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Quantitative Finance · Glosarium

Apa itu SABR model?

Definition 11.1 Derivatives and Volatility · Bab 11 — SABR and Smile Dynamics

The SABR model (stochastic alpha, beta, rho) describes a forward FtF_t, driftless under its forward measure, and its volatility αt\alpha_t:

dFt=αtFtβ dWt1,dαt=ν αt dWt2,d⟨W1,W2⟩t=ρ dt,dF_t=\alpha_tF_t^{\beta}\,dW^1_t,\qquad d\alpha_t=\nu\,\alpha_t\,dW^2_t,\qquad d\langle W^1,W^2\rangle_t=\rho\,dt,

with an exponent β∈[0,1]\beta\in[0,1], a correlation ρ\rho and a volatility of volatility ν\nu; the initial value α=α0\alpha=\alpha_0 is the fourth parameter.

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