Pricing and Duration of an Inverse Floater

This question focuses on valuing an inverse floater in a simple term-structure setting, and then extracting its interest rate sensitivity. The instrument has coupons that move opposite to a reference rate, with standard fixed maturity and regular payments, under a flat yield environment. Candidates must translate a nonstandard coupon formula into concrete cash flows over time, then aggregate and discount them consistently with the given yield. Because the coupon depends linearly on the reference rate, the setup is a clean test of whether someone can see past the exotic label and treat the instrument as a structured combination of simpler bonds, a theme that often appears in fixed income quant and structuring interviews.

On the technical side, the question leans on bond pricing, present value as a linear operator, and duration as a first-derivative sensitivity. Strong answers typically use replication: decomposing the inverse floater into a portfolio of a fixed-rate bond and a position in a standard floater or zero-coupon instruments, then pricing and combining their durations. Interviewers watch for algebraic precision, consistent treatment of compounding and payment frequency, and a clear grasp of why duration is linear in cash flows for instruments whose coupons are linear in rates.

What it tests

The core structure behind inverse floaters is replication: any security with cash flows that are a linear combination of standard instruments (like fixed-rate and floating-rate bonds) can be valued and risk-analyzed by expressing it as a portfolio of those simpler instruments. This works because bond pricing and duration are both linear in cash flows, so the price and sensitivity of the composite instrument are just the corresponding linear combinations of the components. The reason this holds is that present value is an additive operation, and duration (as the first derivative of price with respect to yield) is also linear when the cash flows themselves are linear in the underlying rates. This means that even seemingly complex coupon structures can be decomposed into sums and differences of standard bonds, making their valuation and risk straightforward once the replication is found. The principle generalizes: whenever you see a nonstandard bond with cash flows that are algebraic functions of market rates, look for a replicating portfolio of standard instruments whose combined cash flows match.