Hostname: page-component-66d9dcfd78-5vcr7 Total loading time: 0 Render date: 2026-08-07T23:26:42.572Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation of Multivariate Asset Models with Jumps

Published online by Cambridge University Press:  28 September 2018

Laura Ballotta Open the ORCID record for Laura Ballotta [Opens in a new window] ,
Gianluca Fusai Open the ORCID record for Gianluca Fusai [Opens in a new window] ,
Angela Loregian  and
M. Fabricio Perez Open the ORCID record for M. Fabricio Perez [Opens in a new window]
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose a consistent and computationally efficient 2-step methodology for the estimation of multidimensional non-Gaussian asset models built using Lévy processes. The proposed framework allows for dependence between assets and different tail behaviors and jump structures for each asset. Our procedure can be applied to portfolios with a large number of assets because it is immune to estimation dimensionality problems. Simulations show good finite sample properties and significant efficiency gains. This method is especially relevant for risk management purposes such as, for example, the computation of portfolio Value at Risk and intra-horizon Value at Risk, as we show in detail in an empirical illustration.

Information

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 54 , Issue 5 , October 2019 , pp. 2053 - 2083
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

1

We thank Gurdip Bakshi (the referee), Cecilia Mancini, Roberto Renò, Lorenzo Trapani, and David Veredas for useful comments and suggestions. Perez acknowledges the financial support received by the Arthur Wesley Downe Professorship of Finance and the Social Sciences and Humanities Research Council of Canada. Fusai acknowledges the financial support received by Università del Piemonte Orientale. This article has been presented at the Arizona State University Economics Reunion Conference. A previous version of this article was circulated with the title “Multivariate Lévy Models by Linear Combination: Estimation” and has been presented at the 2014 International Conference of the Financial Engineering and Banking Society (FEBS). We thank all the participants for their helpful feedback. The usual caveat applies.

