Skip to main content

Stochastic Volatility Model with Jumps in Returns and Volatility: An R-Package Implementation

  • Conference paper
  • First Online:
Advances in Social Science Research Using R

Part of the book series: Lecture Notes in Statistics ((LNSP,volume 196))

Abstract

In this chapter we estimate the stochastic volatility model with jumps in return and volatility introduced by [7]. In this model the conditional volatility of returns can not only increase rapidly but also persistently. Moreover, as shown by [8], this new model performs better than previous models presenting almost no misspecification in the volatility process. We implement the model coding the algorithm using R language. We estimate the model parameters and latent variables using FTSE 100 daily returns. The values of some of our estimated parameters are close to values found in previous studies. Also, as expected, our estimated state variable paths show high probabilities of jumps in the periods of financial crisis.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bakshi, G., Cao, C., Chen, Z.: Empirical performance of alternative option pricing models. Journal of Finance 52, 2003 – 2049 (1997)

    Article  Google Scholar 

  2. Bates, D.: Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Review of Financial Studies 9, 69–107 (1996)

    Article  Google Scholar 

  3. Bates, D.: Post-’87 Crash fears in S&P 500 futures options. Journal of Econometrics 94, 181–238 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Black, F., Scholes, M.: The valuation of options and corporate liabilities. Journal of Political Economy 81, 637–654 (1973)

    Article  Google Scholar 

  5. Chernov, M., Gallant, A.R., Ghysels, E., Tauchen, G.E.: A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation. SSRN eLibrary (1999). DOI 10.2139/ssrn.189628

    Google Scholar 

  6. Cox, J.C., Ross, S.A.: The valuation of options for alternative stochastic processes. Journal of Financial Economics 3, 145–166 (1976)

    Article  Google Scholar 

  7. Duffie, D., Pan, J., Singleton, K.: Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68, 1343–1376 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Eraker, B., Johannes, M., Polson, N.: The Impact of Jumps in Volatility and Returns. Journal of Finance 58, 1269–1300 (2003)

    Article  Google Scholar 

  9. Heston, S.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies 6, 327–343 (1993)

    Article  Google Scholar 

  10. Hull, J.C., White, A.: The pricing of options on assets with stochastic volatilities. ,Journal of Finance 42, 281–300 (1987)

    Article  Google Scholar 

  11. Johannes, M., Polson, N.: Mcmc methods for continuous-time financial econometrics. In: Y. Ait-Sahalia, L. Hansen (eds.) Handbook of Financial Econometrics. Elsevier, New York (2003)

    Google Scholar 

  12. Merton, R.C.: Option Pricing when Underlying Stock Returns Are Discontinuous. Journal of Financial Economics 3(1–2), 125–144 (1976)

    Article  MATH  Google Scholar 

  13. Pan, J.: The jump-risk premia implicit in options: Evidence from an integrated time-series study. Journal of Financial Economics 63, 3–50 (2002)

    Article  Google Scholar 

  14. Rubinstein, M.: Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978. Journal of Finance 40(2), 455–80 (1985)

    Google Scholar 

  15. Scott, L.: Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates: Applications of Fourier inversion methods. Mathematical Finance 7, 413–426 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Scott, L.O.: Option pricing when the variance changes randomly: Theory, estimation, and an application. Journal of Financial and Quantitative Analysis 22, 419–438 (1987)

    Article  Google Scholar 

  17. Vinod, H.D.: Hands-on Intermediate Econometrics Using R: Templates for Extending Dozens of Practical Examples. World Scientific, Hackensack, NJ (2008). URL http://www.worldscibooks.com/economics/6895.html. ISBN 10-981-281-885-5.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Adjoa Numatsi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag New York

About this paper

Cite this paper

Numatsi, A., Rengifo, E.W. (2010). Stochastic Volatility Model with Jumps in Returns and Volatility: An R-Package Implementation. In: Vinod, H. (eds) Advances in Social Science Research Using R. Lecture Notes in Statistics(), vol 196. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1764-5_12

Download citation

Publish with us

Policies and ethics