Two price economic equilibria and financial market bid/ask prices

Robert J. Elliott, Dilip B. Madan*, Tak Kuen Siu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Demand and supply uncertainty lead to a model of markets that set prices to acceptable risk levels for excess supplies and net revenues. The result is a two price partial equilibrium economy. The equilibrium solutions are applied to two price financial market data to infer demand and supply elasticities and log normal volatilities from market quotes on bid and ask prices. Demand elasticities are observed to be higher than supply elasticities as are the volatilities. Normalizing observed volatilities to the volatility of the daily traded volume a market implied duration of the economic equilibrium is inferred. The median level of duration is around a minute and half with an interquartile range from 37 s to 2 min. For larger orders, bid and ask prices may be constructed by calibrating the demand and supply volatilities.

Original languageEnglish
Pages (from-to)27-43
Number of pages17
JournalAnnals of Finance
Issue number1
Early online date9 Nov 2020
Publication statusPublished - Mar 2021


  • Acceptable risks
  • Convex risk measures
  • Distorted expectations
  • Minmaxvar distortion


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