A Pricing Method in a Constrained Market with Differential Informational Frameworks

Ivan Peñaloza () and Pablo Padilla ()
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Ivan Peñaloza: Universidad Nacional Autónoma de México(UNAM)
Pablo Padilla: Universidad Nacional Autónoma de México(UNAM)

Computational Economics, 2022, vol. 60, issue 3, No 11, 1055-1100

Abstract: 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.

Keywords: Informational framework; Entropy; Components of volatility; Stock sectors; Utility function (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10614-021-10178-7

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