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Towards a General Theory of Good-Deal Bounds

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  • Tomas Björk
  • Irina Slinko

Abstract

We consider an incomplete market in the form of a multidimensional Markovian factor model, driven by a general marked point process (representing discrete jump events), as well as by a standard multidimensional Wiener process. Within this framework, we study arbitrage-free gooddeal pricing bounds for derivative assets, thereby extending the results by Cochrane and Saá Requejo (2000) to the point process case, while, at the same time, obtaining a radical simplification of the theory. To illustrate, we present numerical results for the classic Merton jump-diffusion model. As a by-product of the general theory, we derive extended Hansen-Jagannathan bounds for the Sharpe Ratio process in the point process setting. Copyright 2006, Oxford University Press.

Suggested Citation

  • Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
  • Handle: RePEc:oup:revfin:v:10:y:2006:i:2:p:221-260
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    File URL: http://hdl.handle.net/10.1007/s10679-006-8279-1
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    Cited by:

    1. Bayraktar, Erhan & Milevsky, Moshe A. & David Promislow, S. & Young, Virginia R., 2009. "Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 33(3), pages 676-691, March.
    2. Josa-Fombellida, Ricardo & Rincón-Zapatero, Juan Pablo, 2012. "Stochastic pension funding when the benefit and the risky asset follow jump diffusion processes," European Journal of Operational Research, Elsevier, vol. 220(2), pages 404-413.
    3. Young, Virginia R., 2008. "Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 691-703, April.
    4. Akuzawa, Toshinao & Nishiyama, Yoshihiko, 2013. "Implied Sharpe ratios of portfolios with options: Application to Nikkei futures and listed options," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 335-357.
    5. repec:eee:insuma:v:79:y:2018:i:c:p:107-123 is not listed on IDEAS
    6. Ibáñez, Alfredo, 2008. "Factorization of European and American option prices under complete and incomplete markets," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 311-325, February.
    7. Jocelyne Bion-Nadal & Giulia Nunno, 2013. "Dynamic no-good-deal pricing measures and extension theorems for linear operators on L ∞," Finance and Stochastics, Springer, vol. 17(3), pages 587-613, July.
    8. Marroquı´n-Martı´nez, Naroa & Moreno, Manuel, 2013. "Optimizing bounds on security prices in incomplete markets. Does stochastic volatility specification matter?," European Journal of Operational Research, Elsevier, vol. 225(3), pages 429-442.
    9. L. Carassus & E. Temam, 2014. "Pricing and hedging basis risk under no good deal assumption," Annals of Finance, Springer, vol. 10(1), pages 127-170, February.
    10. Bion-Nadal, Jocelyne, 2009. "Bid-ask dynamic pricing in financial markets with transaction costs and liquidity risk," Journal of Mathematical Economics, Elsevier, vol. 45(11), pages 738-750, December.
    11. repec:spr:finsto:v:22:y:2018:i:2:d:10.1007_s00780-017-0352-4 is not listed on IDEAS

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