Advertisement

Filtering for Stochastic Volatility by Using Exact Sampling and Application to Term Structure Modeling

  • ShinIchi AiharaEmail author
  • Arunabha Bagchi
  • Saikat Saha
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 325)

Abstract

The Bates stochastic volatility model is widely used in the finance problem and the sequential parameter estimation problem becomes important. By using the exact simulation technique, a particle filter for estimating stochastic volatility is constructed. The system parameters are sequentially estimated with the aid of parallel filtering algorithm with the new resampling procedure. The proposed filtering procedure is also applied to the modeling of the term structure dynamics. Simulation studies for checking the feasibility of the developed scheme are demonstrated.

Keywords

Particle filter Stochastic volatility Parameter identification Adaptive filter 

References

  1. 1.
    Aihara, S., Bagchi, A.: Filtering and identification of Heston’s stochastic volatility and its market risk. J. Econ. Dyn. Control 30, 2363–2388 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Aihara, S., Bagchi, A.: Filtering and identification of affine term structures from yield curve data. IJTAF 13, 259–283 (2010)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Aihara, S., Bagchi, A., Saha, S.: Estimating volatility and model parameters of stochastic volatility models with jumps using particle filter. In: Proceedings of 17th IFAC World Congress, vol. 15/1, pp. 6490–6495 (2008)Google Scholar
  4. 4.
    Aihara, S., Bagchi, A., Saha, S.: Identification of bates stochastic volatility model by using non-central chi-square random generation method. In: Proceedings of IEEE ICASSP 2012, pp. 3905–3908 (2012)Google Scholar
  5. 5.
    Anderson, B.D.O., Moore, J.B.: Optimal Filtering. Prentice-Hall Inc, Englewood Cliffs (1979)zbMATHGoogle Scholar
  6. 6.
    Bensoussan, A.: Stochastic Control of Partially Observable Systems. Cambridge University Press, Cambridge (1992)CrossRefzbMATHGoogle Scholar
  7. 7.
    Broadie, M., Kaya, O.: Exact simulation of stochastic volatility and other affine jump diffusion processes. Oper. Res. 54(2), 217–231 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Cappé, O., Moulines, E., Rydén, T.: Inference in Hidden Markov Models. Springer Science+Business Media Inc, New York (2005)Google Scholar
  9. 9.
    Doucet, A., Godsil, S., Andrieu, C.: On sequential monte carlo sampling methods for bayesian filtering. Stat. Comput. 10, 197–208 (2000)CrossRefGoogle Scholar
  10. 10.
    Javaheri, A.: Inside Volatility Arbitrage. Wiley, Hoboken (2005)Google Scholar
  11. 11.
    Johannes, M., Polson, N.: MCMC method for financial econometrics. In: Ait-Sahalia, Y., Hansen, L. (eds.) Handbook of Financial Econometrics. Elsevier, Amsterdam (2006)Google Scholar
  12. 12.
    Kalman, R., Bucy, R.: New results in linear filtering and prediction theory. Trans. ASME J. Basic Eng. 83(Series D), 95–108 (1961)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Smith, R.: An almost exact simulation method for the heston model. J. Comput. Finance 11(1), 115–125 (2008)Google Scholar
  14. 14.
    van Haastrecht, A., Pelsser, A.: Efficient, almost exact simulation of the heston stochastic volatility model. IJTAF 13, 1–43 (2010)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer MediaTokyo University of Science SuwaChinoJapan
  2. 2.Department of Applied MathematicsUniversity of TwenteEnschedThe Netherlands
  3. 3.Department of Electrical EngineeringLinköping UniversityLink öpingSweden

Personalised recommendations