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A Damped Diffusion Framework for Financial Modeling and Closed-form Maximum Likelihood Estimation

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  • Li, Minqiang

Abstract

Asset price bubbles can arise unintentionally when one uses continuous-time diffusion processes to model financial quantities. We propose a flexible damped diffusion framework that is able to break many types of bubbles and preserve the martingale pricing approach. Damping can be done on either the diffusion or drift function. Oftentimes, certain solutions to the valuation PDE can be ruled out by requiring the solution to be a limit of martingale prices for damped diffusion models. Monte Carlo study shows that with finite time-series length, maximum likelihood estimation often fails to detect the damped diffusion function while fabricates nonlinear drift function.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 11185.

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Date of creation: 30 Jul 2008
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Handle: RePEc:pra:mprapa:11185

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Keywords: Damped diffusion; asset price bubbles; martingale pricing; maximum likelihood estimation;

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  1. Kirchler, Michael, 2009. "Underreaction to fundamental information and asymmetry in mispricing between bullish and bearish markets. An experimental study," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(2), pages 491-506, February.
  2. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, Elsevier, vol. 83(1), pages 123-170, January.
  3. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 12(04), pages 627-627, November.
  4. Bakshi, Gurdip & Ju, Nengjiu & Ou-Yang, Hui, 2006. "Estimation of continuous-time models with an application to equity volatility dynamics," Journal of Financial Economics, Elsevier, Elsevier, vol. 82(1), pages 227-249, October.
  5. David A. Chapman & Neil D. Pearson, 1998. "Is the Short Rate Drift Actually Nonlinear?," Finance, EconWPA 9808005, EconWPA.
  6. Levy, Moshe, 2008. "Stock market crashes as social phase transitions," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 32(1), pages 137-155, January.
  7. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-77.
  8. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, Springer, vol. 9(4), pages 477-492, October.
  9. Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, American Finance Association, vol. 54(4), pages 1361-1395, 08.
  10. Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 7(1), pages 1-32.
  11. Bali, Turan G. & Wu, Liuren, 2006. "A comprehensive analysis of the short-term interest-rate dynamics," Journal of Banking & Finance, Elsevier, Elsevier, vol. 30(4), pages 1269-1290, April.
  12. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
  13. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, Finance Press, number ovsv.
  14. Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, Elsevier, vol. 116(1-2), pages 181-224.
  15. Durham, Garland B., 2003. "Likelihood-based specification analysis of continuous-time models of the short-term interest rate," Journal of Financial Economics, Elsevier, Elsevier, vol. 70(3), pages 463-487, December.
  16. Friedman, Daniel & Abraham, Ralph, 2009. "Bubbles and crashes: Gradient dynamics in financial markets," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(4), pages 922-937, April.
  17. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, Elsevier, vol. 83(2), pages 413-452, February.
  18. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, American Finance Association, vol. 44(1), pages 211-19, March.
  19. Yacine Ait-Sahalia, 1995. "Nonparametric Pricing of Interest Rate Derivative Securities," NBER Working Papers 5345, National Bureau of Economic Research, Inc.
  20. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 16(3), pages 793-843, July.
  21. Chacko, George & Viceira, Luis M., 2003. "Spectral GMM estimation of continuous-time processes," Journal of Econometrics, Elsevier, Elsevier, vol. 116(1-2), pages 259-292.
  22. Fernandes, Marcelo, 2006. "Financial crashes as endogenous jumps: estimation, testing and forecasting," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 30(1), pages 111-141, January.
  23. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, American Finance Association, vol. 47(3), pages 1209-27, July.
  24. Kirman, Alan & Teyssiere, Gilles, 2005. "Testing for bubbles and change-points," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 29(4), pages 765-799, April.
  25. Li, Minqiang & Pearson, Neil D. & Poteshman, Allen M., 2004. "Conditional estimation of diffusion processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 74(1), pages 31-66, October.
  26. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, Econometric Society, vol. 70(1), pages 223-262, January.
  27. Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
  28. Diebold, Francis X., 1988. "Testing for bubbles, reflecting barriers and other anomalies," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(1), pages 63-70, March.
  29. Manuel Arapis & Jiti Gao, 2006. "Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 310-345.
  30. Beckers, Stan, 1980. " The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, American Finance Association, vol. 35(3), pages 661-73, June.
  31. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 145-166.
  32. Boyle, Phelim P. & Tian, Yisong “Sam”, 1999. "Pricing Lookback and Barrier Options under the CEV Process," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 34(02), pages 241-264, June.
  33. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 17(04), pages 533-554, November.
  34. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
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Cited by:
  1. Lee, Yoon Dong & Song, Seongjoo & Lee, Eun-Kyung, 2014. "The delta expansion for the transition density of diffusion models," Journal of Econometrics, Elsevier, Elsevier, vol. 178(P3), pages 694-705.
  2. Li, Minqiang, 2013. "An examination of the continuous-time dynamics of international volatility indices amid the recent market turmoil," Journal of Empirical Finance, Elsevier, Elsevier, vol. 22(C), pages 128-139.
  3. Choi, Seungmoon, 2013. "Closed-form likelihood expansions for multivariate time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, Elsevier, vol. 174(2), pages 45-65.

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