Gaussian moving averages, semimartingales and option pricing

By Patrick Cheridito. 2004

53 citations recorded by the source corpus.

We provide a characterization of the Gaussian processes with stationary increments that can be represented as a moving average with respect to a two-sided Brownian motion. For such a process we give a necessary and sufficient condition to be a semimartingale with respect to the filtration generated by the two-sided Brownian motion. Furthermore, we show that this condition implies that the process is either of finite variation or a multiple of a Brownian motion with respect to an equivalent probability measure. As an application we discuss the problem of option pricing in financial models driven by Gaussian moving averages with stationary increments. In particular, we derive option prices in a regularized fractional version of the Black-Scholes model.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/c383585cafad613c6e0ea21d339f1421a4894e2a

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In Economics and Econometrics

In Finance

Citations in the corpus

Sample path properties of bifractional Brownian motion (2006, background): “Many authors have also proposed using more general self-similar Gaussian processes and random fields as stochastic models (see, e.g., Addie et al. [1], Anh et al. [3], Benassi et al. [7], Mannersalo and Norros [30], Bonami and Estrade [12], Cheridito [13] and Benson et al. [8]).”