The Forward Curve

1. The prior curve
Andrew Lesniewski January 28, 2008

Con ecstasyts
1 LIBOR and LIBOR based instruments 1.1 Forward reckon agreements . . . . . . . . . . . . . . . . . . . . . . 1.2 LIBOR futures . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Valuation of LIBOR based instruments 2.1 Zero coupon bonds . . . . . . . . . 2.2 Valuation of FRAs and frontward rates 2.3 Valuation of swaps and swap rates . 2.4 Valuation of forward starting swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 3 3 4 4 5 6 8 8 9 11 13 14 14 14 16

3 Building a LIBOR forward curve 3.1 Bootstrapping techniques . . . . . . . . . . . . . . . . . . . . . . 3.2 Smoothing B-splines ?tting . . . . . . . . . . . . . . . . . . . . . 3.3 Pros and cons of the two methods . . . . . . . . . . . . . . . . . 4 Curve sensitivities and position hedging 4.1 Input perturbation sensitivities . . . . . . . . . . . . . . . . . . . 4.2 reversal based sensitivities . . . . . . . . . . . . . . . . . . . .



A B-splines and smoothing B-splines

1

LIBOR and LIBOR based instruments

LIBOR (= capital of the United Kingdom Interbank Offered Rate) is the interest rate at which banks borrow large amounts of money from each other. It is a widely used benchmark for short term (overnight to 1 year) interest rates. Daily ?xings of LIBOR are published by the British Banking Association on each London business day at 11 a.m. 1

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Interest Rate & Credit Models

London time. These ?xings are calculated from quotes provided by a number of move banks. LIBOR is not a risk free rate, but it is shut up to it: the participating banks have high credit ratings. LIBOR is offered in ten major currencies: GBP, USD, EUR, JPY, CHF, CAD, AUD, DKK, SED, and NZD. Throughout this course we shall assume a iodin currency, namely the USD. In the USD, LIBOR applies to deposits that begin...If you want to get a near essay, order it on our website: Ordercustompaper.com



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