Estimating conditional volatility with neural networks

It is well known that one of the obstacles to effective forecasting of exchange rates is heteroscedasticity (non-stationary conditional variance). The autoregressive conditional heteroscedastic (ARCH) model and its variants have been used to estimate a time dependent variance for many financial time series. However, such models are essentially linear in form and we can ask whether a non-linear model for variance can improve results just as non-linear models (such as neural networks) for the mean have done. In this paper we consider two neural network models for variance estimation. Mixture Density Networks (Bishop 1994, Nix and Weigend 1994) combine a Multi-Layer Perceptron (MLP) and a mixture model to estimate the conditional data density. They are trained using a maximum likelihood approach. However, it is known that maximum likelihood estimates are biased and lead to a systematic under-estimate of variance. More recently, a Bayesian approach to parameter estimation has been developed (Bishop and Qazaz 1996) that shows promise in removing the maximum likelihood bias. However, up to now, this model has not been used for time series prediction. Here we compare these algorithms with two other models to provide benchmark results: a linear model (from the ARIMA family), and a conventional neural network trained with a sum-of-squares error function (which estimates the conditional mean of the time series with a constant variance noise model). This comparison is carried out on daily exchange rate data for five currencies.

Volatility changes in drachma exchange rates

In January 2001 Greece joined the eurozone. The aim of this article is to examine whether an intention to join the eurozone had any impact on exchange rate volatility. We apply the Iterated Cumulative Sum of Squares (ICSS) algorithm of Inclan and Tiao (1994) to a set of Greek drachma exchange rate changes. We find evidence to suggest that the unconditional volatility of the drachma exchange rate against the dollar, British pound, yen, German mark and ECU/Euro was nonstationary, exhibiting a large number of volatility changes prior to European Monetary Union (EMU) membership. We then use a news archive service to identify the events that might have caused exchange rate volatility to shift. We find that devaluation of the drachma increased exchange rate volatility but ERM membership and a commitment to joining the eurozone led to lower volatility. Our findings therefore suggest that a strong commitment to join the eurozone may be sufficient to reduce some exchange rate volatility which has implications for countries intending to join the eurozone in the future.

Explaining volatility and serial correlation in opening and closing returns:a study of the FT-30 components

In this paper the performance of opening and closing returns, for the components of the FT-30 will be studied. It will be shown that for these stocks opening returns have higher volatility and a greater tendency towards negative serial correlation than closing returns. Unlike previous studies this contrasting performance cannot solely be attributed to differences in the trading mechanism across the trading day. All the stocks used in our sample trade thought the day using a uniform trading mechanism. In this paper, we suggest that it is differences in the speed that closing and opening returns adjust to new information that causes differences in return performance. By estimating the Amihud and Mendelson (1987) [Amihud, Yakov, & Mendelson, Haim (1987). Trading mechanisms and stock returns: An empirical investigation, Journal of Finance, 62 533-553.] partial adjustment model with noise, we show that opening returns have a tendency towards over-reaction, while closing returns have a tendency towards under-reaction. We suggest that it is these differences that cause a substantial proportion (although not all) of the asymmetric return patterns associated with opening and closing returns. © 2005 Elsevier Inc. All rights reserved.

Volatility changes caused by the trading system:a Markov switching application

An expanding literature exists to suggest that the trading mechanism can influence the volatility of security returns. This study adds to this literature by examining the impact that the introduction of SETS, on the London Stock Exchange, had on the volatility of security returns. Using a Markov switching regime change model security volatility is categorized as being in a regime of either high or low volatility. It is shown that prior to the introduction of SETS securities tended to be in a low volatility regime. At the time SETS was introduced securities moved to a high volatility regime. This suggests that volatility increased when SETS was introduced.

Stochastic volatility and the goodness-of-fit of the Heston model

Recently, Drǎgulescu and Yakovenko proposed an analytical formula for computing the probability density function of stock log returns, based on the Heston model, which they tested empirically. Their research design inadvertently favourably biased the fit of the data to the Heston model, thus overstating their empirical results. Furthermore, Drǎgulescu and Yakovenko did not perform any goodness-of-fit statistical tests. This study employs a research design that facilitates statistical tests of the goodness-of-fit of the Heston model to empirical returns. Robustness checks are also performed. In brief, the Heston model outperformed the Gaussian model only at high frequencies and even so does not provide a statistically acceptable fit to the data. The Gaussian model performed (marginally) better at medium and low frequencies, at which points the extra parameters of the Heston model have adverse impacts on the test statistics. © 2005 Taylor & Francis Group Ltd.

