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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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    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Horatio Cuesdeanu & Jens Carsten Jackwerth, 2018. "The pricing kernel puzzle: survey and outlook," Annals of Finance, Springer, vol. 14(3), pages 289-329, August.
    9. 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.
    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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