# Interest Rate Derivative Pricing. IRD Valuation Caps, Floors and Collars Swaptions.

## Presentation on theme: "Interest Rate Derivative Pricing. IRD Valuation Caps, Floors and Collars Swaptions."— Presentation transcript:

Interest Rate Derivative Pricing

IRD Valuation Caps, Floors and Collars Swaptions

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

Caps and Floors Application of Put-Call Parity 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) D 1 =.227N(D 1 )=.5898 D 2 =.077N(D 2 )=.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) D 1 =.227N(-D 1 )=.4102 D 2 =.077N(-D 2 )=.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. 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.

Payer (Call) Swaption