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Asset Prices and Alternative Characterizations of the Pricing Kernel

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  • Lüders, Erik

Abstract

In a continuous-time representative investor economy with an exogenously given information process, asset prices are derived for alternative characterizations of the pricing kernel. In addition to the characterization of forward prices in a general representative investor economy a detailed analysis of forward prices for the HARA-class is given. In particular, analytical and numerical solutions of forward prices are derived for a representative investor with non-constant relative risk aversion. The derived asset prices are consistent with empirically well documented characteristics as mean reversion and random volatility. Hence, they are viable alternatives to the geometric Brownian motion.

Suggested Citation

  • Lüders, Erik, 2002. "Asset Prices and Alternative Characterizations of the Pricing Kernel," ZEW Discussion Papers 02-10, ZEW - Leibniz Centre for European Economic Research.
    • Handle: RePEc:zbw:zewdip:887
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    1. Kothari, S. P. & Shanken, Jay, 1997. "Book-to-market, dividend yield, and expected market returns: A time-series analysis," Journal of Financial Economics, Elsevier, vol. 44(2), pages 169-203, May.
    2. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Lüders, Erik & Peisl, Bernhard, 2001. "How do investors' expectations drive asset prices?," ZEW Discussion Papers 01-15, ZEW - Leibniz Centre for European Economic Research.
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. Franke, Günter & Weber, Martin, 2001. "Heterogeneity of Investors and Asset Pricing in a Risk-Value World," CoFE Discussion Papers 01/08, University of Konstanz, Center of Finance and Econometrics (CoFE).
    7. repec:bla:jfinan:v:53:y:1998:i:5:p:1705-1736 is not listed on IDEAS
    8. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    9. Cox, John C. & Huang, Chi-fu, 1991. "A variational problem arising in financial economics," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 465-487.
    10. Guntar Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterizations of the Pricing Kernel," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-003, New York University, Leonard N. Stern School of Business-.
    11. Franke, Günter & Stapleton, Richard C. & Subrahmanyam, Marti G., 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," CoFE Discussion Papers 99/01, University of Konstanz, Center of Finance and Econometrics (CoFE).
    12. Günter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black—Scholes Model and Alternative Characterisations of the Pricing Kernel," Review of Finance, European Finance Association, vol. 3(1), pages 79-102.
    13. Franke, Gunter & Stapleton, Richard C. & Subrahmanyam, Marti G., 1998. "Who Buys and Who Sells Options: The Role of Options in an Economy with Background Risk," Journal of Economic Theory, Elsevier, vol. 82(1), pages 89-109, September.
    14. Kim, Dongcheol & Kon, Stanley J, 1994. "Alternative Models for the Conditional Heteroscedasticity of Stock Returns," The Journal of Business, University of Chicago Press, vol. 67(4), pages 563-598, October.
    15. Franke, Gunter, 1984. "Conditions for Myopic Valuation and Serial Independence of the Market Excess Return in Discrete Time Models," Journal of Finance, American Finance Association, vol. 39(2), pages 425-442, June.
    16. Wang Susheng, 1993. "The Integrability Problem of Asset Prices," Journal of Economic Theory, Elsevier, vol. 59(1), pages 199-213, February.
    17. Luders, Erik & Peisl, Bernhard, 2001. "How Do Investors' Expectations Drive Asset Prices?," The Financial Review, Eastern Finance Association, vol. 36(4), pages 75-98, November.
    18. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-681.
    19. A. Lazrak & J.P. DÊcamps, 2000. "A martingale characterization of equilibrium asset price processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(1), pages 207-213.
    20. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
    21. Lüders, Erik & Peisl, Bernhard, 2000. "On the Relationship of Information Processes and Asset Price Processes," CoFE Discussion Papers 00/09, University of Konstanz, Center of Finance and Econometrics (CoFE).
    22. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    23. Bick, Avi, 1990. "On Viable Diffusion Price Processes of the Market Portfolio," Journal of Finance, American Finance Association, vol. 45(2), pages 673-689, June.
    24. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    25. Guenter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," Finance 9904004, University Library of Munich, Germany.
    26. Huyěn Pham & Nizar Touzi, 1996. "Equilibrium State Prices In A Stochastic Volatility Model1," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 215-236, April.
    27. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    28. Hodges, Stewart & Carverhill, Andrew, 1993. "Quasi Mean Reversion in an Efficient Stock Market: The Characterisation of Economic Equilibria which Support Black-Scholes Option Pricing," Economic Journal, Royal Economic Society, vol. 103(417), pages 395-405, March.
    29. Blume, Marshall E & Friend, Irwin, 1975. "The Asset Structure of Individual Portfolios and Some Implications for Utility Functions," Journal of Finance, American Finance Association, vol. 30(2), pages 585-603, May.
    30. Christian Gollier, 2004. "The Economics of Risk and Time," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262572249, April.
    31. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
    32. Bick, Avi, 1987. "On the Consistency of the Black-Scholes Model with a General Equilibrium Framework," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(3), pages 259-275, September.
    33. Cuoco, Domenico & Zapatero, Fernando, 2000. "On the Recoverability of Preferences and Beliefs," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 417-431.
    34. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    35. 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 637-654, May-June.
    36. Rubinstein, Mark, 1983. "Displaced Diffusion Option Pricing," Journal of Finance, American Finance Association, vol. 38(1), pages 213-217, March.
    37. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    38. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    39. Jackwerth, Jens Carsten & Rubinstein, Mark, 2003. "Recovering Probabilities and Risk Aversion from Option Prices and Realized Returns," MPRA Paper 11638, University Library of Munich, Germany, revised 2004.
    40. He, Hua & Leland, Hayne, 1993. "On Equilibrium Asset Price Processes," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 593-617.
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    Cited by:

    1. Lüders, Erik, 2002. "Why Are Asset Returns Predictable?," ZEW Discussion Papers 02-48, ZEW - Leibniz Centre for European Economic Research.
    2. Schröder, Michael & Lüders, Erik, 2004. "Modeling Asset Returns: A Comparison of Theoretical and Empirical Models," ZEW Discussion Papers 04-19 [rev.], ZEW - Leibniz Centre for European Economic Research.

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    More about this item

    Keywords

    equilibrium price processes; displaced diffusion process; random volatility; mean-reversion;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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