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Quantitative Finance · शब्दावली

Stochastic-local volatility model क्या है?

Definition 20.9 Derivatives and Volatility · अध्याय 20 — FX Derivatives

A stochastic-local volatility model (SLV) lets the underlying’s volatility be the product of a function of time and spot and a stochastic factor:

dStSt=(rd−rf) dt+L(t,St)vt dWt1,dvt=κ(vˉ−vt) dt+ληvt dWt2,\frac{dS_t}{S_t}=(r_d-r_f)\,dt+L(t,S_t)\sqrt{v_t}\,dW^1_t,\qquad dv_t=\kappa(\bar v-v_t)\,dt+\lambda\eta\sqrt{v_t}\,dW^2_t,

with a mixing weight λ∈[0,1]\lambda\in[0,1] scaling the volatility of variance: λ=0\lambda=0 reduces the model to local volatility and λ=1\lambda=1 with L(t,S)=1L(t,S)=1 to Heston.

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