Risk-Neutral Systemic Risk Indicators

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThis paper describes a set of indicators of systemic risk computed from current market prices of equity and equity index options. It displays results from a prototype version, computed daily from January 2006 to January 2013. The indicators represent a systemic risk event as the realization of an extreme loss on a portfolio of large-intermediary equities. The technique for computing them combines risk-neutral return distributions with implied return correlations drawn from option prices, tying together the single-firm return distributions via a copula to simulate the joint distribution and thus the financial-sector portfolio return distribution. The indicators can be computed daily using only current market prices; no historical data are involved. They are therefore forward-looking and can exploit all the information impounded in current prices. However, the indicators blend both market expectations and the market's desire to protect itself against volatility and tail risk, so they cannot be readily decomposed into these two elements. The paper presents evidence that the indicators have some predictive power for systemic risk events and that they can serve as a meaningful market-adjusted point of comparison for fundamentalsbased systemic risk indicators.

Extreme-Strike Comparisons and Structural Bounds for SPX and VIX Options

“…The SVI parameterization is related to extreme strikes because its construction is consistent with the moment formulas in (3.2) and (3.3), namely that the square of large-strike implied volatility is proportional to log-moneyness divided by the square-root of time-to-maturity (see [Gat06,BGK13]). The result of this section can be applied as a risk-neutral systemic risk indicator, which is related to those proposed in [Mal13]. This section's main technical hurdle is that the limiting behavior for VIX options given in Proposition 3.4 cannot be differentiated in K. In other words, the limit in (3.4) shows a rate of convergence for C vix , but cannot be differentiated to find an asymptotic for the tail distribution ∂ ∂K C vix .…”

International Oil Market Risk Anticipations and the Cushing Bottleneck: Option-implied Evidence

“…The financial literature shows that option-implied moments are relevant ex ante risk metrics that relate to systematic risk and provide insightful economic interpretation (Dennis and Mayhew, 2002;Duan and Wei, 2009). For example, option-implied volatility (e.g., the VIX index in stock markets) is seen as an investor "fear gauge" (Whaley, 2000;Malz, 2013;Panigirtzoglou and Skiadopoulos, 2004). Option-implied skewness is linked to negative asymmetric returns in asset markets, and negative skewness in equity indexes is often interpreted as "crash-phobia" (Rubinstein, 1994).…”

“…There is a well-known literature documenting how to extract individual risk-neutral moments from options data, but this literature has focused so far on equity indexes. This literature includes Bakshi et al (2003), Birru and Figlewski (2012), Conrad et al (2013), Gagnon et al (2016), Jurek (2014), andMalz (2013). Our methodology is based on Birru and Figlewski's (2012) approach to recover the option-implied distribution with a Generalized Extreme Value method to model the tails.…”

A Simple and Reliable Way to Compute Option-Based Risk-Neutral Distributions

“…We denote the observed time-t market value of a European call struck at X and with a tenor of τ = T − t by c (t, X, τ). Absent arbitrage, therefore, the option value is equal to the present expected value of the terminal payoff under the risk-neutral distribution: S t ≡ time-t underlying price r t ≡ time-t continuously compounded financing ratẽ E t [·] ≡ an expectation taken under the time-t risk-neutral probability measurẽ π t (·) ≡ time-t risk-neutral probability density of S T 1 The technique set out here is applied to the measurement of systemic risk in Malz (2013). It is also used in the Federal Reserve Bank of New York's market monitoring.…”