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Quantitative Finance · Glossário

O que é Black–Scholes equation?

Também chamado de: Black--Scholes equation

Definition 3.2 Derivatives and Volatility · Capítulo 3 — Black–Scholes Three Ways

The Black–Scholes equation is the parabolic partial differential equation

∂tV+(r−q)S ∂SV+12σ2S2 ∂SSV−rV=0,V(T,S)=g(S),\partial_tV+(r-q)S\,\partial_SV+\tfrac12\sigma^2S^2\,\partial_{SS}V-rV=0, \qquad V(T,S)=g(S),

satisfied by the value of any European claim on the share in the Black–Scholes model.

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