Estimation of stochastic volatility models by nonparametric filtering

Abstract

A new estimation method of stochastic volatility models is proposed based on the nonparametric …lter of the instantaneous volatility process of Kristensen (2008). We use standard estimation methods for fully observed di¤usion processes but with the …ltered volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and we give theoretical results for both. The proposed estimators will carry biases due to the use of the …ltered volatility instead of the actual volatility, but under regularity conditions this vanishes asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and we give theoretical results for both. A simulation study examines the …nite-sample properties of the proposed estimators.The authors wish to thank Professor Bruce Hansen for fruitful discussions and helpful suggestions. They also wish to thank participants at a seminar at University of Wisconsin, the CREATES opening Conference, and the 2007 EC 2 Meeting for comments and suggestions.

Matching Function Equilibria: Existence, Uniqueness and Estimation

“…Non-additive random utility models have been studied extensively in Apesteguia and Ballester (2014) and Kristensen, Nesheim, and de Paula (2015). These models are relevant in a wide range of settings, in particular those involving (waiting) time.…”

“…This literature goes back at least to Gale and Nikaido (1965), who showed that a differentiable function is injective if its domain is rectangular and its Jacobian is everywhere a P -matrix. Following the results of Gale and Nikaido (1965), Chiappori and Komunjer (2009) and Kristensen, Nesheim, and de Paula (2015) imposed assumptions on the functional form and support to ensure invertibility in multinomial choice and nonadditive random utility models. The main limitation of applying Gale and Nikaido (1965)'s result is that these restrictions (on differentiability, support, and the Jacobian) are often violated and/or are difficult to check.…”

“…Berry 1994;Berry, Levinsohn, and Pakes 1995;Esteban and Shum 2007;Song 2007), and dynamic discrete choice models (e.g. Hotz and Miller 1993;Aguirregabiria and Mira 2002;Bajari, Benkard, and Levin 2007;Kristensen, Nesheim, and de Paula 2015).…”

“…This literature is split between additive random utility models (ARUMs hereafter) and non-additive random utility models (NARUMs hereafter). See e.g., Berry (1994), Berry, Levinsohn, and Pakes (1995), Esteban and Shum (2007), and Song (2007) on ARUMs, and Cohen and Einav (2007), Apesteguia and Ballester (2014), Kristensen, Nesheim, and de Paula (2015) on NARUMs. 7…”