Small time central limit theorems for semimartingales with applications

Stefan Gerhold, Max Kleinert, Piet Porkert, Mykhaylo Shkolnikov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We give conditions under which the normalized marginal distribution of a semimartingale converges to a Gaussian limit law as time tends to zero. In particular, our result is applicable to solutions of stochastic differential equations with locally bounded and continuous coefficients. The limit theorems are subsequently extended to functional central limit theorems on the process level. We present two applications of the results in the field of mathematical finance: to the pricing of at-the-money digital options with short maturities and short time implied volatility skews.

Original languageEnglish (US)
Pages (from-to)723-746
Number of pages24
JournalStochastics
Volume87
Issue number5
DOIs
StatePublished - Sep 3 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation

Keywords

  • central limit theorem
  • digital option
  • functional central limit theorem
  • implied volatility skew
  • semimartingale

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