Abstract
This chapter introduces an algorithm called particle filtering used for the inference of the most likely sample path of a hidden process driving stock prices in nested models. Particle filtering is a simulation-based method approximating the likelihood of observations. This approach allows us to fit processes for which the probability density function does not admit any closed form expression. The first part of the chapter introduces particle filtering applied to the Heston model for stock prices. In this dynamic, the instantaneous return is Brownian with a mean reverting variance. As the particle filter yields a non-smooth estimate of the log-likelihood function, we propose in the second part of the chapter to combine the particle filter with the Metropolis–Hastings procedure of Chap. 2 to estimate parameters. This approach, called the Particle Markov Chain Monte Carlo (PMCMC) algorithm, will be used in Chap. 10 to quantify illiquidity and in Chap. 9 to fit Volterra processes. The particle filter serves in Chap. 4 to estimate the sample path of jump intensity.
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Hainaut, D. (2022). Particle Filtering and Estimation. In: Continuous Time Processes for Finance. Bocconi & Springer Series, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-031-06361-9_3
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DOI: https://doi.org/10.1007/978-3-031-06361-9_3
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