Market Making via Sub-scale Invariant Dynamic Acceptability Indices by Tao Chen (PSTAT)

Event Date: 

Monday, October 16, 2017 -
3:30pm to 4:30pm

Event Location: 

  • Sobel Seminar Room
  • seminar

Title: Market making via sub-scale invariant Dynamic Acceptability Indices

Abstract: The main goal of this study is to develop a general theoretical pricing framework that will capture some practically relevant properties, such as: the prices are not homogeneous in number of shares traded; the underlying securities bear transaction costs; the securities pay dividends; the dividends may be different for a long or short position. To achieve this goal, we use sub-scale invariant Dynamic Acceptability Indices (DAIs) as the main tool in developing the pricing methodology, and consequently, we present a representation of proposed prices in terms of a class of Backward Stochastic Difference Equations and g-Expectations. Besides the above mentioned properties, we also prove that: considered market models do not admit arbitrage; bid and ask prices do shrink the super hedging pricing interval; the prices are time consistent in some appropriate sense; if the drivers are linear we recover the classical martingale pricing theory.

Finally, we provide some practical examples.

 

This is a joint work with Tomasz R. Bielecki and Igor Cialenco (Illinois Institute of Technology).