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Caps

Limit floating-rate payments through a strip of caplets.

Reviewed 2026-08-10TheQuantBateman ResearchReading note
01Intuition

Read the contractual cash flows first.

Start from the payoff, fixing schedule and settlement currency. Limit floating-rate payments through a strip of caplets. The valuation method comes after the contractual exposure is unambiguous.

ONE-LINE DEFINITION

Limit floating-rate payments through a strip of caplets.

02Mathematics

Express payoff and present value precisely.

Vcap=∑iNδiP(0,Ti)Black76⁡(Fi,K,σi,Ti−1)V_{cap}=\sum_iN\delta_iP(0,T_i)\operatorname{Black76}(F_i,K,\sigma_i,T_{i-1})
Notation and units

Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.

03Assumptions

Make conventions part of the contract.

01

Contract dates, calendars, settlement, notionals and payoff currency are part of the valuation input.

02

Discounting and projection conventions must match the collateral and quotation framework.

03

The displayed payoff omits legal terms and lifecycle events unless stated otherwise.

“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
04Market use

Locate the quote and replication instruments.

Caps enters IR valuation through its contractual cash flows, quotation and lifecycle. Scenario analysis should separate market moves from convention or settlement changes.

Intuition→Mathematics→Implementation→Desk risk
05Desk view
FRONT OFFICE VIEW

Map cash-flow changes into hedge risk.

Reconcile the contractual payoff before reading the IR risk. Small date or convention changes can move cash flows before any model parameter moves.

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06Related

Continue to the nearest instrument or model.