Asymptotic expansion for Barndorff-Nielsen and Shephard's stochastic volatility model

Hiroki Masuda, Nakahiro Yoshida

    Research output: Contribution to journalArticlepeer-review

    13 Citations (Scopus)

    Abstract

    With the help of a general methodology of asymptotic expansions for mixing processes, we obtain the Edgeworth expansion for log-returns of a stock price process in Barndorff-Nielsen and Shephard's stochastic volatility model, in which the latent volatility process is described by a stationary non-Gaussian Ornstein - Uhlenbeck process (OU process) with invariant selfdecomposable distribution on ℝ+. The present result enables us to simultaneously explain non-Gaussianity for short time-lags as well as approximate Gaussianity for long time-lags. The Malliavin calculus formulated by Bichteler, Gravereaux and Jacod for processes with jumps and the exponential mixing property of the OU process play substantial roles in order to ensure a conditional type Cramér condition under a certain truncation. Owing to several inherent properties of OU processes, the regularity conditions for the expansions can be verified without any difficulty, and the coefficients of the expansions up to any order can be explicitly computed.

    Original languageEnglish
    Pages (from-to)1167-1186
    Number of pages20
    JournalStochastic Processes and their Applications
    Volume115
    Issue number7
    DOIs
    Publication statusPublished - Jul 2005

    All Science Journal Classification (ASJC) codes

    • Statistics and Probability
    • Modelling and Simulation
    • Applied Mathematics

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