A new market model in the large volatility case

TL;DR

This paper compares different pricing models in markets with large volatility, highlighting discrepancies and proposing that market models should distinguish between small and large volatility scenarios.

Contribution

It introduces a new perspective on market models by emphasizing the differences in pricing approaches under large volatility conditions.

Findings

Rational prices can contradict common sense in complete markets.

Market models should differentiate between small and large volatility cases.

Comparison of three pricing types reveals inconsistencies in traditional models.

Abstract

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