Black's formula

Quantitative Finance Glossary

Closed-form pricing of European options on forwards/futures: C = e^-rT,[F,N(d_1) - K,N(d_2)], with d_1 = (ln(F/K) + tfrac12σ^2 T)/(σ√(T)), d_2 = d_1 - σ√(T). The market standard for caplets (replacing F with the forward rate L and multiplying by accrual τ), swaptions (under the annuity measure), and commodity futures options. Black-76 is the workhorse rates-and-commodities cousin of BSM.

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