ExtendingtheLIBORCurveAlternative 1: Create a term structure of interest ratesshowing the rate of interest at which a AA-ratedcompany can borrow for 1, 2, 3 ... yearsAlternative 2: Use swap rates so that the termstructure represents future short term AA borrowingratesAlternative 2 is the usual approach. It creates theLIBOR/swap term structure of interest ratesRiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull20126
Extending the LIBOR Curve ⚫ Alternative 1: Create a term structure of interest rates showing the rate of interest at which a AA-rated company can borrow for 1, 2, 3 . years ⚫ Alternative 2: Use swap rates so that the term structure represents future short term AA borrowing rates ⚫ Alternative 2 is the usual approach. It creates the LIBOR/swap term structure of interest rates Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 6
Risk-FreeRate Traders has traditionally assumed that theLIBOR/swapzero curveis the risk-freezero curveThe Treasury curve is about 50 basispoints below the LIBOR/swap zero curveTreasury rates are considered to beartificially low for a variety of regulatoryandtaxreasonsRiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull20127
Risk-Free Rate ⚫ Traders has traditionally assumed that the LIBOR/swap zero curve is the risk-free zero curve ⚫ The Treasury curve is about 50 basis points below the LIBOR/swap zero curve ⚫ Treasury rates are considered to be artificially low for a variety of regulatory and tax reasons Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 7
OIS RateLIBOR/swap rates were clearly not “risk-free'during the crisisAs a result there has been a trend toward usingovernight indexed swap (OiS) rates as proxiesfor the risk-free rate instead of LIBOR and swapratesThe OiS rate is the rate swapped for thegeometric average of overnight borrowing rates(ln the U.S. the relevant overnight rate is the fedfunds rate)RiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull20128
OIS Rate ⚫ LIBOR/swap rates were clearly not “risk-free” during the crisis ⚫ As a result there has been a trend toward using overnight indexed swap (OIS) rates as proxies for the risk-free rate instead of LIBOR and swap rates ⚫ The OIS rate is the rate swapped for the geometric average of overnight borrowing rates. (In the U.S. the relevant overnight rate is the fed funds rate) Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 8
Duration (page164)Duration of a bond that provides cash flow c, at time t, isnVttBi=1where Bis itsprice and yis itsyield (continuouslycompounded)This leads to△B-D△YB9RiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull2012
Duration (page 164) ⚫ Duration of a bond that provides cash flow ci at time t i is where B is its price and y is its yield (continuously compounded) ⚫ This leads to Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 9 − = B c e t yti i n i i 1 D y B B = −
Calculation ofDuration for a3-year bondpayingacoupon10%.Bondyield=12%.(Table8.3,page166)PV ($)Time (yrs)CashFlowWeightTime X($)Weight50.54.7090.0500.02551.04.4350.0470.04751.54.1760.0440.06652.03.9330.0420.08352.53.7040.0390.0983.010573.2560.7782.333Total1301.00094.2132.65310RiskManagementandFinancialInstitutions,3e,Chapter8,CopyrightJohnC.Hull2012
Calculation of Duration for a 3-year bond paying a coupon 10%. Bond yield=12%. (Table 8.3, page 166) Risk Management and Financial Institutions, 3e, Chapter 8, Copyright © John C. Hull 2012 10 Time (yrs) Cash Flow ($) PV ($) Weight Time × Weight 0.5 5 4.709 0.050 0.025 1.0 5 4.435 0.047 0.047 1.5 5 4.176 0.044 0.066 2.0 5 3.933 0.042 0.083 2.5 5 3.704 0.039 0.098 3.0 105 73.256 0.778 2.333 Total 130 94.213 1.000 2.653