Caps, Floors, and  Collars Lecture

# Caps, Floors, and  Collars Lecture  - Debt...

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Debt Instruments and Markets Professor Carpenter Caps, Floors, and Collars 1 Caps, Floors, and Collars Caps Capped Floaters Floors Floaters with Floors Collars Floaters with Collars Strike rate, settlement frequency, index, notional amount, calls on yields, puts on yields, portfolio of options Concepts and Buzzwords Reading Veronesi, pp.387‐392 Tuckman, pp. 413 – 416

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Debt Instruments and Markets Professor Carpenter Caps, Floors, and Collars 2 Interest Rate Caps A cap provides a guarantee to the issuer of a ﬂoating or variable rate note or adjustable rate mortgage that the coupon payment each period will be no higher than a certain amount. In other words, the coupon rate will be capped at a certain ceiling or cap rate or strike rate . Caps are either offered over‐the‐counter by dealers or embedded in a security. Payoff Rule for a Typical Cap Each payment date, the cap pays the difference, if positive, between a ﬂoating index rate and the cap rate, multiplied by a prespecified notional amount of principle or par value, divided by the annual payment frequency . For example, a T ‐year, semi‐annual cap, indexed to the 6‐month rate, with \$100 notional principle, and cap rate k pays 100 max( t ‐0.5 r t k , 0)/2 at time t , t = 0.5,1,1.5,…, T
Debt Instruments and Markets Professor Carpenter Caps, Floors, and Collars 3 Capped Floater Consider the net position of the issuer of \$100 par of a ﬂoating rate note who either buys a matching cap from a dealer or else embeds the cap in the note at issue: Capped Floater = Floater minus Cap Time t Coupon Payment of Capped Floater 100 min( t‐0.5 r t ,k )/2 = 100 t ‐0.5 r t /2 – 100 max( t‐ 0.5 r – k, 0) / 2 Cap and Capped Floater Coupons Cap rate Uncapped ﬂoater coupons

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Debt Instruments and Markets Professor Carpenter Caps, Floors, and Collars 4 Example: Cap Payments Time 0.5 Time 1 Time 0 5.54% 6.004% 0 4.721% 6.915% \$0.127 5.437% 4.275% Consider a \$100 notional of 1.5‐year semi‐annual cap with strike rate k = 5.75%, indexed to the 6‐month rate.
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