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Interest Rate Derivative Pricing. IRD Valuation. Caps, Floors and Collars Swaptions. Caps and Floors. Application of B-S model as modified by Black (1976):. Application of Put-Call Parity by Black (1976):. Caps and Floors. Caps & Floors Example.

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Presentation Transcript
ird valuation
IRD Valuation
  • Caps, Floors and Collars
  • Swaptions
caps and floors
Caps and Floors
  • Application of B-S model as modified by Black (1976):
caps floors example
Caps & Floors Example
  • Assume you are concerned with rising rates on a $100m, variable debt your company owes in 1 year.
  • Currently the variable rate is 6.5%, and you would like to fix it for no charge. The current forward rate is 6.65%, the riskless rate is 4.35%, and the rate volatility is 15%.
  • (Note: days = Actual/360)
cap caplet
Cap (Caplet)
  • D1= .227 N(D1)=.5898
  • D2 = .077 N(D2)=.5307
  • Black-76 = .004525 or 45 ¼ BPs
  • Adjustment for $1 Notional Value = 0.93765
  • Cap = .004243 or a bit less than 42 ½ BPs
  • On $100m NP = $424,284…expensive!
floor floorlet
Floor (Floorlet)
  • D1= .227 N(-D1)=.4102
  • D2 = .077 N(-D2)=.4693
  • Black-76 = .003089 or 31 BPs
  • Adjustment for $1 Notional Value = 0.93765
  • Floor = .002896 or a bit less than 29 BPs
  • On $100m NP = $289,624
collar
Collar
  • Collar = Buy Cap and Sell Floor
  • Collar = - Cap + Floor

= - 424,284 + 289,624

= $134,660 Payment

  • As F > X, Collar in-the-money.
  • Fix rate at 6.5%, no higher, but none of the benefit if lower.
  • If set strike rate at 6.65%, zero-cost collar.
swaptions
Swaptions
  • Also usage of Black (76) extension
  • Payer (Call) swaption:
    • The right (but not the obligation) to pay the fixed rate, and receive the floating rate in a swap of pre-specified term and rate.
    • The right to be the swap buyer.
  • Receiver (Put) swaption:
    • The right (but not the obligation) to receive the fixed rate, and pay the floating rate in a swap of pre-specified term and rate.
    • The right to be the swap seller.
swaption example
Swaption Example
  • 2 year call (put) swaption on a 4 year swap (semi-annual resets) that has a pay fixed rate of 7%. The call strike is 7.5%, the riskless rate is 6% and rate volatility is 20%.
swaption example13
Swaption Example
  • D1= -.1025 N(D1)=.4592
  • D2 = -.3854 N(D2)=.3500
  • Black-76 Call = .0052 or 52 BPs
  • Adjustment for $1 Notional Value = 3.4370
  • Call Swaption =.01796 or a bit less than 180 BPs
swaption example14
Swaption Example
  • D1= -.1025 N(D1)=.4592
  • D2 = -.3854 N(D2)=.3500
  • Black-76 Put = .0097 or 97 BPs
  • Adjustment for $1 Notional Value = 3.4370
  • Put Swaption =.03221 or a bit more than 322 BPs
  • Note: Put more expensive as F < X, so put (not call) in-the-money.