That is what we appear, increasingly, to find in financial market prices in practice, whether in volatility and correlation or in fat tails and persistence. This change in price dynamics will in turn influence market-making behaviour. Consider the problem facing an HFT market-maker. They face inventory risk from market fluctuations and information risk from adverse selection. Pricing these risks means forming a guess about the future path of prices. The greater the potential range of future prices, the larger the insurance premium they will demand. The future price range (maximum – minimum) for a price series at some future date T, R(T), can be written generically as: 20 (1) where κ is a constant and σT is the standard deviation of the process up to time T. H is our old friend the Hurst coefficient, dredged up from the Nile; it can be thought to summarise the degree of fat-tailedness and persistence in prices. When the holding period is short (say T=1), as with HFT, the future price range is the volatility of the series magnified by the Hurst coefficient. In other words, the fatter and more persistent the tails (H), the greater the market risk and the wider the bid-ask spread of the HFT. This has implications for the dynamics of bid-ask spreads, and hence liquidity, among HFT firms. During a market crash, the volatility of prices (σ) is likely to spike. From equation (1), fractality heightens the risk-sensitivity of HFT bid-ask spreads to such a volatility event.
Both private consumption and investment provided an important stimulus to the growth rate in the first quarter of this year. More up-to-date indicators point towards continued expansion in the second quarter, albeit at a possibly more moderate pace than in the first quarter. The outlook on consumption is supported by higher real earnings growth and declining unemployment, and is reflected in consumer confidence. The evidence for the corporate sector is perhaps more mixed. As compared to the first quarter of 1998, industrial production figures show a somewhat slower rate of increase in the period from April to May, but capacity utilisation has continued to increase and this, combined with low interest rates, should underpin investment. European Commission survey data, such as confidence indicators and the assessment of order books, bear witness to relatively high levels, both with respect to their longterm averages and recent peaks. This can also be taken as a favourable indicator for continued growth in the short term, although some indicators have not improved further since the spring. Unemployment has also been declining, but at a modest pace, and from a high level. In discussing the cyclical uncertainties, one should not forget that work on badly needed structural reforms has not so far made much progress. Considering recent price developments, HICP inflation for the euro area as a whole remained stable at 1.4% between May and July. Both domestic and external factors still appear to be favourable, suggesting that euro area inflation may be expected to remain subdued in the future.