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IRfoundationconcept

Discount Factors

Present value of one unit of currency paid at a future date.

Reviewed 2026-08-10TheQuantBateman Research1 linked labs
01Intuition

Build the mental model first.

A discount factor is the price today of a future unit under the relevant collateral and currency rules.

ONE-LINE DEFINITION

Present value of one unit of currency paid at a future date.

02Mathematics

Now make it exact.

P(0,T)=ez(0,T)TP(0,T)=e^{-z(0,T)T}
Notation and units

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

03Assumptions

Every model has a price.

01

Educational conventions are stated explicitly and may simplify market quotation or settlement details.

02

Rates are continuously compounded unless the section says otherwise.

03

Inputs are deterministic in the base model.

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

Why a quant cares.

Every cashflow PV and curve construction step depends on them.

IntuitionMathematicsImplementationDesk risk
05Desk view
FRONT OFFICE VIEW

The hedge has opinions.

Start with the quote convention, then ask which IR risk survives the hedge. A number without its convention is merely well-dressed ambiguity.

Ask Bateman about this model
06Related

Continue through the graph.