Maximum-likelihood estimation for diffusion processes via closed-form density expansions

By Chenxu Li. 2013

79 citations recorded by the source corpus.

This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and accompanied by an algorithm containing only basic and explicit calculations for delivering any arbitrary order of the expansion. The likelihood function is thus approximated explicitly and employed in statistical estimation. The performance of our method is demonstrated by Monte Carlo simulations from implementing several examples, which represent a wide range of commonly used diffusion models. The convergence related to the expansion and the estimation method are theoretically justified using the theory of Watanabe [Ann. Probab. 15 (1987) 1-39] and Yoshida [J. Japan Statist. Soc. 22 (1992) 139-159] on analysis of the generalized random variables under some standard sufficient conditions.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/54f4a953776f81cf7216d955af1b9cb315b437cb

Citations in the corpus

• Hermite Polynomial Based Expansion of European Option Prices (2014, unknown): “…discussed in Hagan and Woodward (1999), Hagan et al. (2002), Fouque et al. (2000), Lewis (2000), Berestycki et al. (2002), Medvedev and Scaillet (2007), Henry-Labordere (2008), Takahashi et al. (2009), Gatheral et al. (2012), Li (2013a), Li (2013b), Lorig et al. (2013), and Forde et al. (2013).”