References

Ahn, S. C., and Horenstein, A. R.. “Eigenvalue Ratio Test for the Number of Factors.” Econometrica, 81 (2013), 1203–1227.Google Scholar
Ahn, S. C., and Perez, M. F.. “GMM Estimation of the Number of Latent Factors: With Application to International Stock Markets.” Journal of Empirical Finance, 17 (2010), 783–802l.Google Scholar
Aït-Sahalia, Y.“Disentangling Diffusion from Jumps.” Journal of Financial Economics, 74 (2004), 487–528.Google Scholar
Aït-Sahalia, Y., and Jacod, J.. “Testing Whether Jumps Have Finite or Infinite Activity.” Annals of Statistics, 39 (2011), 1689–1719.Google Scholar
Anderson, T. W.“Maximum Likelihood Estimates for a Multivariate Normal Distribution When Some Observations Are Missing.” Journal of the American Statistical Association, 52 (1957), 200–203.Google Scholar
Bai, J.“Inferential Theory for Factor Models of Large Dimensions.” Econometrica, 71 (2003), 135–171.Google Scholar
Bai, J., and Ng, S.. “Determining the Number of Factors in Approximate Factor Models.” Econometrica, 70 (2002), 191–221.Google Scholar
Bai, J., and Ng, S.. “Extremum Estimation When the Predictors Are Estimated from Large Panels.” Annals of Economics and Finance, 9 (2008), 201–222.Google Scholar
Bakshi, G., and Panayotov, G.. “First-Passage Probability, Jump Models, and Intra-Horizon Risk.” Journal of Financial Economics, 95 (2010), 20–40.Google Scholar
Ballotta, L., and Bonfiglioli, E.. “Multivariate Asset Models Using Lévy Processes and Applications.” European Journal of Finance, 22 (2016), 1320–1350.Google Scholar
Ballotta, L.; Deelstra, G.; and Rayée, G.. “Multivariate FX Models with Jumps: Triangles, Quantos and Implied Correlation.” European Journal of Operational Research, 260 (2017), 1181–1199.Google Scholar
Ballotta, L., and Rayée, G.. “Smiles & Smirks: A Tale of Factors.” Working Paper, available at https://ssrn.com/abstract=2980349 (2017).Google Scholar
Barndorff-Nielsen, O. E.“Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling.” Scandinavian Journal of Statistics, 24 (1997), 1–13.Google Scholar
Basel. “Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems.” Technical Report, Bank for International Settlements, available at http://www.bis.org/publ/bcbs189.pdf(2010).Google Scholar
Basel. “Regulatory Consistency Assessment Programme (RCAP): Second Report on Risk-Weighted Assets for Market Risk in the Trading Book.” Technical Report, Bank for International Settlements, available at http://www.bis.org/publ/bcbs267.pdf(2013).Google Scholar
Boudoukh, J.; Richardson, M.; Stanton, R.; and Whitelaw, R.. “MaxVaR: Long Horizon Value at Risk in a Mark-to-Market Environment.” Journal of Investment Management, 2 (2004), 1–6.Google Scholar
Carr, P., and Wu, L.. “Time-Changed Lévy Processes and Option Pricing.” Journal of Financial Economics, 71 (2004), 113–141.Google Scholar
Carr, P., and Wu, L.. “Stochastic Skew in Currency Options.” Journal of Financial Economics, 86 (2007), 213–247.Google Scholar
Cont, R., and Tankov, P.. Financial Modelling with Jump Processes, 2nd ed. Boca Raton, FL: Chapman and Hall/CRC (2004).Google Scholar
Duncan, J.; Randal, J.; and Thomson, P.. “Fitting Jump Diffusion Processes Using the EM Algorithm.” Contributed Talk at the Australasian Meeting of the Econometric Society, Canberra, Australia (2009).Google Scholar
Eberlein, E.; Frey, R.; and von Hammerstein, E. A.. “Advanced Credit Portfolio Modeling and CDO Pricing.” In Mathematics: Key Technology for the Future, Jager, W. and Krebs, H. J., eds. New York, NY: Springer (2008).Google Scholar
Eberlein, E., and Madan, D.. “On Correlating Lévy Processes.” Journal of Risk, 13 (2009), 3–16.Google Scholar
Efron, B.“Bootstrap Methods: Another Look at the Jackknife.” Annals of Statistics, 7 (1979), 1–26.Google Scholar
Fang, F., and Oosterlee, C. W.. “A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions.” SIAM Journal on Scientific Computing, 31 (2008), 826–848.Google Scholar
Fusai, G.; Abrahams, I.; and Sgarra, C.. “An Exact Analytical Solution for Discrete Barrier Options.” Finance and Stochastics, 10 (2006), 1–26.Google Scholar
Fusai, G.; Germano, G.; and Marazzina, D.. “Spitzer Identity, Wiener-Hopf Factorization and Pricing of Discretely Monitored Exotic Options.” European Journal of Operational Research, 251 (2016), 124–134.Google Scholar
Glasserman, P. Monte Carlo Methods in Financial Engineering. New York, NY: Springer (2004).Google Scholar
Honoré, P.“Pitfalls in Estimating Jump-Diffusion Models.” Working Paper, available at https://ssrn.com/abstract=61998 (1998).Google Scholar
Jackson, K.; Jaimungal, S.; and Surkov, V.. “Fourier Space Time-Stepping for Option Pricing with Lévy Models.” Journal of Computational Finance, 12 (2008), 1–29.Google Scholar
Kritzman, M., and Rich, D.. “The Mismeasurement of Risk.” Financial Analysts Journal, 58 (2002), 91–99.Google Scholar
Lee, S. S., and Hannig, J.. “Detecting Jumps from Lévy Jump Diffusion Processes.” Journal of Financial Economics, 96 (2010), 271–290.Google Scholar
Loregian, A.“Multivariate Lévy Models: Estimation and Asset Allocation.” Ph.D. Thesis, Università degli Studi di Milano-Bicocca (2013).Google Scholar
Luciano, E.; Marena, M.; and Semeraro, P.. “Dependence Calibration and Portfolio Fit with Factor-Based Time Changes.” Quantitative Finance, 16 (2016), 1037–1052.Google Scholar
Luciano, E., and Semeraro, P.. “Multivariate Time Changes for Lévy Asset Models: Characterization and Calibration.” Journal of Computational and Applied Mathematics, 233 (2010), 1937–1953.Google Scholar
Merton, R. C.“Option Pricing When Underlying Stocks Are Discontinuous.” Journal of Financial Economics, 3 (1976), 125–144.Google Scholar
Meucci, A. Risk and Asset Allocation. New York, NY: Springer (2005).Google Scholar
Ornthanalai, C.“Lévy Jump Risk: Evidence from Options and Returns.” Journal of Financial Economics, 112 (2014), 69–90.Google Scholar
Stulz, R. M.“Rethinking Risk Management.” Journal of Applied Corporate Finance, 9 (1996), 8–25.Google Scholar
Vašíček, O.“Probability of Loss on Loan Portfolio.” Memo, KMV Corporation (1987).Google Scholar