Pricing an inverse floater

An inverse floater pays a semiannual coupon of 30%−3r30\% - 3r on $100 face (where rr is the prevailing rate) and redeems $100 at its 5-year maturity. The yield curve is flat at 7.5%7.5\%. Rather than model the rate-dependent coupon directly, find a static portfolio of ordinary instruments - plain fixed-rate bonds and par floating-rate notes - that reproduces this exact coupon and redemption, and use it to price the inverse floater. What is its price (in dollars)?

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  1. Match the coupon 30%−3r30\%-3r: the −3r-3r needs 3 short floaters; the +30%+30\% needs fixed bonds at the 7.5%7.5\% coupon.
  2. Check the redemption nets to $100, then price each leg - coupon = yield and par floaters both sit at par.

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