关键词: 价格极差, CARR模型, 拟得分驱动, 波动的波动, QSD-CHARR

Abstract:

The latent volatility process of asset returns is relevant for a wide variety of applications， such as option pricing and risk management， and return-based volatility models， including GARCH models and related extensions， are widely used to model the dynamics of volatility. Standard return-based models mainly utilize daily returns （typically squared returns） to extract information about the current level of volatility and to form out-of-sample forecast. It is， however， well-known that squared returns are quite noisy proxies of volatility， which further translates to a relatively poor performance of related models. Volatility measures based on high-frequency financial data are far more informative about the “true” volatility than is the square return， but they are readily available for only a small number of assets. A sub-optimal alternative is to employ range-based volatility measures which are constructed from daily high and low prices， and achieve significantly higher efficiency than squared returns.A benchmark model for describing the dynamic feature of range-based measures is the conditional autoregressive range （CARR） model and it generally provides far more accurate volatility nowcast and forecast than comparable GARCH-type models. Despite its empirical superiority， CARR model implicitly imposes a strong link between the conditional distribution of volatility measures and the updating equation of volatility， which is not always desirable. More importantly， it formulates volatility as a function of lagged samples， thus ignoring the contemporaneous observations which is apparently more informative about the current level of volatility and the empirically relevant “volatility of volatility” effect， that is， the conditional heteroskedasticity of volatility.Inspired by the real-time GARCH models of Smetanina （2017）， the SHARV models of Ding （2023） and the quasi score-driven models of Blasques et al. （2023）， a new range-based volatility model， Quasi Score-Driven Conditional Heteroskedastic AutoRegressive Range （QSD-CHARR） model， is introduced that incorporates a quasi score-driven term in the volatility dynamics which generalizes the corresponding term in CARR model， and accounts for contemporaneous information and “volatility of volatility” effect simultaneously. Compared to the news impact curve of CARR model， that of QSD-CHARR model presents a more reasonable pattern. The conditional distribution of volatility measures is derived and the QMLE of parameters is defined. A preliminary Monte Carlo study shows that the QMLE performs reasonably well in finite samples. An empirical application utilizing daily Parkinson estimator series of Shanghai securities composite index and Standard & Poor’s 500 index reveals that a parsimonious QSD-CHARR structure leads to substantial improvements in volatility filtering and short-period volatility forecasting over CARR models， and the results highlight the empirical relevance of contemporaneous information and the conditional heteroskedasticity of volatility.

Key words: price range, CARR, quasi score-driven, volatility of volatility, QSD-CHARR