Finite Mixture Approximation of CARMA(p,q) Models

Lorenzo Mercuri; Andrea Perchiazzo; Edit Rroji

doi:10.1137/20M1363248

Finite Mixture Approximation of CARMA(p,q) Models

Lorenzo Mercuri, Andrea Perchiazzo, Edit Rroji

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper we show how to approximate the transition density of a CARMA(p,q) model driven by a time-changed Brownian motion based on the Gauss-Laguerre quadrature. This approach allows us to introduce an estimation method that maximizes a likelihood function constructed using the approximated transition density. We also provide formulas for the futures term structures and for prices of options written on futures when the underlying follows an exponential CARMA(p,q) model.

Original language	English
Pages (from-to)	1416-1458
Number of pages	43
Journal	SIAM Financial Mathematics
Volume	12
Issue number	4
DOIs	https://doi.org/10.1137/20M1363248
Publication status	Published - 2021

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© 2021 Society for Industrial and Applied Mathematics.

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abstract = "In this paper we show how to approximate the transition density of a CARMA(p,q) model driven by a time-changed Brownian motion based on the Gauss-Laguerre quadrature. This approach allows us to introduce an estimation method that maximizes a likelihood function constructed using the approximated transition density. We also provide formulas for the futures term structures and for prices of options written on futures when the underlying follows an exponential CARMA(p,q) model.",

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AB - In this paper we show how to approximate the transition density of a CARMA(p,q) model driven by a time-changed Brownian motion based on the Gauss-Laguerre quadrature. This approach allows us to introduce an estimation method that maximizes a likelihood function constructed using the approximated transition density. We also provide formulas for the futures term structures and for prices of options written on futures when the underlying follows an exponential CARMA(p,q) model.

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JO - SIAM Financial Mathematics

JF - SIAM Financial Mathematics

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Finite Mixture Approximation of CARMA(p,q) Models

Abstract

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