Jump to ContentJump to Main Navigation
Show Summary Details
In This Section

Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

4 Issues per year


Cite Score 2016: 0.33

Mathematical Citation (MCQ) Quotient 2015: 0.29

Online
ISSN
2196-7040
See all formats and pricing
In This Section
Volume 33, Issue 1-2 (Jun 2016)

Issues

Implied basket correlation dynamics

Wolfgang Karl Härdle
  • Ladislaus von Bortkiewicz Chair of Statistics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany; and Sim Kee Boon Institute for Financial Economics, Singapore Management University, Administration Building, 81 Victoria Street, 188065, Singapore
  • Email:
/ Elena Silyakova
  • Corresponding author
  • Ladislaus von Bortkiewicz Chair of Statistics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
  • Email:
Published Online: 2016-07-28 | DOI: https://doi.org/10.1515/strm-2014-1176

Abstract

Equity basket correlation can be estimated both using the physical measure from stock prices, and also using the risk neutral measure from option prices. The difference between the two estimates motivates a so-called “dispersion strategy”. We study the performance of this strategy on the German market and propose several profitability improvement schemes based on implied correlation (IC) forecasts. Modelling IC conceals several challenges. Firstly the number of correlation coefficients would grow with the size of the basket. Secondly, IC is not constant over maturities and strikes. Finally, IC changes over time. We reduce the dimensionality of the problem by assuming equicorrelation. The IC surface (ICS) is then approximated from the implied volatilities of stocks and the implied volatility of the basket. To analyze the dynamics of the ICS we employ a dynamic semiparametric factor model.

Keywords: Correlation risk; dimension reduction; dispersion strategy; dynamic factor models

MSC 2010: 62H25; 62H15; 62H20

References

  • [1]

    Allen P. and Granger N., Correlation vehicles. Techniques for trading equity correlation, Technical Report, JPMorgan, London, 2005.

  • [2]

    Bai Z. D., Methodologies in spectral analysis of large dimensional random matrices, Statist. Sinica 9 (1999), 611–677.

  • [3]

    Bakshi G., Cao C. and Chen Z., Do call and underlying prices always move in the same direction?, Rev. Financial Stud. 13 (2000), no. 3, 549–584.

  • [4]

    Bakshi G., Kapadia N. and Madan D., Stock return characteristics, skew laws, and differential pricing of individual equity options, Rev. Financial Stud. 16 (2003), 101–143.

  • [5]

    Bickel P. J. and Levina E., Covariance regularization by thresholding, Ann. Statist. 36 (2008), no. 6, 2577–2604. [Web of Science]

  • [6]

    Bickel P. J. and Levina E., Regularized estimation of large covariance matrices, Ann. Statist. 36 (2008), no. 1, 199–227.

  • [7]

    Blair B. J., Poon S.-H. and Taylor S. J., Forecasting S&P100 volatility: The incremental information content of implied volatilities and high-frequency index returns, J. Econom. 105 (2001), no. 1, 5–26.

  • [8]

    Bollerslev T., Engle R. F. and Wooldridge J. M., A capital asset pricing model with time-varying covariances, J. Political Econom. 96 (1988), no. 1, 116–31.

  • [9]

    Bossu S., Strasser S. and Guichard R., Just what you need to know about variance swaps, Technical Report, JPMorgan, London, 2005.

  • [10]

    Bourgoin F., Stress-testing correlations: An application to portfolio risk management, Developments in Forecast Combination and Portfolio Choice, Wiley, New York, (2001).

  • [11]

    Breeden D. T. and Litzenberger R. H., Prices of state-contingent claims implicit in option prices, J. Business 51 (1978), no. 4, 621–51.

  • [12]

    Britten-Jones M. and Neuberger A. J., Option prices, implied price processes, and stochastic volatility, J. Finance 55 (2000), no. 2, 839–866.

  • [13]

    Campa J. M. and Chang P., The forecasting ability of correlations implied in foreign exchange options, J. Int. Money Finance 17 (1998), no. 6, 855–880.

  • [14]

    Carr P. and Madan D., Towards a theory of volatility trading, Reprinted in Option Pricing, Interest Rates, and Risk Management, Cambridge University Press, Cambridge (1998), 417–427.

  • [15]

    Carr P. and Wu L., Variance risk premiums, Rev. Financial Stud. 22 (2009), no. 3, 1311–1341.

  • [16]

    Christensen B. and Prabhala N., The relation between implied and realized volatility, J. Financial Econom. 50 (1998), no. 2, 125–150.

  • [17]

    Cont R. and Da Fonseca J., Dynamics of implied volatility surfaces, Quant. Finance 2 (2002), 45–60.

