Irreducible Risks: Fallacy of Risk-Neutral Approach to Options

Abstract

This paper compares two approaches to options: (1) Risk-Aware Approach, and (2) Risk-Neutral Approach. The risk-aware approach requires a probabilistic specification of the underlying’s returns, addressing higher than second moments, as hedging errors are singularly dependent on the excess kurtosis of the returns. Becoming risk-aware requires explicitly assessing hedge slippage of a hedging strategy to attempt option replication. In contrast, the risk-neutral tautology sets the option price equal to an expectation of option payoff under a risk-neutral probability that is inferred from option prices and under which the asset does not expect to accrete/deplete wealth. In the presence of irreducible risks, while a risk-neutral probability measure may be fit to observed option prices, it does not inform about the partitioning between expected attempted replication costs and compensation for irreducible risks. In segmented option markets with distinct risk premiums such a risk-neutral probability measure fails to exist.