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Multifrequency Jump-Diffusions: An Equilibrium Approach

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  • Laurent E. Calvet
  • Adlai J. Fisher

Abstract

This paper proposes that equilibrium valuation is a powerful method to generate endogenous jumps in asset prices, which provides a structural alternative to traditional reduced-form specifications with exogenous discontinuities. We specify an economy with continuous consumption and dividend paths, in which endogenous price jumps originate from the market impact of regime-switches in the drifts and volatilities of fundamentals. We parsimoniously incorporate shocks of heterogeneous durations in consumption and dividends while keeping constant the number of parameters. Equilibrium valuation creates an endogenous relation between a shock's persistence and the magnitude of the induced price jump. As the number of frequencies driving fundamentals goes to infinity, the price process converges to a novel stochastic process, which we call a multifractal jump-diffusion.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12797.

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Date of creation: Dec 2006
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Publication status: published as Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
Handle: RePEc:nbr:nberwo:12797

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  1. Laurent E. Calvet & Adlai J. Fisher & Samuel B. Thompson, 2004. "Volatility Comovement: A Multifrequency Approach," NBER Technical Working Papers 0300, National Bureau of Economic Research, Inc.
  2. Martin Lettau & Sydney C. Ludvigson, 2004. "The Declining Equity Premium: What Role Does Macroeconomic Risk Play?," 2004 Meeting Papers 644, Society for Economic Dynamics.
  3. Garcia, Rene & Luger, Richard & Renault, Eric, 2003. "Empirical assessment of an intertemporal option pricing model with latent variables," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 49-83.
  4. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  5. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  6. Robert Anderson & Roberto Raimondo, 2005. "Market clearing and derivative pricing," Economic Theory, Springer, vol. 25(1), pages 21-34, 01.
  7. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  8. Roberto Raimondo, 2005. "Market clearing, utility functions, and securities prices," Economic Theory, Springer, vol. 25(2), pages 265-285, 02.
  9. Laurent E. Calvet, 1999. "Incomplete Markets and Volatility," Harvard Institute of Economic Research Working Papers 1865, Harvard - Institute of Economic Research.
  10. Ole E. Barndorff-Nielsen, 1997. "Processes of normal inverse Gaussian type," Finance and Stochastics, Springer, vol. 2(1), pages 41-68.
  11. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, 08.
  12. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
  13. Laurent E. Calvet & Adlai J. Fisher, 2005. "Multifrequency News and Stock Returns," NBER Working Papers 11441, National Bureau of Economic Research, Inc.
  14. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
  15. S. James Press, 1967. "A Compound Events Model for Security Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 317.
  16. Laurent Calvet & Adlai Fisher, 2003. "Regime-Switching and the Estimation of Multifractal Processes," NBER Working Papers 9839, National Bureau of Economic Research, Inc.
  17. Geert Bekaert & Guojun Wu, 1997. "Asymmetric Volatility and Risk in Equity Markets," NBER Working Papers 6022, National Bureau of Economic Research, Inc.
  18. Veronesi, Pietro, 1999. "Stock Market Overreaction to Bad News in Good Times: A Rational Expectations Equilibrium Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 975-1007.
  19. John Y. Campbell & Ludger Hentschel, 1991. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," NBER Working Papers 3742, National Bureau of Economic Research, Inc.
  20. Huang, Chi-fu, 1987. "An Intertemporal General Equilibrium Asset Pricing Model: The Case of Diffusion Information," Econometrica, Econometric Society, vol. 55(1), pages 117-42, January.
  21. Cochrane, John H. & Campbell, John, 1999. "By Force of Habit: A Consumption-Based Explanation of Aggregate Stock Market Behavior," Scholarly Articles 3119444, Harvard University Department of Economics.
  22. Nicolae Garleanu & Lasse Heje Pedersen & Allen M. Poteshman, 2005. "Demand-Based Option Pricing," NBER Working Papers 11843, National Bureau of Economic Research, Inc.
  23. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
  24. Jarrow, Robert A & Rosenfeld, Eric R, 1984. "Jump Risks and the Intertemporal Capital Asset Pricing Model," The Journal of Business, University of Chicago Press, vol. 57(3), pages 337-51, July.
  25. Philip H. Dybvig, Chi-fu Huang, 1988. "Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 377-401.
  26. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-40, April.
  27. Laurent Calvet, 2000. "Forecasting Multifractal Volatility," Harvard Institute of Economic Research Working Papers 1902, Harvard - Institute of Economic Research.
  28. Barsky, Robert B, 1989. "Why Don't the Prices of Stocks and Bonds Move Together?," American Economic Review, American Economic Association, vol. 79(5), pages 1132-45, December.
  29. Duffie, Darrell & Skiadas, Costis, 1994. "Continuous-time security pricing : A utility gradient approach," Journal of Mathematical Economics, Elsevier, vol. 23(2), pages 107-131, March.
