Discount Factor (DF)

The present value of $1 receivable at a future time T, derived from the zero curve: DF = e^(−rT).

Discount factors are fundamental building blocks of derivative pricing. Under continuous compounding: DF(T) = e^(−r(T)×T) where r(T) is the zero rate at maturity T. Alternatively, DF(T) = 1/(1+r)^T under annual compounding. The full SOFR zero curve generates a set of discount factors used to price all fixed-income derivatives. Σ(DF_i×δ_i) is called the 'annuity factor' or 'PV01' — it represents the PV of $1 received each period.

Formula

DF(T) = e^{-r(T) \cdot T}

Related Terms

Equity Forward Contract

A commitment to buy or sell an equity at a fixed price F₀(T) at a future date T, priced to have zero value at inception.

FX Forward Rate

The agreed exchange rate for a future currency transaction, derived from Covered Interest Rate Parity.

Risk-Neutral Probability

The artificial probability measure under which all assets earn the risk-free rate, used to price derivatives by expectation.