Yield Curve Building with Futures &amp; Swaps

# Yield Curve Building with Futures &amp; Swaps - Yield...

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Yield Curve Modeling Constructing the Curve with Copyright © 1996-2006 Investment Analytics

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Slide: 2 Copyright © 1996-2006 Investment Analytics Ingredients for Building the Zero Coupon Spot Curve ¾ Cash Rates ¾ FRA Rates (T-Bills) ¾ Futures Prices ¾ Swap Rates
Slide: 3 Copyright © 1996-2006 Investment Analytics Lab: Constructing the Short End Ask Bid Days 3 Month \$ LIBOR 4.25% 4.23% 91 \$ FRAs 3-6 4.40% 4.35% 91 6-9 4.55% 4.50% 92 9-12 4.70% 4.65% 91

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Slide: 4 Copyright © 1996-2006 Investment Analytics Lab: Constructing the Short End ¾ Excel Spreadsheet: Yield Curve Modeling.xls ¾ Worksheet: Short End ¾ Use discount factor method ¾ See cell notes for hints
Slide: 5 Copyright © 1996-2006 Investment Analytics Solution: Short End Period DF Spot Rate 3 months 0.9894 4.2500% 6 months 0.9785 4.3486% 9 months 0.9672 4.4498% 12 months 0.9559 4.5519% ¾ Notes: 9 DF 6-3 = (1 + Ask x Days / 360) 9 DF 6 = DF 6-3 x DF 3 9 R 6 = (-1 + 1/DF 6 ) x 360 / (91 + 91)

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Slide: 6 Copyright © 1996-2006 Investment Analytics Futures Libor Rates ¾ Yield = 100 - Settlement Price ¾ Example: 9 Futures price = 93.0 9 Futures yield = 100 - 93.0 = 7.0% ¾ Note: this is not exactly the forward rate
Slide: 7 Copyright © 1996-2006 Investment Analytics ¾ Assumption is often that 100-F = forward rate ¾ Not exact for several reasons: 9 9 Futures are marked to market 9 “Convexity” - stochastic interest rates give rise to differences (Cox, Ingersoll, Ross JFE)

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Copyright © 1996-2006 Investment Analytics Convexity Definition: Positive Convexity Present value increases with rate decline exceeds Present value decline with rate increase ¾ What is the convexity of a Euro \$ future and an interest rate swap? ¾
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Yield Curve Building with Futures &amp; Swaps - Yield...

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