Nikola Gradojevic

Asymmetry of Information Flow Between Volatilities Across Time Scales

Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price changes. On the other hand, statistical properties of monthly price changes are often not fully covered by a model based on daily price changes. In this paper, we simultaneously model regimes of volatilities at multiple time scales through wavelet-domain hidden Markov models. We establish an important stylized property of volatility across different time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state at shorter time horizons. Our analysis provides evidence that volatility is a mixture of high and low volatility regimes, resulting in a distribution that is non-Gaussian. This result has important implications regarding the scaling behavior of volatility, and consequently, the calculation of risk at different time scales.

Option Pricing With Modular Neural Networks

This paper investigates a nonparametric modular neural network (MNN) model to price the S&P-500 European call options. The modules are based on time to maturity and moneyness of the options. The option price function of interest is homogeneous of degree one with respect to the underlying index price and the strike price. When compared to an array of parametric and nonparametric models, the MNN method consistently exerts superior out-of-sample pricing performance. We conclude that modularity improves the generalization properties of standard feedforward neural network option pricing models (with and without the homogeneity hint).

Investment information content in Bollinger Bands

This article tests the profitability of Bollinger Bands (BB) technical indicators. It is found that, after adjusting for transaction costs, the BB are consistently unable to earn profits in excess of the buy-and-hold trading strategy. However, the profitability is improved using a contrarians approach.

Errors-in-Variables Estimation with Wavelets

This paper proposes a wavelet (spectral) approach to estimate the parameters of a linear regression model where the regressand and the regressors are persistent processes and contain a measurement error. We propose a wavelet filtering approach which does not require instruments and yields unbiased estimates for the intercept and the slope parameters. Our Monte Carlo results also show that the wavelet approach is particularly effective when measurement errors for the regressand and the regressor are serially correlated. With this paper, we hope to bring a fresh perspective and stimulate further theoretical research in this area.

Financial Applications of Nonextensive Entropy [Applications Corner]

Many traditional signal processing techniques in finance have limited ability to explain trading processes and distributional properties of the actual market prices. This is typically manifested in model misspecification and pricing and forecasting inaccuracy. For instance, the assumption that log stock returns are normally distributed is widely used in modern mathematical finance.

The Tale of Two Financial Crises: An Entropic Perspective

This paper provides a comparative analysis of stock market dynamics of the 1987 and 2008 financial crises and discusses the extent to which risk management measures based on entropy can be successful in predicting aggregate market expectations. We find that the Tsallis entropy is more appropriate for the short and sudden market crash of 1987, while the approximate entropy is the dominant predictor of the prolonged, fundamental crisis of 2008. We conclude by suggesting the use of entropy as a market sentiment indicator in technical analysis.

A market microstructure analysis of the Canadian dollar depreciation episodes in the 1990s

This article analyses two sudden depreciations of the Canadian dollar in the 1990s: July/August 1998 and November/December 1994. It is found that a nonparametric exchange rate model based on a combination of fundamental and microstructure (order flow) variables can be used not only to explain, but to also predict such excessive currency movements. During the depreciation periods, the forecast accuracy of the model is significantly superior to that of the linear model. The results provide an illustrative example that order flow variables have a substantial explanatory power for a very short-run exchange rate prediction.

Improving non-parametric option pricing during the financial crisis

Financial option prices have experienced excessive volatility in response to the recent economic and financial crisis. During the crisis periods, financial markets are, in general, subject to an abrupt regime shift which imposes a significant challenge to option pricing models. In this context, swiftly evolving markets and institutions require valuation models that are capable of recognizing and adapting to such changes. Both parametric and non-parametric pricing models have shown poor forecast ability for options traded in late 1987 and 2008. Surprisingly, the pricing inaccuracy was more pronounced for non-parametric models than for parametric models. To address this problem, we propose a novel hybrid methodology - modular neural network-fuzzy learning vector quantization (MNN-FLVQ) model - that uses the Kohonen unsupervised learning and fuzzy clustering algorithms to classify the S&P 500 stock market index options, and thereby detect a regime shift. In our empirical application, the results for the 2008 financial crisis demonstrate that the MNN-FLVQ model is superior to the competing methods in regards to option pricing during regime shifts.

The marketing-entrepreneurship paradox: A frequency-domain analysis

THE MARKETING-ENTREPRENEURSHIP PARADOX: A FREQUENCY-DOMAIN ANALYSIS Slavka T. Nikolić, Nikola Gradojević, Vladimir Đaković, Valentina Mladenović,

High-Frequency Technical Trading: Insights for Practitioners

This chapter investigates the profitability of technical trading rules applied to high-frequency data across two time periods: (1) periods of increased market volatility; and (2) periods of the markets upward trend. The analysis utilizes 5-min data for the S&P 500 Index and the VIX (Chicago Board Options Exchange Market Volatility Index) from 2011 to 2013. Three variants of four common trading rules are tested (moving averages, filter rules, Bollinger bands, and breakouts). The results suggest that the VIX is not a useful indicator for technical trading profitability at high frequencies regardless of the volatility regime. The S&P 500 Index data are shown to generate profitable trading signals during periods of higher volatility, but not during steady market increases. Overall, the results suggest that technical trading strategies calculated at high frequencies are more profitable when the market is volatile.This chapter investigates the profitability of technical trading rules applied to high-frequency data across two time periods: (1) periods of increased market volatility; and (2) periods of the markets upward trend. The analysis utilizes 5-min data for the S&P 500 Index and the VIX (Chicago Board Options Exchange Market Volatility Index) from 2011 to 2013. Three variants of four common trading rules are tested (moving averages, filter rules, Bollinger bands, and breakouts). The results suggest that the VIX is not a useful indicator for technical trading profitability at high frequencies regardless of the volatility regime. The S&P 500 Index data are shown to generate profitable trading signals during periods of higher volatility, but not during steady market increases. Overall, the results suggest that technical trading strategies calculated at high frequencies are more profitable when the market is volatile.