Continuous-Time Models and Discrete Observations for Financial Data

Chapter
Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Abstract

We introduce continuous-time financial models and the stochastic processes of diffusions and jumps. This chapter reviews recent developments in mathematical finance and financial econometrics and then summarizes the basic financial problems that motivate the SIML estimation in this book.

References

  1. Bachelier, L. 1900. Th\(\acute{e}\)orie de Sp\(\acute{e}\)culation. In A translation in random character of stock prices, ed. P. Coortner, 17–79. MIT Press.Google Scholar
  2. Billingsley, P. 1995. Probability and measure, 3rd ed. New York: Wiley.MATHGoogle Scholar
  3. Black, F., and M. Scholes. 1972. The pricing options and corporate liabilities. Journal of Political Economy 81: 7637–659.MathSciNetMATHGoogle Scholar
  4. Ikeda, N., and S. Watanabe. 1989. Stochastic differential equations and diffusion processes, 2nd ed. North-Holland.Google Scholar
  5. Kunitomo, N., and D. Kurisu. 2017. Effects of jumps and small noise in high-frequency financial econometrics. Asia-Pasific Financial Markets 24: 39–73.CrossRefGoogle Scholar
  6. Kurisu, D. 2017. Power variations and testing for co-jumps: the small noise approach. Scandinavian Journal of Statistics. http://onlinelibrary.wiley.com/doi/10.1111/sjos.12309/abstract.
  7. Jacod, J., and P. Protter. 2012. Discretization of Processes. Berlin: Springer.CrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.School of Political Science and EconomicsMeiji UniversityTokyoJapan
  2. 2.Graduate School of EconomicsThe University of TokyoBunkyo-kuJapan
  3. 3.School of EngeneeringTokyo Institute of TechnologyTokyoJapan

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