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Implied volatility can signal that market turmoil has become more likely in the near future. Based on implied volatility, a practical warning signal is developed that can help risk managers posture themselves for stress events.
Introduction
Standard risk management procedures, both on the trading desk and in the corporate risk management office, assume a model in which asset returns are tolerably close to independently and identically normally distributed. Delta hedging and value-at-risk (VaR) are obvious examples. In fact, asset returns generally display economically important deviations from this baseline model. Traders and risk managers therefore have an intense interest in market indicators which can help them predict extreme moves in asset prices.
Awareness of the quantitative importance of non-normality has motivated risk managers to supplement standard risk measures, such as VaR, with reports focused on the potential losses induced by large-magnitude asset returns. Prominent among these are stress tests, which "estimate potential losses in abnormal markets" (Laubsch (1999), p. 21). Stress testing describes an array of tools used by financial institutions to quantify their exposures to extreme price moves, or exposures to "normal" price moves which are amplified by portfolio concentration. A standard best-practice recommendation for the use of stress tests is to apply them regularly during abnormal market conditions. Ideally, risk managers should apply stress tests not when abnormal market conditions already prevail, but in advance, so portfolios can be altered while liquidity is still deep and before losses occur. In efficient markets, risk managers cannot guarantee their ability to do so any more than traders can guarantee their ability to exit trades at the optimal time.
Market analysts have searched for leading indicators of financial events or crises among macroeconomic data, such as current account balances, central bank reserves, or corporate earnings, or among forward-looking asset prices, such as futures and forwards. Macroeconomic data are valuable in highlighting potential shifts in market equilibrium, but fresh data are available only infrequently and with long lags. More importantly, macroeconomic data are used to signal events up to 24 months in the future, a lead time which is far too short for trading and risk management purposes.
Financial market prices, in contrast, are available daily or even intraday and contain implicit information regarding short-term market moves. Our study will focus on a small number of widely traded assets and present evidence that option-implied volatilities can help warn risk managers of large price moves. Option prices are an obvious candidate for such a warning signal of large price moves, since options are traded, among other reasons, to enable market participants to tailor their exposures to large moves in asset prices. They tend to rise in price when markets expect or fear greater turbulence or consider a wider range of future asset prices plausible. Option volatilities may also rise in anticipation of large price moves because of liquidity concerns. End-users, for example, may buy or sell options because they replace the execution risk of a limit or stop-loss order with credit risk.
Futures and forwards can be observed virtually in real time, but may change only marginally in response to changes in market perceptions of large magnitude, but low-probability, events. Forward and futures prices are determined in part by the expected mean value of the future asset price, while option prices are determined primarily by the expected variance of the future asset price. We can illustrate the difference in how forwards and options react to changes in market views with a simple example. Imagine that forward prices are equal to the mean future asset price and option implied-volatilities are equal to the standard deviation of returns. In Scenario 1, there are two possible outcomes, both with a probability of 50%: the future asset price will be either $0.90 or $1.10. In this scenario, the forward price is $1.00 and the option implied volatility is 10% per period.
Now imagine the market view of the future changes to Scenario 2, in which there are three possible outcomes. The future asset price will be $0.90 or $1.10 with a 45% probability each, or $0.50 with a 10% probability. Introducing a small probability of a large asset price move changes the implied volatility far more dramatically than the forward price. In this scenario, the forward price is $1.05 and the option implied volatility is 17.75% per period. The forward price thus falls by less than 5%, but the option-implied volatility rises by 78% in the wake of the market's change in view from Scenario 1 to Scenario2.
There is another motivation for studying the relation between implied volatility and stress events. Previous research finds that implied volatility contains information about future volatility which is not captured in time series of returns. This finding suggests that implied volatility may contain information about stress events not contained in past returns. The present study extends this research to the question: does implied volatility contain information regarding higher-than-second moments of returns?
In the next section, we describe the data used in this study. Section 3 will present statistical evidence that implied volatility contains useful information about future large magnitude returns. Section 4 describes the predictive performance of a warning signal for stress testing based on implied volatility.
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