Definition 10.1 Derivatives and Volatility · Chapter 10 — Stochastic Volatility A stochastic volatility model specifies, under the pricing measure, dSt=(r−q)St dt+vt St dWt1,dvt=α(vt) dt+β(vt) dWt2,d⟨W1,W2⟩t=ρ dt,dS_t=(r-q)S_t\,dt+\sqrt{v_t}\,S_t\,dW^1_t,\qquad dv_t=\alpha(v_t)\,dt+\beta(v_t)\,dW^2_t,\qquad d\langle W^1,W^2\rangle_t=\rho\,dt,dSt=(r−q)Stdt+vtStdWt1,dvt=α(vt)dt+β(vt)dWt2,d⟨W1,W2⟩t=ρdt, where the instantaneous variance vtv_tvt is a second state variable. The spot–volatility correlation ρ\rhoρ ties the two shocks together, and the scale of β\betaβ relative to vvv is the volatility of volatility. Read in context →
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