ریسک بازار و مفهوم نوسانات اساسی: اندازه گیری نوسانات در بازارهای دارایی و مشتقات و آزمون برای تاثیر بازار مشتقات بر بازارهای مالی

This paper proposes an unobserved fundamental component of volatility as a measure of risk. This concept of fundamental volatility may be more meaningful than the usual measures of volatility for market regulators. Fundamental volatility can be obtained using a stochastic volatility model, which allows us to `filter’ out the signal in the volatility information. We decompose four FTSE100 stock index related volatilities into transitory noise and unobserved fundamental volatility. Our analysis is applied to the question as to whether derivative markets destabilise asset markets. We find that introducing European options reduces fundamental volatility, while transitory noise in the underlying and futures markets does not show significant changes. We conclude that, for the FTSE100 index, introducing a new options market has stabilised both the underlying market and existing derivative markets.

Traditionally, the efficient market hypothesis views price volatility as a result of the random arrival of new information which changes returns. However, empirical studies such as Shiller (1981), Schwert (1989), and French and Roll (1986) suggest that volatility cannot be explained only by changes in fundamentals. Significant amounts of volatility in asset prices come from `noise trading’ of irrational traders. From this point of view, volatility may be defined as the sum of transitory volatility caused by noise trading and unobserved fundamental volatility caused by stochastic information arrival. Our modelling of fundamental volatility in this paper assumes that the fundamental volatility is an unobserved random variable; it changes through time. There are many volatilities related to only one underlying asset which are measurable at a given time point: the return volatility of the underlying asset, futures return volatility on the asset, and call and put option implied volatilities over various maturities and exercise prices, etc. However, it is natural to assume that there is only one fundamental volatility defined over the underlying asset and all its derivatives. This is because information which affects the fundamentals of the underlying asset is the same across all derivatives of the asset and, thus, results in the same fundamental volatility. Other factors will also influence this single fundamental volatility as well as information arrival: the structure of related markets, the distribution of assets held by investors, transaction costs and numerous other factors in the global economy, including all the macroeconomic information available at the time. This study does not address these other factors which may be important. Our decision to not include them was driven by unavailability of data and the difficulties of specifying a plausible model that covers all these points. Our study proceeds by decomposing the FTSE100 stock index related volatilities into transitory noise and fundamental volatility and utilises the decomposition to investigate the effect of the introduction of derivatives on the volatility. Using the stochastic volatility model (SVM) developed by Harvey and Shephard, 1993 and Harvey and Shephard, 1996 and Harvey et al. (1994), we calculate the portion of transitory noise in the observed volatility (i.e., signal-to-noise ratio), and are able to infer the fundamental volatility process and also the relationship between transitory noises of different volatilities. Our analysis reveals the following results. Noise in the options market is not correlated with noise in the underlying and/or futures markets. However, the different noises associated with different options contracts are correlated with each other, and noise in the underlying market is correlated with that of the futures market. In addition, fundamental volatility has a high degree of persistence, a feature often observed in high frequency financial data; see Engle and Bollerslev (1986). An interesting area of study for volatility is to investigate the effect of the introduction of derivatives on the underlying asset volatility. In a frictionless no-arbitrage world, derivatives are redundant assets and will not effect the underlying market. However, in the real world where markets are incomplete, effects of the introduction of derivatives markets on the underlying market exist. Derivative markets may stabilise underlying markets by more efficient risk allocation or destabilise underlying markets by increasing speculation. Our study investigates the effects of the introduction of derivatives on the unobserved fundamental volatility and the transitory noise of the FTSE100 index related volatilities. Futures and American options on the FTSE100 index were introduced on 3 May 1984 and European options were listed on 1 February 1990. We are not able to show the effects of the introduction of futures and American options on the FTSE100 index volatility, since the impact of introducing two derivatives at the same time can not be separated and the number of daily observations before the introduction of the derivatives is relatively small (i.e., 85 observations). However, we find that introducing European options reduced fundamental volatility, while the transitory noise in the underlying and futures markets did not show significant changes. On the basis of the evidence, we conclude that, for the FTSE100 index, introducing an options market stabilised the other financial markets (that is, underlying and derivative markets).

Using stochastic volatility models, we decomposed four different volatilities, the FTSE100 index return volatility, the return volatility for futures on the FTSE100 index, and the FTSE100 index American and European call option implied volatilities, into what we call unobserved fundamental volatility and transitory noise. For the return volatilities such as the FTSE100 index and its futures, transitory noise is much larger than the fundamental volatility, while implied volatilities of European and American call options consist of fundamental volatility rather than transitory noise. In addition, transitory noises of the FTSE100 index return volatility and futures return volatility are correlated with each other, and transitory noises of FTSE100 American and European call option implied volatilities are also correlated with each other. However, transitory noises of return volatilities are not correlated with those of implied volatilities, suggesting that trading noise in options markets is different from that in an underlying market or futures market. We have obtained two types of volatility changes: changes in levels, and changes in the underlying dynamic process which correspond to a change in overall persistence of all the markets. Whilst both are interesting to asset managers or regulators, we feel that large changes in the latter should be of particular interest as they reflect the fact that shocks may accumulate rather than die away. Unfortunately, we cannot reach a firm conclusion on the effect of the introduction of the futures or American options on the fundamental volatility and transitory noise, since there is only a small number of observations prior to the American options and futures on the FTSE100 index and their simultaneous introduction. The finding that persistence increases as a result of the introduction of derivatives needs to be supported by more data and analysis in other markets. This may reflect better risk management whereby anticipated shocks are spread out over longer periods through the use of derivatives. However, following the introduction of European options, we find that the level of fundamental volatility is reduced but there is no significant change in the fundamental volatility process. Furthermore, the transitory noise of American call options decreased significantly, while other transitory noises do not show significant change. Our study proposes that fundamental volatility may be the correct measure of risk for the total market. Changes in fundamental volatility rather than observed volatility may be more appropriate for market regulators when they investigate the systematic effect of the introduction of derivatives on the market or the current state of the market. Regulators who currently compute the risk-neutral density of returns implied by option prices may wish to consider our procedure as a complimentary calculation to assess changes in the riskiness of market.