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Understanding Interest Rate Swaps: A Guide to Plain Vanilla Swaps and Their Valuation

This comprehensive guide delves into the mechanics of interest rate swaps, focusing on plain vanilla swaps. An interest rate swap is a financial derivative where parties exchange interest payments, allowing fixed-rate payors to convert to floating rates and vice versa. The guide provides a detailed analysis of cash flows, including fixed interest payments versus floating LIBOR payments. It also explains the structure of swaps, revaluation processes, and how changes in interest rates impact payments, highlighting the importance of strategic structuring for both fixed and floating rates.

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Understanding Interest Rate Swaps: A Guide to Plain Vanilla Swaps and Their Valuation

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  1. Swaps: Introduction

  2. Swaps • Interest Rate Swaps • Plain Vanilla • Cash Flows • Structure • Revaluation

  3. Plain Vanilla Swaps • Fixed Interest Payments for Floating Interest Payments • Swap Buyer is Fixed Rate Payor • Assume 4 year swap of 10% fixed rate payments vs. unknown LIBOR on $100,000,000 notional principal (NP). Note, no payments up front or terminally. Only NET interest payments between parties.

  4. Plain Vanilla Swap • Payments are: LIBOR rates: 9.5, 10.5, 9 and 10.5 Time LIBOR Pymt $ Pymt Diff. 1 $9.5 million $10Mill -500K 2 $10.5 million $10Mill +500K 3 $9.0 million $10Mill -1Mill 4 $ 10.5 million $10Mill +500K

  5. Point of Plain Vanilla Swap • Without adjustment to existing securities, Floating became Fixed, and Fixed became Floating. Floating ID’d at start of each period! • Lower Transaction Costs. • Ability to Activate Perceptions: • Fixed wants to be Floating if rates are falling. • Floating wants to be Fixed if rates are rising.

  6. Structuring a Swap • Observe interest rates on yield curve: 10% Interest Rate 8% 1 year 6 month

  7. Forward Rates • Rate of 6-month loan in 6 months (6-month FRA, termed a 6x12). • A 1-year rate must be equivalent to 6-month rate combined with 6x12 rate. • (1 + 0R12) = (1+ ½0R6)(1+ ½6R12) • Thus, price 6x12 off of known 6 & 12 month rates.

  8. Structuring a Swap • (1 + 0R12) = (1+ ½0R6)(1+ ½6R12) • (1+.10) = (1 + ½ (.08)) * (1 + ½ (6R12)) • 6R12 = [(1.10/1.04) – 1] * 2 = 11.54% • Floating CFs as a % of any face amount will be: • 6-month: .08 * ½ = .04 1-year: .1154 * ½ = .0577

  9. Structuring a Swap • Fixed Payments are where: (.04 – Fixed) (.0577 – Fixed) • 0 = -------------------- + ----------------------- (1 + ½ (.08)) (1.10) • Fixed = .0486  9.72% Fixed (annual)

  10. Now 6mo 1yr Swap Structure(on $100M in Notional Prin.) $0.91M Pymt From Fixed to Fltg $4M $5.77M $4.86M $4.86M $0.86M Pymt From Fltg to Fixed -$0.85M / (1.04) + $0.91M / (1.10) = 0

  11. Swap Revaluation(Marking-to-Market) • What if rates jumped 1% next day? (6-month=9%, 1-year=11%) • (1 + 0R12) = (1+ ½0R6)(1+ ½6R12) • (1+.11) = (1 + ½ (.09)) * (1 + ½ (6R12)) • 6R12 = [(1.11/1.045) – 1] * 2 = 12.44% • 1-yr CF now .1244*½ = .0622

  12. Now 6mo 1yr Swap Revaluation $1.36M Pymt From Fixed to Fltg (on $100M NP) 6-month CF does not change as determined at swap origination $4M $6.22M $4.86M $4.86M $0.86M Pymt From Fltg to Fixed -$0.85M / (1.045) + $1.36M / (1.11) = $0.40M Gain to Fixed Rate Payor

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