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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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  • 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.
    • Handle: RePEc:eee:ejores:v:225:y:2013:i:3:p:429-442
    DOI: 10.1016/j.ejor.2012.10.015
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    1. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    2. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    3. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-262, April.
    6. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Dimitris Bertsimas & Ioana Popescu, 2002. "On the Relation Between Option and Stock Prices: A Convex Optimization Approach," Operations Research, INFORMS, vol. 50(2), pages 358-374, April.
    14. Oleg Bondarenko & Iñaki Longarela, 2009. "A general framework for the derivation of asset price bounds: an application to stochastic volatility option models," Review of Derivatives Research, Springer, vol. 12(2), pages 81-107, July.
    15. Albanese, Claudio & Tompaidis, Stathis, 2008. "Small transaction cost asymptotics and dynamic hedging," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1404-1414, March.
    16. 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.
    17. 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.
    18. Basso, A. & Pianca, P., 2001. "Option pricing bounds with standard risk aversion preferences," European Journal of Operational Research, Elsevier, vol. 134(2), pages 249-260, October.
    19. 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.
    20. Antonio E. Bernardo & Olivier Ledoit, 2000. "Gain, Loss, and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 144-172, February.
    21. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    22. Franke, Günter & Huang, James & Stapleton, Richard C., 2007. "Two-dimensional risk neutral valuation relationships for the pricing of options," CoFE Discussion Papers 07/08, University of Konstanz, Center of Finance and Econometrics (CoFE).
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    Cited by:

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    2. Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    3. Chiu, Mei Choi & Wong, Hoi Ying & Zhao, Jing, 2015. "Commodity derivatives pricing with cointegration and stochastic covariances," European Journal of Operational Research, Elsevier, vol. 246(2), pages 476-486.
    4. Dirk Becherer & Klebert Kentia, 2017. "Hedging under generalized good-deal bounds and model uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 171-214, August.
    5. Giampietro, Marta & Guidolin, Massimo & Pedio, Manuela, 2018. "Estimating stochastic discount factor models with hidden regimes: Applications to commodity pricing," European Journal of Operational Research, Elsevier, vol. 265(2), pages 685-702.
    6. Marta Giampietro & Massimo Guidolin & Manuela Pedio, 2015. "Can No-Arbitrage SDF Models with Regime Shifts Explain the Correlations Between Commodity, Stock, and Bond Returns?," BAFFI CAREFIN Working Papers 1619, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    7. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    8. Balter, Anne G. & Pelsser, Antoon, 2020. "Pricing and hedging in incomplete markets with model uncertainty," European Journal of Operational Research, Elsevier, vol. 282(3), pages 911-925.
    9. Kim, Junseok & Kim, Taekkeun & Jo, Jaehyun & Choi, Yongho & Lee, Seunggyu & Hwang, Hyeongseok & Yoo, Minhyun & Jeong, Darae, 2016. "A practical finite difference method for the three-dimensional Black–Scholes equation," European Journal of Operational Research, Elsevier, vol. 252(1), pages 183-190.
    10. Dirk Becherer & Klebert Kentia, 2016. "Hedging under generalized good-deal bounds and model uncertainty," Papers 1607.04488, arXiv.org, revised Apr 2017.

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