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Optimizing bounds on security prices in incomplete markets. Does stochastic volatility specification matter?

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  • Marroquı´n-Martı´nez, Naroa
  • Moreno, Manuel

Abstract

We extend and generalize some results on bounding security prices under two stochastic volatility models that provide closed-form expressions for option prices. In detail, we compute analytical expressions for benchmark and standard good-deal bounds. For both models, our findings show that our benchmark results generate much tighter bounds. A deep analysis of the properties of option prices and bounds involving a sensitivity analysis and analytical derivation of Greeks for both option prices and bounds is also presented. These results provide strong practical applications taking into account the relevance of pricing and hedging strategies for traders, financial institutions, and risk managers.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 225 (2013)
Issue (Month): 3 ()
Pages: 429-442

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Handle: RePEc:eee:ejores:v:225:y:2013:i:3:p:429-442

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Web page: http://www.elsevier.com/locate/eor

Related research

Keywords: Incomplete markets; Stochastic volatility model; CIR process; Ornstein–Uhlenbeck process; Good-deal bounds;

References

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  1. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of Security Market Data for Models of Dynamic Economies," NBER Technical Working Papers 0089, National Bureau of Economic Research, Inc.
  2. Jizba, Petr & Kleinert, Hagen & Haener, Patrick, 2009. "Perturbation expansion for option pricing with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3503-3520.
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  10. PInar, Mustafa Ç. & Salih, AslIhan & CamcI, Ahmet, 2010. "Expected gain-loss pricing and hedging of contingent claims in incomplete markets by linear programming," European Journal of Operational Research, Elsevier, vol. 201(3), pages 770-785, March.
  11. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
  12. 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.
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  14. Reynaerts, Huguette & Vanmaele, Michele & Dhaene, Jan & Deelstra, Griselda, 2006. "Bounds for the price of a European-style Asian option in a binary tree model," European Journal of Operational Research, Elsevier, vol. 168(2), pages 322-332, January.
  15. Nowak, Piotr & Romaniuk, Maciej, 2010. "Computing option price for Levy process with fuzzy parameters," European Journal of Operational Research, Elsevier, vol. 201(1), pages 206-210, February.
  16. Zuluaga, Luis F. & Peña, Javier & Du, Donglei, 2009. "Third-order extensions of Lo's semiparametric bound for European call options," European Journal of Operational Research, Elsevier, vol. 198(2), pages 557-570, October.
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