Irregular Discretization Schemes

Jacod, Jean; Protter, Philip

doi:10.1007/978-3-642-24127-7_14

Cited by 6 publications

(34 citation statements)

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“…The upper bound depends on and , and for these terms to converge to zero equally fast, we should take . This is consistent with the literature on spot variance estimation; see, e.g., Jacod and Protter ( 2012 ).…”

Section: Estimation Of the Local Variancesupporting

confidence: 93%

“…If the volatility does not meet the boundedness condition, which it does not for most stochastic volatility models, one can resort to the localization technique from Sect. 4.4.1 in Jacod and Protter ( 2012 ). In most financial applications, however, Assumption (A) is not too stringent if the drift and volatility do not vary strongly over short time intervals, such as a day.…”

Section: Theoretical Frameworkmentioning

confidence: 95%

“…To estimate , we follow Jacod and Protter ( 2012 ) and apply a localized realized variance, which is defined over a block of log-price increments with . The RV computed over the time window , for , is then defined as follows: The corresponding penalized version is computed as or by using Proposition 2.1 with replaced by .…”

Section: Estimation Of the Local Variancementioning

confidence: 99%

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High-dimensional estimation of quadratic variation based on penalized realized variance

Christensen

Nielsen

Podolskij

2022

Stat Inference Stoch Process

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In this paper, we develop a penalized realized variance (PRV) estimator of the quadratic variation (QV) of a high-dimensional continuous Itô semimartingale. We adapt the principle idea of regularization from linear regression to covariance estimation in a continuous-time high-frequency setting. We show that under a nuclear norm penalization, the PRV is computed by soft-thresholding the eigenvalues of realized variance (RV). It therefore encourages sparsity of singular values or, equivalently, low rank of the solution. We prove our estimator is minimax optimal up to a logarithmic factor. We derive a concentration inequality, which reveals that the rank of PRV is—with a high probability—the number of non-negligible eigenvalues of the QV. Moreover, we also provide the associated non-asymptotic analysis for the spot variance. We suggest an intuitive data-driven subsampling procedure to select the shrinkage parameter. Our theory is supplemented by a simulation study and an empirical application. The PRV detects about three–five factors in the equity market, with a notable rank decrease during times of distress in financial markets. This is consistent with most standard asset pricing models, where a limited amount of systematic factors driving the cross-section of stock returns are perturbed by idiosyncratic errors, rendering the QV—and also RV—of full rank.

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Section: Estimation Of the Local Variancesupporting

confidence: 93%

Section: Theoretical Frameworkmentioning

confidence: 95%

Section: Estimation Of the Local Variancementioning

confidence: 99%

See 1 more Smart Citation

High-dimensional estimation of quadratic variation based on penalized realized variance

Christensen

Nielsen

Podolskij

2022

Stat Inference Stoch Process

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“…We note here that the application of the Law of Large Numbers with normalization for discretized processes (Jacod and Protter, 2012, Theorem 7.2.2(a)) here introduces an extra factor of 1∕ √ 𝑇, which did not appear in the original version in the book Jacod and Protter (2012) in which 𝑇 = 1 is assumed for simplicity.…”

Section: Appendix A: Proofs For Sectionmentioning

confidence: 99%

“…Using limit theorems in the spirit of Jacod and Protter (2012), we show that for frequent trades and small transaction costs, the limiting wealth dynamics can be computed in closed form. For a given target strategy, this in turn allows us to determine the optimal limit‐order exposure in closed form by a simple pointwise maximization.…”

Section: Introductionmentioning

confidence: 99%

A Leland model for delta hedging in central risk books

Muhle‐Karbe

Wang

Webster

2023

Mathematical Finance

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Using a tractable extension of the model of Leland (1985), we study how a delta-hedging strategy can realistically be implemented using market and limit orders in a centralized, automated market-making desk that integrates trading and liquidity provision for both options and their underlyings. In the continuous-time limit, the optimal limit-order exposure can be computed explicitly by a pointwise maximization. It is determined by the relative magnitudes of adverse selection, bid-ask spreads, and volatilities. The corresponding option price-from which the option can be replicated using market and limit orders-is characterized via a nonlinear PDE. Our results highlight the benefit of tactical liquidity provision for contrarian trading strategies, even for a trading desk that is not a competitive market maker. More generally, the paper also showcases how reduced-form models are competitive with "brute force" numerical approaches to market microstructure. Both the estimation of microstructure parameters and the simulation of the optimal trading strategy are made concrete and reconciled with real-life high frequency data.

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Robust estimation of integrated and spot volatility

Li,

Linton

2023

Journal of Econometrics

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Irregular Discretization Schemes

Cited by 6 publications

References 0 publications

High-dimensional estimation of quadratic variation based on penalized realized variance

High-dimensional estimation of quadratic variation based on penalized realized variance

A Leland model for delta hedging in central risk books

Robust estimation of integrated and spot volatility

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