The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing

Christensen, Kim; Thyrsgaard, Martin; Veliyev, Bezirgen

doi:10.1016/j.jeconom.2019.06.002

Cited by 9 publications

(3 citation statements)

References 82 publications

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“…We correct the log-volatility forecast via Jensen's inequality:E exp f (Z t ) = exp E f (Z t ) + 0.5var f (Z t ) , whichis suitable for Gaussian data. The distribution of realized variance is reportedly close to log-normal, see, e.g., Andersen,Bollerslev, Diebold, and Ebens (2001);Christensen, Thyrsgaard, and Veliyev (2019). var f (Z t ) is estimated from the unconditional variance of the residuals in the training and validation set.…”

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confidence: 91%

A Machine Learning Approach to Volatility Forecasting

Christensen

Siggaard

Veliyev

2022

Journal of Financial Econometrics

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We inspect how accurate machine learning (ML) is at forecasting realized variance of the Dow Jones Industrial Average index constituents. We compare several ML algorithms, including regularization, regression trees, and neural networks, to multiple heterogeneous autoregressive (HAR) models. ML is implemented with minimal hyperparameter tuning. In spite of this, ML is competitive and beats the HAR lineage, even when the only predictors are the daily, weekly, and monthly lags of realized variance. The forecast gains are more pronounced at longer horizons. We attribute this to higher persistence in the ML models, which helps to approximate the long memory of realized variance. ML also excels at locating incremental information about future volatility from additional predictors. Lastly, we propose an ML measure of variable importance based on accumulated local effects. This shows that while there is agreement about the most important predictors, there is disagreement on their ranking, helping to reconcile our results.

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confidence: 91%

A Machine Learning Approach to Volatility Forecasting

Christensen

Siggaard

Veliyev

2022

Journal of Financial Econometrics

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“…Using OV, we can estimate this distribution by a standard kernel density estimator. For the estimation of the marginal volatility distribution from the high-frequency returns, we compute the empirical characteristic function of the high-frequency returns and then perform a regularized inversion as done in Todorov and Tauchen (2012) (see Christensen et al, (2019) for an alternative approach). We note that this approach has the advantage of "built-in" robustness towards jumps; that is, unlike the computation of TV, it does not require explicit truncation of the returns, and the associated choice of a tuning parameter for it, to filter out the jumps.…”

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confidence: 99%

Information gains from using short‐dated options for measuring and forecasting volatility

Todorov

Zhang

2021

J of Applied Econometrics

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We study the gains from using short-dated options for volatility measurement and forecasting. Using option portfolios, we estimate nonparametrically spot volatility under weak assumptions for the underlying asset. This volatility estimator complements existing ones constructed from high-frequency returns. We show empirically, using the market index and Dow 30 stocks, that combining optimally return and option data can lead to nontrivial gains for volatility forecasting. These gains are due to "diversification" of the measurement error in the two volatility proxies. The information content of short-dated options, not spanned by the current spot volatility, is of limited relevance for volatility forecasting.

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“…The use of 5-minute observations to measure instantaneous variance is common and we think it is a reasonable compromise, but we should stress that it does not tell the whole story about what goes on at higher frequencies; see for instance Christensen et al (2019).…”

Section: Evidence From Realized Variancementioning

confidence: 99%

How Does the Volatility of Volatility Depend on Volatility?

Rømer

Poulsen

2020

Risks

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We investigate the state dependence of the variance of the instantaneous variance of the S&P 500 index empirically. Time-series analysis of realized variance over a 20-year period shows strong evidence of an elasticity of variance of the variance parameter close to that of a log-normal model, albeit with an empirical autocorrelation function that one-factor diffusion models fail to capture at horizons above a few weeks. When studying option market behavior (in-sample pricing as well as out-of-sample pricing and hedging over the period 2004–2019), messages are mixed, but systematic, model-wise. The log-normal but drift-free SABR (stochastic-alpha-beta-rho) model performs best for short-term options (times-to-expiry of three months and below), the Heston model—in which variance is stationary but not log-normal—is superior for long-term options, and a mixture of the two models does not lead to improvements.

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The realized empirical distribution function of stochastic variance with application to goodness-of-fit testing

Cited by 9 publications

References 82 publications

A Machine Learning Approach to Volatility Forecasting

A Machine Learning Approach to Volatility Forecasting

Information gains from using short‐dated options for measuring and forecasting volatility

How Does the Volatility of Volatility Depend on Volatility?

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