In this paper we consider two processes driven by diffusions and jumps. We consider both finite activity and infinite activity jump components. Given discrete observations we disentangle the covariation between the two diffusion parts from the co-jumps. A commonly used approach to estimate the diffusion covariation part is to take the sum of the cross products of the two processes increments; however this estimator can be highly biased in the presence of jump components, since it approaches the quadratic covariation containing also the co-jumps. Our estimator is based on a threshold principle allowing to isolate the jumps. As a consequence we find an estimator which is consistent. In the case of finite activity jump components the estimator is also asymptotically Gaussian. We assess the performance of our estimator for finite samples on four different simulated models.

Gobbi, F., & Mancini, C. (2007). Estimating the diffusion part of the covariation between two volatility models with jumps of Lévy type. In Applied and Industrial Mathematics in Italy II. Selected contributions from the 8th SIMAI Conference (pp.399-409). World Scientific Publishing.

Estimating the diffusion part of the covariation between two volatility models with jumps of Lévy type

Gobbi Fabio;
2007

Abstract

In this paper we consider two processes driven by diffusions and jumps. We consider both finite activity and infinite activity jump components. Given discrete observations we disentangle the covariation between the two diffusion parts from the co-jumps. A commonly used approach to estimate the diffusion covariation part is to take the sum of the cross products of the two processes increments; however this estimator can be highly biased in the presence of jump components, since it approaches the quadratic covariation containing also the co-jumps. Our estimator is based on a threshold principle allowing to isolate the jumps. As a consequence we find an estimator which is consistent. In the case of finite activity jump components the estimator is also asymptotically Gaussian. We assess the performance of our estimator for finite samples on four different simulated models.
978-9812709387
Gobbi, F., & Mancini, C. (2007). Estimating the diffusion part of the covariation between two volatility models with jumps of Lévy type. In Applied and Industrial Mathematics in Italy II. Selected contributions from the 8th SIMAI Conference (pp.399-409). World Scientific Publishing.
File in questo prodotto:
File Dimensione Formato  
SIMAI.pdf

non disponibili

Tipologia: PDF editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 539.49 kB
Formato Adobe PDF
539.49 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/1150216