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Valuation of Swaps


  • There are 2 ways to value a swap.
    • Considering it as a difference of two bonds
    • Considering it as a portfolio of FRAs
  • Value using bonds
    • Consider an example in which the swap lasts for n years. If the payments are made at the end of each year then :
    • If the principal is exchanged between the 2 parties at the end of the swap, then Party 1’s cash flow suggests that it’s long a fixed rate bond and short a floating rate bond.
    • Party 2 is short a fixed bond and long a floating rate bond.
    • We can value the swap by looking at the pay offs of either party.
  • Hence the value of the swap can be given as:
    • V = Bfix – Bfl
    • Where:
      • Bfix = PV of payments
      • Bfl = (P+AI)e-rt
  •  Value of a floating bond is equal to the par value at coupon reset dates and equals to the Present Value of Par values (P) and Accrued Interest (AI)

Value using portfolio of FRAs

  • In this case we assume that each payment at a future date is a forward rate agreement.
  • For payment at time t,  the rate used is the rate for the period between t-1 and t. This rate would be FRA at t-1 

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