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Jump diffusion model

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Abstract

Jump diffusion processes have been used in modern finance to capture discontinuous behavior in asset pricing. Various jump diffusion models are considered in this chapter. Also, the applications of jump diffusion processes on stocks, bonds, and interest rate are discussed.

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References

  1. Ahn, C.M. and Howard, E.T. (1988). “Jump diffusion processes and the term structure of interest rates.” Journal of Finance, 43(1): 155–174.

    CrossRef  Google Scholar 

  2. Akgiray, V. and Booth, G.G. (1988). “Mixed diffusion-jump process modeling of exchange rate movements.” Review of Economics and Statistics, 70(4): 631–637.

    CrossRef  Google Scholar 

  3. Amin, K.L. (1993). “Jump diffusion option valuation in discrete time.” Journal of Finance, 48(5): 1833–1863.

    CrossRef  Google Scholar 

  4. Bachelier, L. (1900). “Theory of speculation.” in P. Costner (ed.) Random Character of Stock Market Prices. Cambridge: MIT Press, 1964, reprint.

    Google Scholar 

  5. Ball, C.A. and Torous, W.N. (1983). “A simplified jump process for common stock returns.” Journal of Financial and Quantitative analysis, 18(1): 53–65.

    CrossRef  Google Scholar 

  6. Ball, C.A. and Torous, W.N. (1985). “On jumps in common stock prices and their impact on call option pricing.” Journal of Finance, 40(1): 155–173.

    CrossRef  Google Scholar 

  7. Bandi, F.M. and Nguyen, T.H. (2003). “On the functional estimation of jump-diffusion models.” Journal of Econometrics, 116: 293–328.

    CrossRef  Google Scholar 

  8. Bates, D.S. (1991). “The crash of &s’87: was it expected? The evidence from options markets.” Journal of Finance, 46(3): 1009–1044.

    CrossRef  Google Scholar 

  9. Bates, D.S. (1996). “Jumps and stochastic volatility: exchange rate processes implicit in Deutsche Mark options.” Review of Financial Studies, 46(3): 1009–1044.

    Google Scholar 

  10. Beckers, S. (1981). “A note on estimating the parameters of the diffusion-jump model of stock returns.” Journal of Financial and Quantitative Analysis, XVI(1): 127–140.

    CrossRef  Google Scholar 

  11. Chacko, G. and Viceria, L.M. (2003). “Spectral GMM estimation of continuous time processes.” Journal of Econometrics, 116: 259–292.

    CrossRef  Google Scholar 

  12. Chamberlain, G. (1988). “Asset pricing in multiperiod securities markets.” Econometrica, 56: 1283–1300.

    CrossRef  Google Scholar 

  13. Chan, W.H. and Maheu, J.M. (2002). “Conditional jump dynamics in stock market returns,” Journal of Business and Economic Statistics, 20(3): 377–389.

    CrossRef  Google Scholar 

  14. Clark, P.K. (1973). “A subordinated stochastic process model with finite variance for speculative prices.” Econometrica, 41(1): 135–155.

    CrossRef  Google Scholar 

  15. Cox, J.C., Ingersoll, J.E. Jr., and Ross, S.A. (1981). “A re-examination of traditional hypotheses about the term structure of interest rate.” Journal of Finance, 36: 769–799.

    CrossRef  Google Scholar 

  16. Cox, J.C., Ingersoll, J.E. Jr., and Ross, S.A. (1985a). “An intertemporal general equilibrium model of asset prices.” Econometrica, 53: 363–384.

    CrossRef  Google Scholar 

  17. Cox, J.C., Ingersoll, J.E. Jr., and Ross, S.A. (1985b). “A theory of the term structure of interest rate.” Econometrica, 53: 385–407.

    CrossRef  Google Scholar 

  18. Das, S.R. (2002). “The surprise element: jumps in interest rates.” Journal of Econometrics, 106: 27–65.

    CrossRef  Google Scholar 

  19. Duffie, D. and Kan, R. (1996). “A yield-factor model of interest rate.” Mathematical Finance, 6: 379–406.

    CrossRef  Google Scholar 

  20. Duffie, D., Pan, J., and Singleton, K. (2000). “Transform analysis and asset pricing for affine jump diffusion.” Econometrica, 68: 1343–1376.

    CrossRef  Google Scholar 

  21. Drost, F.C. and Werker, B.J.M. (1996). “Closing the GARCH gap: continuous time GARCH modeling,” Journal of Econometrics, 74: 31–57.

    CrossRef  Google Scholar 

  22. Drost, F.C., Nijman, T.E., and Werker, B.J.M. (1998). “Estimation and testing in models containing both jumps and conditional heteroscedasticity.” Journal of Business and Economic Statistics, 16(2).

