Discussion Paper Series 2014-E-4

A Pricing Theory under a Finite Number of Securities Issued:
A Synthesis of “Market Microstructure” and “Mathematical Finance”

Yoshihiko Uchida, Daisuke Yoshikawa

Traditional finance theory generally assumes a frictionless market, in which a risk premium is described only by price volatility. In reality, however, the risk premium is influenced by a range of factors including the market microstructure. This paper constructs a novel no-arbitrage and complete model that explicitly incorporates among the market microstructure factors a constraint on a finite number of securities issued. From the theoretical perspective, the model is a synthesis of market microstructure and mathematical finance in that it makes it possible to derive a risk-neutral price applicable to a market with a detailed market microstructure. We also calibrate the model to show that the price in the Japanese government bond futures market is significantly affected by the factor of number of securities issued.

Keywords: Security price; Number of securities issued; Risk neutral pricing rule; Market microstructure; No-arbitrage; Quasi risk aversion; Quasi risk neutral measure

Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.

Copyright © 2014 Bank of Japan All Rights Reserved.

Home Japanese Home