A NEW MARKET MODEL IN THE LARGE VOLATILITY CASE

Yukio Hirashita (Japan)

Received March 11, 2008

Abstract

We compare three types of prices, namely, rational (hedging) prices, geometric (growth rate) prices and martingale (measure) prices and show that rational prices in the complete market theory are sometimes contrary to the expected ones. In the continuous-time case, we insist that the market model should differ between the small volatility case  and the large volatility case

Keywords and phrases: complete market, rational price, geometric price, martingale price.