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Acceptable Bilateral Gamma Parameters

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  • Yoshihiro Shirai

Abstract

The purpose of this paper is to utilize statistical methodologies to infer from market prices of assets and their derivatives the magnitude of the set of a measure M that defines acceptance sets of risky future cash flows. Specifically, we estimate upper and lower boundaries of the compensation needed for a given bilateral gamma distributed future cash flow to be acceptable. We show that prospects theory provides a natural interpretation of the behaviors implied by such boundaries, which are not compatible with expected utility theory over terminal wealth. Boundaries for bilateral gamma risk neutral scale parameters for given speed parameters are also estimated and tested against market data and, in particular, comparisons are made with known empirical facts about the magnitude of the acceptance set of a common class of risk measures.

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  • Yoshihiro Shirai, 2023. "Acceptable Bilateral Gamma Parameters," Papers 2301.05333, arXiv.org.
    • Handle: RePEc:arx:papers:2301.05333
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    References listed on IDEAS

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    1. Dilip B. Madan, 2020. "Multivariate Distributions For Financial Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(06), pages 1-32, September.
    2. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    3. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    4. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    5. Ernst Eberlein & Dilip B. Madan, 2009. "Hedge Fund Performance: Sources And Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 267-282.
    6. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
    7. Ali, Mukhtar M., 1975. "Stochastic dominance and portfolio analysis," Journal of Financial Economics, Elsevier, vol. 2(2), pages 205-229, June.
    8. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    9. Eberlein & Madan & Pistorius & Yor, 2013. "A Simple Stochastic Rate Model for Rate Equity Hybrid Products," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(5), pages 461-488, November.
    10. Küchler, Uwe & Tappe, Stefan, 2008. "Bilateral gamma distributions and processes in financial mathematics," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 261-283, February.
    11. Dilip B. Madan & Wim Schoutens & King Wang, 2020. "Bilateral multiple gamma returns: Their risks and rewards," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-27, March.
    12. J. Tobin, 1958. "Liquidity Preference as Behavior Towards Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 65-86.
    13. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    14. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    15. 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.
    16. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    17. Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
    18. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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