A Multivariate Jump-Driven Financial Asset Model
AbstractIn this paper, we propose a multivariate model for nancial assets which incorporates jumps, skewness, kurtosis and stochastic volatility, and discuss its applications in the context of equity and credit risk. In the former case we describe the stochastic behavior of a series of stocks or indexes, in the latter we apply the model in a multi- rm, value-based default model. Starting from a independent Brownian world, we will introduce jumps and other deviations from normality, as well as non-Gaussian dependence, by the simple but very strong technique of stochastic time-changing. We work out the details in the case of a Gamma time-change, thus obtaining a multivariate Variance Gamma (VG) setting. We are able to characterize the model from an analytical point of view, by writing down the joint distribution function of the assets at any point in time and by studying their association via the copula technique. The model is also computationally friendly, since numerical results require a modest amount of time and the number of parameters grows linearly with the number of assets. The main feature of the model however is the fact that - opposite to other, non jointly Gaussian settings - its risk neutral dependence can be calibrated from univariate derivative prices. Examples from the equity and credit market show the goodness of fit attained.
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Bibliographic InfoPaper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 6-2005.
Length: 27 pages
Date of creation: Apr 2005
Date of revision:
Other versions of this item:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
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- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-64, May.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Hayne E. Leland., 1994.
"Corporate Debt Value, Bond Covenants, and Optimal Capital Structure,"
Research Program in Finance Working Papers
RPF-233, University of California at Berkeley.
- Leland, Hayne E, 1994. " Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-52, September.
- Frank Milne & Dilip Madan, 1991.
"Option Pricing With V. G. Martingale Components,"
1159, Queen's University, Department of Economics.
- Chunsheng Zhou, 1997. "A jump-diffusion approach to modeling credit risk and valuing defaultable securities," Finance and Economics Discussion Series 1997-15, Board of Governors of the Federal Reserve System (U.S.).
- Merton, Robert C, 1974.
"On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,"
Journal of Finance,
American Finance Association, vol. 29(2), pages 449-70, May.
- Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
- U. Cherubini & E. Luciano, 2002. "Bivariate option pricing with copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(2), pages 69-85.
- Longstaff, Francis A & Schwartz, Eduardo S, 1995. " A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
- Fung, Thomas & Seneta, Eugene, 2011. "The bivariate normal copula function is regularly varying," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1670-1676, November.
- Bedendo, Mascia & Campolongo, Francesca & Joossens, Elisabeth & Saita, Francesco, 2010. "Pricing multiasset equity options: How relevant is the dependence function?," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 788-801, April.
- Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 73-85.
- N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
- Patrizia Semeraro, 2006. "A Multivariate Time-Changed Lévy Model for Financial Applications," ICER Working Papers - Applied Mathematics Series 10-2006, ICER - International Centre for Economic Research.
- Filippo Fiorani & Elisa Luciano & Patrizia Semeraro, 2007. "Single and joint default in a structural model with purely discontinuous assets," Carlo Alberto Notebooks 41, Collegio Carlo Alberto.
- Florence Guillaume, 2013. "The αVG model for multivariate asset pricing: calibration and extension," Review of Derivatives Research, Springer, vol. 16(1), pages 25-52, April.
- Elisa Luciano, 2007. "Copulas and Dependence models in Credit Risk: Diffusions versus Jumps," ICER Working Papers - Applied Mathematics Series 31-2007, ICER - International Centre for Economic Research.
- Elisa Luciano & Patrizia Semeraro, 2007. "Extending Time-Changed Lévy Asset Models Through Multivariate Subordinators," Carlo Alberto Notebooks 42, Collegio Carlo Alberto.
- Elisa Luciano & Marina Marena & Patrizia Semeraro, 2013. "Dependence Calibration and Portfolio Fit with FactorBased Time Changes," Carlo Alberto Notebooks 307, Collegio Carlo Alberto.
- Elisa Luciano, 2007. "Copula-Based Default Dependence Modelling: Where Do We Stand?," ICER Working Papers - Applied Mathematics Series 21-2007, ICER - International Centre for Economic Research.
- Antonis Papapantoleon, 2011. "Computation of copulas by Fourier methods," Papers 1108.1216, arXiv.org, revised Jun 2014.
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