Complexity and financial stability in a large random economy
Quantitative Finance, 2014, vol. 14, issue 9, 1663-1675
I study the limit of a large random economy, in the ideal case of perfect competition, where full information is available to all market participants, and where a set of consumers invests in financial instruments engineered by banks in order to optimize their future consumption. This provides a picture of how unregulated financial innovation pushes an economy towards the ideal limit of complete markets. Hedging new products with existing products allows financial institutions to reduce the associated risk and hence the risk premium. This has the expected consequence that markets, under such ideal conditions, converge to market completeness as the repertoire of financial instruments expands. As markets approach completeness, however, two 'unintended consequences' also arise: (i) equilibrium portfolios develop a marked susceptibility to idiosyncratic shocks and/or parameter uncertainty and (ii) hedging engenders divergent trading volumes in the interbank market. Combining these suggests an inverse relation between financial stability and the size of the financial sector, which can be quantified within the present framework. These results suggest that even under perfect competition and symmetric information, the pursuit of market efficiency-in terms of completeness-may erode financial stability. The proliferation of financial instruments exacerbates the effects of market imperfections and, in order to prevent an escalation of perverse effects, markets may require institutional structures that become more and more substantial as their complexity expands.
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