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Quantitative Finance · शब्दावली

ARCH and GARCH models, volatility persistence क्या है?

अन्य नाम: ARCH model · GARCH model · volatility persistence

Definition 18.2 Quantitative Methods · अध्याय 18 — Volatility Models

In an ARCH model (Engle, 1982), rt=htztr_t = \sqrt{h_t}z_t with iid standardised ztz_t and ht=ω+∑i=1qαirt−i2h_t = \omega + \sum_{i=1}^q\alpha_ir_{t-i}^2. The GARCH model (Bollerslev, 1986) adds lagged variances; GARCH(1,1) is ht=ω+αrt−12+βht−1h_t = \omega + \alpha r_{t-1}^2 + \beta h_{t-1} with ω>0\omega > 0, α,β≥0\alpha, \beta \ge 0. Its volatility persistence is α+β\alpha + \beta, the rate at which a variance shock decays.

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