  30. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA.
  31. Cecchetti, Stephen G & Lam, Pok-sang & Mark, Nelson C, 1990. "Mean Reversion in Equilibrium Asset Prices," American Economic Review, American Economic Association, vol. 80(3), pages 398-418, June.
  32. Bank, Peter & Riedel, Frank, 2000. "Existence and structure of stochastic equilibria with intertemporal substitution," SFB 373 Discussion Papers 2000,104, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  33. Pietro Veronesi, 2000. "How Does Information Quality Affect Stock Returns?," Journal of Finance, American Finance Association, vol. 55(2), pages 807-837, 04.
  34. Jaime Casassus & Pierre Collin-Dufresne & Bryan R. Routledge, . "Equilibrium Commodity Prices with Irreversible Investment and Non-Linear Technologies," GSIA Working Papers 2004-E54, Carnegie Mellon University, Tepper School of Business.
  35. Darrell Duffie & William Zame, 1988. "The Consumption-Based Capital Asset Pricing Model," Discussion Papers 88-10, University of Copenhagen. Department of Economics.
  36. Thomas Lux, 2006. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Working Papers wp06-19, Warwick Business School, Finance Group.
  37. John Y. Campbell, 2002. "Consumption-Based Asset Pricing," Harvard Institute of Economic Research Working Papers 1974, Harvard - Institute of Economic Research.
  38. Pindyck, Robert S, 1984. "Risk, Inflation, and the Stock Market," American Economic Review, American Economic Association, vol. 74(3), pages 335-51, June.
  39. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1999. "A Multifractal Model of Assets Returns," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-072, New York University, Leonard N. Stern School of Business-.
  40. Peter Carr & Liuren Wu, 2002. "What Type of Process Underlies Options? A Simple Robust Test," Finance 0207019, EconWPA.
  41. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-36.
  42. Brennan, Michael J. & Xia, Yihong, 2001. "Stock price volatility and equity premium," Journal of Monetary Economics, Elsevier, vol. 47(2), pages 249-283, April.
  43. Lars Peter Hansen & John Heaton & Nan Li, 2005. "Consumption Strikes Back?: Measuring Long-Run Risk," NBER Working Papers 11476, National Bureau of Economic Research, Inc.
  44. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, 06.
  45. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
  46. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  47. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
  48. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
  49. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
  50. Laurent E. Calvet, 2004. "How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 49-83.
  51. He, Hua & Leland, Hayne, 1993. "On Equilibrium Asset Price Processes," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 593-617.
  52. Abel, Andrew B., 1988. "Stock prices under time-varying dividend risk : An exact solution in an infinite-horizon general equilibrium model," Journal of Monetary Economics, Elsevier, vol. 22(3), pages 375-393.
  53. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  54. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
  55. Christopher D Carroll, 2000. "Portfolios of the Rich," Economics Working Paper Archive 430, The Johns Hopkins University,Department of Economics.
  56. Harjoat S. Bhamra & Lars-Alexander Kuehn & Ilya A. Strebulaev, 2010. "The Levered Equity Risk Premium and Credit Spreads: A Unified Framework," Review of Financial Studies, Society for Financial Studies, vol. 23(2), pages 645-703, February.
  57. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
  58. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
  59. Bick, Avi, 1990. " On Viable Diffusion Price Processes of the Market Portfolio," Journal of Finance, American Finance Association, vol. 45(2), pages 673-89, June.
  60. Jun Liu, 2005. "An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks," Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 131-164.
  61. John M. Maheu & Thomas H. McCurdy, 2003. "News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns," CIRANO Working Papers 2003s-38, CIRANO.
  62. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  63. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
  64. Ball, Clifford A & Torous, Walter N, 1985. " On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-73, March.
  65. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
  66. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
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Cited by:
  1. Jaroslav Borovička & Lars Peter Hansen & Mark Hendricks & José A. Scheinkman, 2009. "Risk Price Dynamics," NBER Working Papers 15506, National Bureau of Economic Research, Inc.
    • Lars Peter Hansen & Jaroslav BoroviÄka & Mark Hendricks & Jose A. Scheinkman, 2010. "Risk Price Dynamics," Working Papers 2010-004, Becker Friedman Institute for Research In Economics.
  2. Hervé Crès & Tobias Markeprand & Mich Tvede, 2009. "Incomplete Financial Markets and Jumps in Asset Prices," Discussion Papers 09-12, University of Copenhagen. Department of Economics.
  3. Massimo Guidolin & Allan Timmerman, 2006. "Asset allocation under multivariate regime switching," Working Papers 2005-002, Federal Reserve Bank of St. Louis.

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