Negative Call Prices

TL;DR

This paper demonstrates that negative prices for European call options can occur even under no-arbitrage conditions like NFLVR, highlighting limitations of standard no-arbitrage arguments and trading constraints.

Contribution

It reveals that the existence of an equivalent local martingale measure does not guarantee non-negative call prices, challenging common assumptions in financial modeling.

Findings

Negative call prices can occur under NFLVR.

Standard admissibility constraints exclude certain arbitrage strategies.

Market prices may differ from replicating prices despite no-arbitrage conditions.

Abstract

We show that the existence of an equivalent local martingale measure for asset prices does not prevent negative prices for European calls written on positive stock prices. In particular, we illustrate that many standard no-arbitrage arguments implicitly rely on conditions stronger than the No Free Lunch With Vanishing Risk (NFLVR) assumption. The discrepancy between replicating prices and market prices for a contingent claim may be observed in a model satisfying NFLVR since certain trading strategies of buying one portfolio and selling another one are often excluded by standard admissibility constraints.