1 / 12

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.

jeroen
Download Presentation

Options and Speculative Markets 2004-2005 Swapnote – Wrap up

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related