Time Consistent Dynamic Limit Order Books Calibrated on Options

In an incomplete nancial market, the axiomatic of Time Consistent Pricing Procedure (TCPP), recently introduced, is used to assign to any nancial asset a dynamic limit order book, taking into account both the dynamics of basic assets and the limit order books for options. Kreps-Yan fundamental theorem is extended to that context. A characterization of TCPP calibrated on options is given in terms of their dual representation. In case of perfectly liquid options, these options can be used as the basic assets to hedge dynamically. A generic family of TCPP calibrated on option prices is constructed, from càdlàg BMO martingales.