Price as a matter of choice and nonstochastic randomness

TL;DR

This paper introduces a novel valuation method for European call options incorporating nonstochastic randomness, extending classical models like Black-Scholes, and reveals that unhedged options tend to yield negative expected profit.

Contribution

It proposes a new indifference valuation framework that accounts for nonstochastic randomness, generalizing classical financial models and analyzing hedge strategies.

Findings

Classical models are special cases of the new valuation method.

Uncovered European options have negative expected profit in the nonstochastic randomness context.

A delta hedge version is proposed for this new valuation framework.

Abstract

A version of indifference valuation of a European call option is proposed that includes statistical regularities of nonstochastic randomness. Classical relations (forward contract value and Black-Scholes formula) are obtained as particular cases. We show that in the general case of nonstochastic randomness the minimal expected profit of uncovered European option position is always negative. A version of delta hedge is proposed.