Coronavirus (COVID-19): market fear as implied by options prices

Prepared by Miguel Ampudia, Ursel Baumann and Fabio Fornari

Introduction

• Although equity markets have partially recovered since then, the Euro Stoxx 50 lost 12.3% in the week ending on 28 February, its largest weekly percentage loss since the global financial crisis in 2008.
• The S&P 500 declined by more than 11% in an equally catastrophic week.
• Overall, equity markets in the euro area and the United States lost around 35% of their value between their peak on 19 February and their trough on 23 March.
• The decline in equity prices has led to a large spike in the variance of their returns.
• Recent turbulence has clearly been global in nature, as shown by the substantial jump in the standard deviation across indices.
• The resulting lack of diversification opportunities also amplifies the potential losses faced by international investors.
• One of the main ways in which this shock has spread is via financial market linkages and, most notably, via the synchronous plunge in global stock markets.
• Knowing the main source of the decline in equity prices (and financial assets in general) may help policymakers understand its persistence and evaluate the policy response.

Risk-neutral densities

• The risk-neutral density therefore reflects both the risk attitudes and price expectations of investors.
• Risk-neutral densities can be thought of as physical densities whose shape has been modified in order to give more prominence to those states of the world that are associated with particularly adverse outcomes and that, as such, result in lower marginal utility for investors.
• [1] We derive the risk-neutral density of future returns from the daily prices of call and put options traded on the Euro Stoxx 50.
• [4] Chart B Euro Stoxx 50 option-implied risk-neutral densities For options with a horizon of approximately one year ahead (densities)

A tail risk aversion indicator

• An indicator of investor risk preferences or risk aversion can be derived by comparing the risk-neutral density with an estimate of the physical density of equity returns.
• The risk-neutral and the physical densities are related to each other through the pricing kernel, which embeds investors risk preferences.
• Expectations of physical densities cannot be determined from market prices, as market prices also embed the risk preferences of investors.
• [6] The tail risk aversion indicator is constructed by comparing the left tails of the risk-neutral and physical distributions.
• [7] A tail risk aversion index above one indicates that investors fear the materialisation of negative tail events and are therefore willing to insure against such an occurrence by paying more than would be justified by its historical likelihood.
• Chart C Euro Stoxx 50 tail risk aversion indicator and tail risk For options with a horizon of 10 to 20 days ahead (index)