Volatility transmission between stock and bond markets

A two-factor no-arbitrage model is used to provide a theoretical link between stock and bond market volatility. While this model suggests that short-term interest rate volatility may, at least in part, drive both stock and bond market volatility, the empirical evidence suggests that past bond market volatility affects both markets and feeds back into short-term yield volatility. The empirical modelling goes on to examine the (time-varying) correlation structure between volatility in the stock and bond markets and finds that the sign of this correlation has reversed over the last 20 years. This has important implications far portfolio selection in financial markets. © 2005 Elsevier B.V. All rights reserved.

Virtual Gires-Tournois etalons realized with phase-modulated wideband chirped fiber gratings

We propose and demonstrate novel virtual Gires–Tournois (GT) etalons based on fiber gratings. By introducing an additional phase modulation in wideband linearly chirped fiber Bragg gratings, we have successfully generated GT resonance with only one grating. This technique can simplify the fabrication procedure while retaining the normal advantages of distributed etalons, including their full compatibility with optical fiber, low insertion loss, and low cost. Such etalons can be used as dispersion compensation devices in optical transmission systems.

Interdependence of international equity market volatility

This paper investigates whether equity market volatility in one major market is related to volatility elsewhere. This paper models the daily conditional volatility of equity market wide returns as a GARCH-(1,1) process. Such a model will capture the changing nature of the conditional variance through time. It is found that the correlation between the conditional variances of major equity markets has increased substantially over the last two decades. This supports work which has been undertaken on conditional mean returns which indicates there has been an increase in equity market integration.

Conditional volatility and firm size:an empirical analysis of UK equity portfolios

The techniques and insights from two distinct areas of financial economic modelling are combined to provide evidence of the influence of firm size on the volatility of stock portfolio returns. Portfolio returns are characterized by positive serial correlation induced by the varying levels of non-synchronous trading among the component stocks. This serial correlation is greatest for portfolios of small firms. The conditional volatility of stock returns has been shown to be well represented by the GARCH family of statistical processes. Using a GARCH model of the variance of capitalization-based portfolio returns, conditioned on the autocorrelation structure in the conditional mean, striking differences related to firm size are uncovered.

Exchange controls and the transmission of equity market volatility:the case of the UK

The paper investigates the impact that the relaxation of UK exchange controls in October 1979, had on the transmission of equity market volatility from the UK to other major equity markets. It is suggested that the existence of exchange controls in the UK was an important source of market segmentation which disturbed the transmission of shocks from one country to another, even when shocks contained global information. It is found that when a spillover GARCH(1,1) model is estimated for the five years before and after the removal of exchange controls, volatility shocks spill over from the UK to other markets much more strongly after the removal of exchange controls. This appears to suggest that volatility as well as returns have become more closely related since the UK removed exchange controls.

Volatility transmission in the UK equity market

We provide evidence of the nature of the transmission of volatility within the UK stock market. We find a distinct asymmetry in that shocks to the return volatility of a portfolio of relatively large firms influence the future volatility of a portfolio of relatively small firms, but find that the reverse is not the case. The characteristics of the volatility process suggest that this result is not caused by thin trading.

Have the GIPSI settled down? Breaks and multivariate stochastic volatility models for, and not against, the European financial integration

We investigate the integration of the European peripheral financial markets with Germany, France, and the UK using a combination of tests for structural breaks and return correlations derived from several multivariate stochastic volatility models. Our findings suggest that financial integration intensified in anticipation of the Euro, further strengthened by the EMU inception, and amplified in response to the 2007/2008 financial crisis. Hence, no evidence is found of decoupling of the equity markets in more troubled European countries from the core. Interestingly, the UK, despite staying outside the EMU, is not worse integrated with the GIPSI than Germany or France. © 2013 Elsevier B.V.

Financial liberalization and stock market volatility:the case of Indonesia

This article examines the relationship between financial liberalization and stock market volatility in Indonesia. By looking at the time series properties of the Jakarta Composite Index (JCI) we identify breaks in stock market volatility which coincide with the timing of major policy events. Our main findings are (i) a significant decrease in volatility after the 'official' opening of the stock market to foreign participation; (ii) a significant increase in volatility in the year before market opening following reforms that eased entry requirements and the issuance of brokerage licenses and (iii) a significant increase in volatility at the time of the Asian crisis followed by a significant decrease in the second and sixth years after the crisis.

Stock market efficiency before and after a financial liberalisation reform:do breaks in volatility dynamics matter?

This article focuses on the deviations from normality of stock returns before and after a financial liberalisation reform, and shows the extent to which inference based on statistical measures of stock market efficiency can be affected by not controlling for breaks. Drawing from recent advances in the econometrics of structural change, it compares the distribution of the returns of five East Asian emerging markets when breaks in the mean and variance are either (i) imposed using certain official liberalisation dates or (ii) detected non-parametrically using a data-driven procedure. The results suggest that measuring deviations from normality of stock returns with no provision for potentially existing breaks incorporates substantial bias. This is likely to severely affect any inference based on the corresponding descriptive or test statistics.