In this paper we propose a continuous time model for modeling the dynamics of a commodity price. In particular, we focus on the term structure of future prices under the assumption that the underlying asset price follows an exponential CARMA(p, q) model where the driving noise is a Time Changed Brownian motion. The use of CARMA models well suits a market where if a shock occurs its effect does not vanish gradually but it may induce a more complex dynamics for the asset. The obtained formula is strictly connected to the cumulant generating function of the subordinator process in the Time Changed Brownian Motion.

Pricing of Futures with a CARMA(p, q) Model Driven by a Time Changed Brownian Motion / L. Mercuri, A. Perchiazzo, E. Rroji - In: Mathematical and Statistical Methods for Actuarial Sciences and Finance / [a cura di] M. Corazza, M. Gilli, C. Perna, C. Pizzi, M. Sibillo. - [s.l] : Springer, 2021. - ISBN 978-3-030-78964-0. - pp. 343-348 [10.1007/978-3-030-78965-7_50]

Pricing of Futures with a CARMA(p, q) Model Driven by a Time Changed Brownian Motion

L. Mercuri;
2021

Abstract

In this paper we propose a continuous time model for modeling the dynamics of a commodity price. In particular, we focus on the term structure of future prices under the assumption that the underlying asset price follows an exponential CARMA(p, q) model where the driving noise is a Time Changed Brownian motion. The use of CARMA models well suits a market where if a shock occurs its effect does not vanish gradually but it may induce a more complex dynamics for the asset. The obtained formula is strictly connected to the cumulant generating function of the subordinator process in the Time Changed Brownian Motion.
CARMA; Futures; Pricing
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/930046
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