Options and Speculative Markets 2004-2005 Swapnote

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)

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

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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

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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

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2. Duration of swap

• As

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Using duration

• Suppose the interest rate change ?r 0.01 (
  1bp)

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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
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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 a1 t a2 t² a3 t3
• where r(t) is the spot rate with continuous
  compounding for maturity t
• 3. The discount factor is d(t) exp(-r(t)t)

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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

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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?

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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