On Local Times: Application to Pricing Using Bid-Ask

Paul C. Kettler, Olivier Menoukeu-Pamen, Frank Proske

Centre of Mathematics for Applications, Department of Mathematics, University of Oslo, Oslo, Norway.
Institute for Financial and Actuarial Mathematics, Department of Mathematics, University of Liverpool, Liverpool, UK.

DOI: 10.4236/jmf.2014.42008                

Abstract

In this paper, we derive the evolution of a stock price from the dynamics of the “best bid” and “best ask”. Under the assumption that the bid and ask prices are described by semimartingales, we study the completeness and the possibility for arbitrage on such a market. Further, we discuss (insider) hedging for contingent claims with respect to the stock price process.

Keywords

Order Statistics; Semimartingales; Local Times; Arbitrage

Conflicts of Interest

The authors declare no conflicts of interest.

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