Change? Banks became increasing reluctant to lend to each other during the crisis. The TED spread was very high during the crisis reaching 450 basis points in October 2008 The LIBOR-OIS spread was also very high during the crisis and reached a record 364 basis points in October

6 LIBOR Is Not Risk-Free The crisis emphasizes that the LIBOR/swap curve is not risk-free LIBOR rates are the unsecured short-term borrowing rates of a AA-rated financial institution Swap rates are continually refreshed shortterm rates. They correspond to the risk in a series of unsecured short-term loans to AArated financial institutions. 6

7 Our Research Conclusions OIS is a better proxy for the risk-free rate than LIBOR It should be used as the discount rate for both collateralized and non-collateralized portfolios 7

8 OIS and the Effective Fed Funds Rate The effective fed funds rate is the average of unsecured overnight borrowing rates (arranged by brokers using the Fedwire system) between financial institutions 3 month OIS rate is the rate swapped for the geometric average of effective fed funds rates Overnight rates and index swaps are defined similarly in other countries (eg, EONIA, SONIA) 8

9 OIS Zero Curve Can be bootstrapped similarly to LIBOR zero curve Maturities of overnight indexed swaps not as long as LIBOR swaps Natural approach is to assume that spread between LIBOR/swap zero rates and OIS zero rates at the long end is the same as it is for the longest maturity OIS rates are very close to risk-free 9

10 CVA For a portfolio of derivatives between dealer and counterparty, CVA is the cost to the dealer of a possible default by the counterparty 10

11 The CVA Calculation Time 0 t 1 t 2 t 3 t 4 t n =T Default probability q 1 q 2 q 3 q 4 PV of net exposure v 1 v 2 v 3 v 4 v n q n CVA (1 n R ) i 1 q i v i where R is the recovery rate 11

12 CVA Calculation continued The default probabilities (i.e., the q i ) are calculated from credit spreads The PVs of the net exposures (i.e., the v i ) is calculated using Monte Carlo simulation. Random paths are chosen for all the market variables underlying the derivatives and the net exposure is calculated at the mid point of each time interval. (These are the default times ) The v i is the present value of the average net exposure at the ith default time 12

13 Calculation of Net Exposure If no collateralization, the net exposure at a default time is the maximum of the value of the derivatives and zero If collateral is posted, we assume that a certain number of days elapse between the counterparty failing to post collateral and the position being unwound This is referred to as the cure period or margin period at risk 13

14 DVA (more controversial than CVA) DVA is an estimate of the cost to the counterparty of a default by the dealer Same formulas apply except that v i is counterparty s exposure to dealer, q i is dealer s probability of default, etc. Accounting standards have pushed banks in the direction of quantifying DVA 14

15 3 rd Quarter Increases in Credit Spreads of US Banks in 2011 Wells Fargo JPMorgan Citigroup Bank of America Morgan Stanley 63 bps 81 bps 179 bps 266 bps 329 bps 15

16 Use of CVA and DVA in Valuation Value of Derivatives Portfolio with Counterparty equals No-default Value + DVA CVA Seems correct intuitively Adjustment for double default possibility. See Brigo and Morini (2011) Consistent with a modification of Black-Scholes- Merton hedging arguments to incorporate credit risk developed by Burgard and Kjaer (2011) 16

17 Use of CVA and DVA in Valuation continued No-default Value + DVA CVA This is true for collateralized and noncollateralized portfolios If we increase the discount rate for noncollateralized portfolios there is a danger that we double count for credit risk 17

18 Can LIBOR Discounting Work for Non- Collateralized Portfolios? We show that LIBOR discounting gives the correct answer if CVA is calculated as the excess of the actual expected loss to the dealer from a counterparty default over the expected loss if the counterparty s borrowing rates are given by the LIBOR/swap curve DVA is calculated as the excess of the actual expected loss to the counterparty from dealer defaults over the expected loss if the dealer s borrowing rates are given by the LIBOR/swap curve (Using the LIBOR/swap rate instead of OIS rate as a benchmark when calculating credit spreads may give a reasonable approximation to the correct answer) 18

19 For Non-Collateralized Portfolios, Can We Use the Discount Rate to Adjust for Credit Risk? If portfolio will always have a positive value to the dealer, it can be correctly valued by discounting at the counterparty s borrowing cost If the portfolio will always have a negative value to the dealer, it can be correctly valued by discounting at the dealer s borrowing cost If the counterparty and dealer are equally creditworthy, any portfolio can be valued by discounting at the common borrowing cost of the two sides 19

20 Using LIBOR /Swap Rates for Discounting Non- Collateralized Portfolios Can Cause Confusion because Interest rates are also used to determine expected returns on assets in a risk-neutral world as well as for discounting. The interest rate used for the first purpose should always be the (OIS) risk-free rate Two different methodologies for calculating CVA and DVA are necessary The discount rate for DVA and CVA calculations should be the OIS rate even if LIBOR has been used as the discount rate for the main valuation 20

21 FVA and DVA Some banks calculate: DVA for their borrowing (as well as for their derivatives) FVA to reflect that they cannot fund at the risk-free (OIS) rate These two should in theory cancel each other 21

22 Conclusions Crisis has taught us the importance of finding a better proxy for the risk-free rate OIS rate appears to be the best proxy for the risk-free rate The OIS rate should be used as the discount rate for all derivatives portfolios, not just those that are collateralized 22

23 Just Out.. 23

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