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Options and Speculative Markets 2004-2005 Swapnote – Wrap up

Options and Speculative Markets 2004-2005 Swapnote – Wrap up. Professor André Farber Solvay Business School Université Libre de Bruxelles. Outline. (1) Piggibank is short (receives fixed rate and pays floating rate) on: a 4% 5-year swap notional principal of €10 million.

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Options and Speculative Markets 2004-2005 Swapnote – Wrap up

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  1. Options and Speculative Markets2004-2005Swapnote – Wrap up Professor André Farber Solvay Business School Université Libre de Bruxelles

  2. Outline (1) Piggibank is short (receives fixed rate and pays floating rate) on: • a 4% 5-year swap • notional principal of €10 million. The current 5-yr swap rate is 3.29% (Exhibit 1). So the value of this swap is positive for Piggibank. Step 1 of the analysis is to calculate this value. (2) Interest rates might change. This would modify the value of the swap. Step 2 of the analysis is to calculate by how much the value of the swap will change if interest rates change by 0.01% (1 basis point – bp) – the Basis Point Value (BVP) of the swap. (3) Piggibank considers hedging its swap position using Swapnote futures. Step 3 of the analysis is to understand by the payoff on one futures contract if interest rates change by 0.01% - the Basis Point Value of one Swapnote. (4) The number of Swapnote to short is equal to the ratio: BVP(Swap)/BVP(Swapnote) Swapnote 2004

  3. Summary of results • Value of swap for Piggibank: VSwap= €325,337 • Duration of Swap: DSwap = 116 Basis Point Value of Swap BVPSwap = - €3,782 • Swapnote = futures on 6% notional bond Tick (Value of ∆F = 0.01) = €10 BVPSwapnote = - €50.35 Note: if interest rates ↑→Futures price ↓  short swapnote • Number of swapnotes to short to hedge position: n = (- 3,782) / (- 50.35) = 75 Swapnote 2004

  4. 1. Current value of the swap of Piggibank • Piggibank is short on a 4% 5 yr swap with a notional principal of €10 million. • To value this swap: • 1- Calculate the discount factors from the current swap rates. • See next slide for details • 2- Calculate the value of the fixed rate bond • Vfix = 400,000 d1 + 400,000 d2 + ...+ 10,400,000 d5 • = 10,325,337 • 3- Subtract the value of the floating rate bond (equal to the principal) • Vfloat = 10,000,000 • Vswap = 10,325,337 – 10,000,000 • = 325,337 Swapnote 2004

  5. Calculation of discount factors • Bootstrap method. Solve the following equations: 100 = 102.30 d1 100 = 2.56 d1 + 102.56 d2 100 = 2.83 d1 + 2.83 d2 + 102.83 d3 100 = 3.07 d1 + 3.07 d2 + 3.07 d3 + 103.07 d4 100 = 3.29 d1 + 3.29 d2 + 3.29 d3 + 3.29 d4 + 103.29 d5 • Use eq.1 to obtain d1 • Replace d1 in eq.2 and solve for d2 • Replace d1 and d2 in eq.3 and solve for d3 • ..... • or use matrix algebra: d = C-1 P Swapnote 2004

  6. 2. Duration of swap • As: Swapnote 2004

  7. Using duration • Suppose the interest rate change ∆r = 0.01% (= + 1bp) Swapnote 2004

  8. Swapnote • A futures contract on a 6% notional coupon bond. • Face value = €100,000 • To calculate the futures price, use general approach: • S0 is the spot price of the underlying asset (a 6% coupon bond) • T is the maturity of the futures contract (2 month = 0.167 yr) • r is the 2-month interest rate (with continuous compounding) Maturity of futures Coupon + Principal Coupon Coupon Today 0 2 m 1yr 2 m 2 yr 2 m 5 yr 2 m 0.167 1.167 2.167 5.167 Swapnote 2004

  9. Spot price calculation • Some sort of interpollation is required to find the proper discount factor. • In the Excel spreadsheet, I proceed as follow: • I compute the spot interest rates (with continuous compounding) for various maturities • I fit a polynomial function: • r(t) = a0 + a1t + a2t² + a3t3 • where r(t) is the spot rate with continuous compounding for maturity t • 3. The discount factor is d(t) = exp(-r(t)t) Swapnote 2004

  10. Swapnote quotation • S0 = 111.71 • F0 = 111.71 / 0.99653 = 112.10 • The duration of the underlying bond is 4.66. • If the interest rate change ∆r = 0.01% (= + 1bp) • ∆F0 = -0.05 (= - 5 bp) (see next slide for details) • As the size of the contract is €100,000: • ∆r = 0.01% → ∆F0 = -0.05 • → BVPSwapnote = €100,000  (-0.05) / 100 = - €50 Swapnote 2004

  11. Duration of swapnote (details) • Suppose the interest rate change ∆r = 0.01% (= + 1bp) • By how much will the price of the swapnote change? • What about the futures price? Swapnote 2004

  12. Setting up the hedge • What do we know? • If ∆r = 0.01% (= + 1 bp) • BVPSwap= - € 3,782 • BVPSwapnote = - €50/contract • To hedge its swap position, Piggibank should short n futures swapnotes contract so that: Swapnote 2004

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