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Interest Rate Derivative Pricing

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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Interest Rate Derivative Pricing

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  1. Interest Rate DerivativePricing

  2. IRD Valuation • Caps, Floors and Collars • Swaptions

  3. Caps and Floors • Application of B-S model as modified by Black (1976):

  4. Application of Put-Call Parity by Black (1976): Caps and Floors

  5. 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)

  6. 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!

  7. 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

  8. 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.

  9. 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.

  10. Payer (Call) Swaption

  11. Receiver (Put) Swaption

  12. 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%.

  13. 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

  14. 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.

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