Nonparametric implied Lévy densities

Qin, Likuan; Todorov, Viktor

doi:10.1214/18-aos1703

Cited by 12 publications

(9 citation statements)

References 33 publications

(47 reference statements)

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“…For the analysis here, we only need 𝜂 t up to a constant as a multiple of 𝜂 t will obviously carry the same predictive content. That said, the short-dated options contain information to identify completely the jump compensator 𝜂 t dt ⊗ F(dx) (see Qin & Todorov, 2019).…”

Section: Risk-neutral Jump Variation Measures and Their Information C...mentioning

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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Section: Risk-neutral Jump Variation Measures and Their Information C...mentioning

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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“…For example, using the above-mentioned spanning results, the cross-section of options can recover the conditional characteristic function E Q t (e iux t+τ ), for u ∈ R. Hence, for the identification condition needed to establish Theorem 2, it suffices to show that θ 0 and S t uniquely identify the conditional characteristic function for the available tenors, which is equivalent to θ 0 and S t uniquely identifying the conditional risk-neutral return distribution for the available tenors. Specifically, if the maturity of the shortest available tenor goes to zero asymptotically, then, as shown by Qin and Todorov (2018), we can identify the density of ν Q (dt, dx) from such short-dated options. In turn, longer dated options may be used to identify the additional parameters that control the risk-neutral dynamics of the latent factors.…”

Section: Consistency Of the Pls Estimatormentioning

confidence: 99%

Inference for Option Panels in Pure-Jump Settings

Andersen¹,

Fusari

Todorov³

et al. 2018

Econom. Theory

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We develop parametric inference procedures for large panels of noisy option data in a setting, where the underlying process is of pure-jump type, i.e., evolves only through a sequence of jumps. The panel consists of options written on the underlying asset with a (different) set of strikes and maturities available across the observation times. We consider an asymptotic setting in which the cross-sectional dimension of the panel increases to infinity, while the time span remains fixed. The information set is augmented with high-frequency data on the underlying asset. Given a parametric specification for the risk-neutral asset return dynamics, the option prices are nonlinear functions of a time-invariant parameter vector and a time-varying latent state vector (or factors). Furthermore, no-arbitrage restrictions impose a direct link between some of the quantities that may be identified from the return and option data. These include the so-called jump activity index as well as the time-varying jump intensity. We propose penalized least squares estimation in which we minimize the L2 distance between observed and model-implied options. In addition, we penalize for the deviation of the model-implied quantities from their model-free counterparts, obtained from the high-frequency returns. We derive the joint asymptotic distribution of the parameters, factor realizations and high-frequency measures, which is mixed Gaussian. The different components of the parameter and state vector exhibit different rates of convergence, depending on the relative (asymptotic) informativeness of the high-frequency return data and the option panel.

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“…In view of the randomness of asset price fluctuation, most studies use stochastic analysis theory to estimate fluctuation [21,32]. In the research of stochastic volatility, it is generally assumed that there are jumps (large fluctuations) in asset prices process [37] and the return rate of assets prices obeys a continuous semi-martingale process [29,39]. Barndorff Nielsen and Shephard creatively constructed the realized quadratic variation estimator to decompose the continuous fluctuation and jump fluctuation in the realized fluctuation [7].…”

Section: Introductionmentioning

confidence: 99%

Modeling dynamic volatility under uncertain environment with fuzziness and randomness

Hui¹,

Sun²,

Zhou³

2022

Preprint

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Predicting the dynamic volatility in financial market provides a promising method for risk prediction, asset pricing and market supervision. Barndorff-Nielsen and Shephard model (BN-S) model, used to capture the stochastic behavior of high-frequency time series, is an accepted stochastic volatility model with Lévy process. Although this model is attractive and successful in theory, it needs to be improved in application. We build a new generalized BN-S model suitable for uncertain environment with fuzziness and randomness. This new model considers the delay phenomenon between price fluctuation and volatility changes, solves the problem of the lack of long-range dependence of classic models. Calculation results show that new model outperforms the classic model in volatility forecasting. Experiments on Dow Jones Industrial Average futures price data are conducted to verify feasibility and practicability of our proposed approach. Numerical examples are provided to illustrate the theoretical result. Three machine learning algorithms are applied to estimate new model parameter. Compared with the classical model, our method effectively combines the uncertain environmental characteristics, which makes the prediction of dynamic volatility more flexible and has ideal performance.

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Nonparametric implied Lévy densities

Cited by 12 publications

References 33 publications

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

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

Inference for Option Panels in Pure-Jump Settings

Modeling dynamic volatility under uncertain environment with fuzziness and randomness

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