Financial market disruption and investor awareness: the case of implied volatility skew

Abstract

The crash of 1987 is considered one of the most significant events in the history of financial markets due to the severity and swiftness of market declines worldwide. In the aftermath of the crash, a permanent change in options market occurred; implied volatility skew started appearing in options markets worldwide. In this article, we argue that the emergence of the implied volatility skew can be understood as arising from increased investor awareness about the stock price process and its implications for delta hedging. Delta-hedging aims to eliminate the directional risk associated with price movements in the underlying asset. Before the crash, investors were unaware of the proposition that "a delta-hedged portfolio is risky". That is, they implicitly believed in the proposition that "a delta-hedged portfolio is risk-free". The crash caused "portfolio insurance delta-hedges" to fail spectacularly. The resulting visceral shock drove home the lesson that "a delta-hedged portfolio is risky", thus, increasing investor awareness. We show that this sudden realization that a delta-hedged portfolio is risky is sufficient to generate the implied volatility skew and is equivalent to replacing the risk-free rate with a higher rate in the European call option formula. It follows that investor awareness (beyond asymmetric information) is an important consideration that matters for financial market behavior.

Keywords

• partial awareness
• restricted awareness
• black scholes model
• analogy making
• generalized principle of no-arbitrage
• implied volatility skew
• implied volatility smile
• portfolio insurance delta-hedge