Autoregressive gamma processes

Gouriéroux, Christian; Jasiak, Joann

doi:10.1002/for.978

“…Therefore, we model RV as an autoregressive gamma process (see Gourieroux and Jasiak, 2006), with p-lags. In our model we set p = 22.…”

Section: Realized Volatility Dynamicsmentioning

confidence: 99%

Realizing smiles: Options pricing with realized volatility

Corsi¹,

Fusari²,

Vecchia³

2013

Journal of Financial Economics

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Bates, our referee, for helpful comments and suggestions. We are also grateful to Torben Andersen, Giovanni Barone-Adesi, Francesco Permanent repository linkCorielli, Christian Gourieroux, Peter Gruber, Patrick Gagliardini, Loriano Mancini, Nour Meddahi, Alain Monfort, Fulvio Pegoraro, Roberto Renó, Viktor Todorov, and Fabio Trojani for their constructive discussions and remarks. We also thank the participants at the SoFiE conference held in Chicago. All errors are our own responsibility. The authors acknowledge the Swiss National Science Foundation Pro*Doc program, the NCCR FinRisk, and the Swiss Finance Institute for partial financial support. AbstractWe develop a discrete-time stochastic volatility option pricing model exploiting the information contained in the Realized Volatility (RV), which is used as a proxy of the unobservable log-return volatility. We model the RV dynamics by a simple and effective long-memory process, whose parameters can be easily estimated using historical data. Assuming an exponentially affine stochastic discount factor, we obtain a fully analytic change of measure. An empirical analysis of Standard and Poor's 500 index options illustrates that our model outperforms competing time-varying and stochastic volatility option pricing models.

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“…The second example that we discuss is the class of realized volatility models known as Autoregressive Gamma Processes (ARG) introduced in Gourieroux and Jasiak (2006), to whom the Heterogeneous Autoregressive Gamma (HARG) model presented in belongs. The process RV t is an ARG(p) if and only if its conditional distribution given (RV t−1 , .…”

Section: General Frameworkmentioning

confidence: 99%

“…Following the reasoning in Appendix F in Gourieroux and Jasiak (2006) one can derive the stationarity condition for RV t process:…”

Section: Physical and Risk-neutral Worldsmentioning

confidence: 99%

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Smile from the past: A general option pricing framework with multiple volatility and leverage components

Majewski

¹

,

Bormetti

²

,

Corsi

³

2015

Journal of Econometrics

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In the current literature, the analytical tractability of discrete time option pricing models is guaranteed only for rather specific types of models and pricing kernels. We propose a very general and fully analytical option pricing framework, encompassing a wide class of discrete time models featuring multiple-component structure in both volatility and leverage, and a flexible pricing kernel with multiple risk premia. Although the proposed framework is general enough to include either GARCH-type volatility, Realized Volatility or a combination of the two, in this paper we focus on realized volatility option pricing models by extending the Heterogeneous Autoregressive Gamma (HARG) model of to incorporate heterogeneous leverage structures with multiple components, while preserving closed-form solutions for option prices. Applying our analytically tractable asymmetric HARG model to a large sample of S&P 500 index options, we demonstrate its superior ability to price out-of-the-money options compared to existing benchmarks.

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“…The resulting model belongs to the family of autoregressive gamma processes, a class of discrete-time affine processes introduced by Gourieroux and Jasiak (2006). Due to this combination, our new model features both long-memory and affine structure.…”

Section: Introductionmentioning

confidence: 99%

Realizing Smiles: Options Pricing with Realized Volatility

Corsi

¹

,

Fusari

²

,

Vecchia

³

2011

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Bates, our referee, for helpful comments and suggestions. We are also grateful to Torben Andersen, Giovanni Barone-Adesi, Francesco Permanent repository linkCorielli, Christian Gourieroux, Peter Gruber, Patrick Gagliardini, Loriano Mancini, Nour Meddahi, Alain Monfort, Fulvio Pegoraro, Roberto Renó, Viktor Todorov, and Fabio Trojani for their constructive discussions and remarks. We also thank the participants at the SoFiE conference held in Chicago. All errors are our own responsibility. The authors acknowledge the Swiss National Science Foundation Pro*Doc program, the NCCR FinRisk, and the Swiss Finance Institute for partial financial support. AbstractWe develop a discrete-time stochastic volatility option pricing model exploiting the information contained in the Realized Volatility (RV), which is used as a proxy of the unobservable log-return volatility. We model the RV dynamics by a simple and effective long-memory process, whose parameters can be easily estimated using historical data. Assuming an exponentially affine stochastic discount factor, we obtain a fully analytic change of measure. An empirical analysis of Standard and Poor's 500 index options illustrates that our model outperforms competing time-varying and stochastic volatility option pricing models.

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Autoregressive gamma processes

Cited by 180 publications

References 25 publications

Realizing smiles: Options pricing with realized volatility

Realizing smiles: Options pricing with realized volatility

Smile from the past: A general option pricing framework with multiple volatility and leverage components

Realizing Smiles: Options Pricing with Realized Volatility

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