    Google Scholar 

  23. Gourieroux, C. and Jasiak, J. (2001). “Financial econometrics,” 1st edn. New Jersey: Princeton University Press.

    Google Scholar 

  24. Ho, M.S., Perraudin, W.R.M., and Sorensen, S.E. (1996). “A continuous time arbitrage pricing model.” Journal of Business and Economic Statistics, 14(1): 31–42.

    Google Scholar 

  25. Hull, J.C. (2000). “Option, futures, other derivatives”, 4th edn. New Jersey: Prientice Hall.

    Google Scholar 

  26. Jarrow, R.A. and Rosenfeld, E.R. (1984). “Jumps risks and the intertemporal capital asset pricing model.” Journal of Business, 57(3): 337–351.

    CrossRef  Google Scholar 

  27. Johannes, M. (2004). “The statistical and economic role of jumps in continuous time interest rate model”, Journal of Finance, 59: 227–260.

    CrossRef  Google Scholar 

  28. Johnson, Timothy C. (2002) “Volatility, momentum, and time-varying skewneww in foreign exchange returns,” Journal of Business and Economic Statistics, Vol20,No 3, 390–411.

    CrossRef  Google Scholar 

  29. Jorion, P. (1988). “On jump processes in the foreign exchange and stock market.” Review of Financial Studies, 1(4): 427–445.

    CrossRef  Google Scholar 

  30. Lawler, G.F. (2000). “Introduction to stochastic processes.” Boca Raton: Chapman and Hall/CRC.

    Google Scholar 

  31. Merton, R.C. (1973). “An intertemporal capital asset pricing model.” Econometrica, 41(5): 867–887.

    CrossRef  Google Scholar 

  32. Merton, R.C. (1976). “Option pricing when underlying stock returns are discontinuous.” Journal of Financial Economics, 3: 125–144.

    CrossRef  Google Scholar 

  33. Neftci, S.N. (2000). “An introduction to the mathematics of financial derivatives,” 2nd edn. New York: Academic press.

    Google Scholar 

  34. Niederhoffer, V. and Osborne, M.F.M. (1966). “Market making and reversal on the stock exchange.” Journal of the American Statistical Association, 61: 897–916.

    CrossRef  Google Scholar 

  35. Nieuwland, F.G.M.C., Verschoor, W.F.C., and Wolff, C.C.P. (1991). “EMS exchange rates.” Journal of International Financial Markets, Institutions and Money, 2: 21–42.

    Google Scholar 

  36. Oksendal, B. (1998). “Stochastic differential equations,” 5th edn. New York: Springer.

    CrossRef  Google Scholar 

  37. Oldfield, G.S., Rogalski, R.J., and Jarrow, R.A. (1977). “An autoregressive jump process for common stock returns.” Journal of Financial Economics, 5: 389–418.

    CrossRef  Google Scholar 

  38. Omberg, E. (1988). “Efficient discrete time jump process models in option pricing.” Journal of Financial and Quantitative Analysis, 23(2): 161–174.

    CrossRef  Google Scholar 

  39. Osborne, M.F.M. (1959). “Brownian motion in the stock market.” Operations Research, 7: 145–173.

    CrossRef  Google Scholar 

  40. Press, S.J. (1967). “A compound events model for security prices.” Journal of Business, 40(3): 317–335.

    CrossRef  Google Scholar 

  41. Singleton, K. (2001). “Estimation of affine asset pricing models using the empirical characteristic function.” Journal of Econometrics, 102(1): 111–141.

    CrossRef  Google Scholar 

  42. Tucker, A.L. and Lallon, P. (1988). “The probability distribution of foreign exchanges: tests of candidate processes.” Review of Economics and Statistics, 70: 638–647.

    CrossRef  Google Scholar 

  43. Vasicek, O. (1977). “An equilibrium characterization of the term structure.” Journal of Financial Economics, 5: 177–188.

    CrossRef  Google Scholar 

  44. Vlaar, P.J.G. and Palm, F.C. (1993). “The Message in weekly exchange rates in the European monetary system: mean reversion, conditional heteroscedasticity, and jumps.” Journal of Business and Economic Statistics, 11(3): 351–360.

    Google Scholar 

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© 2006 Springer Science+Business Media, Inc.

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Wang, SH. (2006). Jump diffusion model. In: Lee, CF., Lee, A.C. (eds) Encyclopedia of Finance. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-26336-6_69

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  • DOI: https://doi.org/10.1007/978-0-387-26336-6_69

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-26284-0

  • Online ISBN: 978-0-387-26336-6

  • eBook Packages: Business and Economics

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