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1 Markets I: The Ecosystem and Exchange-Traded Marketsالأسواق عبر الإنترنت 2 Markets II: Rates, FX and Creditالأسواق عبر الإنترنت 3 Markets III: Commodities, Energy and Cryptoالأسواق عبر الإنترنت 4 Quantitative Methodsالأساليب عبر الإنترنت 5 Derivatives and Volatilityالمشتقات عبر الإنترنت 6 Rates, Credit, XVA and Riskالفائدة والائتمان والمخاطر عبر الإنترنت 7 Research Craft: Predictors, Backtests, Measurement, Portfoliosالبحث عبر الإنترنت 8 Strategies I: Equities and Futuresالاستراتيجيات عبر الإنترنت 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desksالاستراتيجيات عبر الإنترنت 10 Microstructure and Executionالتنفيذ عبر الإنترنت 11 Market Making and High-Frequency Tradingصناعة السوق عبر الإنترنت 12 Machine Learning for Marketsتعلم الآلة عبر الإنترنت 13 Low-Latency Softwareالتكنولوجيا عبر الإنترنت 14 Networks, Hardware and Trading Infrastructureالتكنولوجيا عبر الإنترنت 15 Research, Data and Risk Platformsالتكنولوجيا عبر الإنترنت 16 The Desk and the Firmالشركة عبر الإنترنت 17 The Industry: Firms, Roles and Careersالمسارات المهنية عبر الإنترنت 18 The Interview Bookالمسارات المهنية عبر الإنترنت
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Quantitative Finance · المسرد

ما معنى Rough volatility؟

Definition 12.5 Derivatives and Volatility · الفصل 12 — Rough Volatility and Forward-Variance Models

Rough volatility is the property, and the class of models built on it, that the logarithm of instantaneous volatility behaves at short time scales like a fractional Brownian motion with Hurst exponent H<12H<\frac12, typically near 0.1. Its paths are rougher than any diffusion’s: the typical move over a lag Δ\Delta scales like ΔH\Delta^H rather than Δ1/2\Delta^{1/2}.

Left: the structure function of simulated daily log-volatility over eight years. The slope on log-log axes is 2H. The rough path has H=0.1; the diffusion is an Ornstein–Uhlenbeck process; the third series is the diffusion seen through a realised-variance estimate with a 0.08 error in log. Right: the published estimates for 21 indices. Data: the chapter’s code; Gatheral, Jaisson and Rosenbaum (2014), table B.1.
Figure 12.3. Left: the structure function of simulated daily log-volatility over eight years. The slope on log-log axes is 2H2H. The rough path has H=0.1H=0.1; the diffusion is an Ornstein–Uhlenbeck process; the third series is the diffusion seen through a realised-variance estimate with a 0.08 error in log. Right: the published estimates for 21 indices. Data: the chapter’s code; Gatheral, Jaisson and Rosenbaum (2014), table B.1.
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