  • [18]

    Cox J. C., Ross S. A. and Rubinstein M., Option pricing: A simplified approach, J. Financial Econom. 7 (1979), 229–263.

  • [19]

    Demeterfi K., Derman E., Kamal M. and Zou J., More than you ever wanted to know about volatility swaps, Technical Report, Goldman Sachs, New York, 1999.

  • [20]

    Driessen J., Maenhout P. J. and Vilkov G., The price of correlation risk: Evidence from equity options, J. Finance 9 (2009), 1377–1406.

  • [21]

    Engle R., Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models, J. Bus. Econom. Statist. 20 (2002), no. 3, 339–350.

  • [22]

    Engle R. F., Shephard N. and Sheppard K., Fitting vast dimensional time-varying covariance models, Economics Series Working Papers 403, University of Oxford, Oxford, 2008.

  • [23]

    Fan J., Fan Y. and Lv J., High dimensional covariance matrix estimation using a factor model, J. Econom. 147 (2008), 186–197.

  • [24]

    Fengler M. R., Härdle W. K. and Mammen E., A semiparametric factor model for implied volatility surface dynamics, J. Financial Econom. 5 (2007), no. 2, 189–218.

  • [25]

    Fleming J., The quality of market volatility forecasts implied by S&P100 index option prices, J. Empirical Finance 5 (1998), no. 4, 317–345.

  • [26]

    Hafner R., Stochastic Implied Volatility, Springer, Heidelberg, 2004.

  • [27]

    Hall P., Müller H.-G. and Wang J.-L., Properties of principal component methods for functional and longitudinal data analysis, Ann. Statist. 34 (2006), no. 3, 1493–1517.

  • [28]

    Härdle W., Müller M., Sperlich S. and Werwatz A., Nonparametric and Semiparametric Models, Springer, Heidelberg, 2004.

  • [29]

    Härdle W. and Simar L., Applied Multivariate Statistical Analysis, 4rd ed., Springer, Heidelberg, 2012.

  • [30]

    Indritz J., Methods in Analysis, Macmillan, New York, 1963.

  • [31]

    Laloux L., Cizeau P., Bouchaud J.-P. and Potters M., Noise dressing of financial correlation matrices, Phys. Rev. Lett. 83 (1999), 1467–1470.

  • [32]

    Ledoit O. and Wolf M., Improved estimation of the covariance matrix of stock returns with an application to portfolio selection, J. Empirical Finance 10 (2003), no. 5, 603–621.

  • [33]

    Lopez J. and Walter C., Is implied correlation worth calculating? Evidence from foreign exchange options and historical data, J. Derivatives 7 (2000), no. 3, 65–81.

  • [34]

    Muggeo V. M. R., Estimating regression models with unknown break-points, Stat. Med. 22 (2003), no. 19, 3055–3071.

  • [35]

    Park B., Mammen E., Härdle W. and Borak S., Dynamic semiparametric factor models, J. Amer. Statist. Assoc. 104 (2009), 284–298.

  • [36]

    Plerou V., Gopikrishnan P., Rosenow B., Amaral L. A. N., Guhr T. and Stanley H. E., Random matrix approach to cross correlations in financial data, Phys. Rev. E 65 (2002), Article ID 066126.

  • [37]

    Ramsay J. and Silverman B. W., Functional Data Analysis, 2nd ed., Springer Ser. Statist., Springer, Heidelberg, 2010.

  • [38]

    Skintzi V. and Refenes A., Implied correlation index: A new measure of diversification, J. Futures Markets 25 (2005), 171–197.

  • [39]

    Song S., Härdle W. K. and Ritov Y., High dimensional nonstationary time series modelling with generalized dynamic semiparametric factor model, Econom. J. 17 (2014), 1–32.

  • [40]

    Sperlich S., Linton O. B. and Härdle W. K., Integration and backfitting methods in additive models-finite sample properties and comparison, Test 8 (1999), 419–458.

  • [41]

    Yao F., Müller H.-G. and Wang J.-L., Functional data analysis for sparse longitudinal data, J. Amer. Statist. Assoc. 100 (2005), 577–590.

About the article

Received: 2014-12-25

Revised: 2016-06-14

Accepted: 2016-06-30

Published Online: 2016-07-28

Published in Print: 2016-06-01


Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: CRC 649 “Economic Risk”

The authors gratefully acknowledge financial support from the Deutsche Forschungsgemeinschaft through CRC 649 “Economic Risk”.



Citation Information: Statistics & Risk Modeling, ISSN (Online) 2196-7040, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1515/strm-2014-1176. Export Citation

Comments (0)

Please log in or register to comment.
Log in