Interest Rate Derivative Pricing

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# Interest Rate Derivative Pricing - PowerPoint PPT Presentation

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 &amp; Floors Example.

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### Interest Rate DerivativePricing

IRD Valuation
• Caps, Floors and Collars
• Swaptions
Caps and Floors
• Application of B-S model as modified by Black (1976):
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)
• 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)
• 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 = 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
• 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.
• 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
• 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 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 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.