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A Pricing Method in a Constrained Market with Differential Informational Frameworks

Author

Listed:
  • Ivan Peñaloza

    (Universidad Nacional Autónoma de México(UNAM))

  • Pablo Padilla

    (Universidad Nacional Autónoma de México(UNAM))

Abstract

We create a method to compute the price of some types of derivatives in a micro-market where there are many small investors (retail traders, swing traders, etc), and a big investor (institutional trader). This model takes a linear combination of the prices proposed by each agent plus a stochastic error where the weights will represent the percentage of participation of each agent in the market. For big investors, we develop the multiprice model version of the mixture of diffusion processes as in Brigo (The general mixture-diffusion SDE and its relationship with an uncertain-volatility option model with volatility-asset decorrelation, 2002. https://www.imperial.ac.uk/people/damiano.brigo/publications.html ) and then choose the martingale measure that maximizes the relative entropy function under some specific macroeconomic conditions. This measure provides a posteriori distribution for the macroeconomic events using the a priori distribution and the interactions of correlated economic sectors. In this process, we also break down the volatility of the underlying asset into components of volatility that depend on the trends of other related stocks. The big investor will ultimately use this measure to price the derivative. Small investors, on the other hand, face some constraints on their portfolios due to limited information. We use the results by El Karoui and Rouge (Math Finance 10:259–276, 2000), Duffie and Huang (J Math Econ 15:283–303, 1986) to develop a new formula and an algorithm for the price of different stereotypes of small agents that come from the stochastic game between the big investor and them.

Suggested Citation

  • Ivan Peñaloza & Pablo Padilla, 2022. "A Pricing Method in a Constrained Market with Differential Informational Frameworks," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 1055-1100, October.
    • Handle: RePEc:kap:compec:v:60:y:2022:i:3:d:10.1007_s10614-021-10178-7
    DOI: 10.1007/s10614-021-10178-7
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    References listed on IDEAS

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    1. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    2. Ahmed Mushfiq Mobarak, 2005. "Democracy, Volatility, and Economic Development," The Review of Economics and Statistics, MIT Press, vol. 87(2), pages 348-361, May.
    3. Justin Sirignano & Rama Cont, 2018. "Universal features of price formation in financial markets: perspectives from Deep Learning," Papers 1803.06917, arXiv.org.
    4. Thomas Goll & Ludger Rüschendorf, 2001. "Minimax and minimal distance martingale measures and their relationship to portfolio optimization," Finance and Stochastics, Springer, vol. 5(4), pages 557-581.
    5. Patrick Cheridito & Ulrich Horst & Michael Kupper & Traian A. Pirvu, 2016. "Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 174-195, February.
    6. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    7. Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52, January.
    8. Aurelijus Dabušinskas & Dmitry Kulikov & Martti Randveer, 2013. "The impact of volatility on economic growth," Bank of Estonia Working Papers wp2012-7, Bank of Estonia, revised 04 Feb 2013.
    9. Duffie, Darrell & Huang, Chi-fu, 1986. "Multiperiod security markets with differential information : Martingales and resolution times," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 283-303, June.
    10. Consiglio, Andrea & De Giovanni, Domenico, 2008. "Evaluation of insurance products with guarantee in incomplete markets," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 332-342, February.
    11. Liu, Jicheng & Ren, Jiagang, 2002. "Comparison theorem for solutions of backward stochastic differential equations with continuous coefficient," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 93-100, January.
    12. Justin Sirignano & Rama Cont, 2018. "Universal features of price formation in financial markets: perspectives from Deep Learning," Working Papers hal-01754054, HAL.
    13. Richard Rouge & Nicole El Karoui, 2000. "Pricing Via Utility Maximization and Entropy," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 259-276, April.
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