Volume no :3, Issue no: 1, March (2010)

Journal of Statistics: Advances in Theory and Applications

STATISTICAL TESTING FOR ASYMPTOTIC NO-ARBITRAGE IN FINANCIAL MARKETS

Author's: Ippei Hatai, Hiroshi Shiraishi and Masanobu Taniguchi
Pages: [27] - [42]
Received Date: March 16, 2010
Submitted by:

Abstract

This paper deals with the notion of a large financial market and the concept of asymptotic no-arbitrage. This concept is closely related to that of contiguity of the equivalent martingale measures. Here, assuming a time varying ARCH return for financial asset, we derive the stochastic expansion of the log-likelihood ratio for the equivalent martingale measure. Then we give a sufficient condition that, there is no asymptotic arbitrage. Related to this condition, a test statistic for this is proposed. The asymptotics are elucidated. Numerical studies of the test are provided, and they show that our test is useful for testing asymptotic no- arbitrage.

Keywords

Keywords and phrases: large financial market, asymptotic no-arbitrage, martingale, contiguity, likelihood ratio, time-varying ARCH model.