News-driven Expectations and Volatility Clustering

Financial volatility obeys two fascinating empirical regularities that apply to various assets, on various markets, and on various time scales: it is fat-tailed (more precisely power-law distributed) and it tends to be clustered in time. Many interesting models have been proposed to account for these regularities, notably agent-based models, which mimic the two empirical laws through a complex mix of nonlinear mechanisms such as traders' switching between trading strategies in highly nonlinear way. This paper explains the two regularities simply in terms of traders' attitudes towards news, an explanation that follows almost by definition of the traditional dichotomy of financial market participants, investors versus speculators, whose behaviors are reduced to their simplest forms. Long-run investors' valuations of an asset are assumed to follow a news-driven random walk, thus capturing the investors' persistent, long memory of fundamental news. Short-term speculators' anticipated returns, on the other hand, are assumed to follow a news-driven autoregressive process, capturing their shorter memory of fundamental news, and, by the same token, the feedback intrinsic to the short-sighted, trend-following (or herding) mindset of speculators. These simple, linear, models of traders' expectations, it is shown, explain the two financial regularities in a generic and robust way. Rational expectations, the dominant model of traders' expectations, is not assumed here, owing to the famous no-speculation, no-trade result

News-Driven Expectations and Volatility Clustering

Financial volatility obeys two fascinating empirical regularities that apply to various assets, on various markets, and on various time scales: it is fat-tailed (more precisely power-law distributed) and it tends to be clustered in time. Many interesting models have been proposed to account for these regularities, notably agent-based models, which mimic the two empirical laws through a complex mix of nonlinear mechanisms such as traders switching between trading strategies in highly nonlinear way. This paper explains the two regularities simply in terms of traders’ attitudes towards news, an explanation that follows from the very traditional dichotomy of financial market participants, investors versus speculators, whose behaviors are reduced to their simplest forms. Long-run investors’ valuations of an asset are assumed to follow a news-driven random walk, thus capturing the investors’ persistent, long memory of fundamental news. Short-term speculators’ anticipated returns, on the other hand, are assumed to follow a news-driven autoregressive process, capturing their shorter memory of fundamental news, and, by the same token, the feedback intrinsic to the short-sighted, trend-following (or herding) mindset of speculators. These simple, linear models of traders’ expectations explain the two financial regularities in a generic and robust way. Rational expectations, the dominant model of traders’ expectations, is not assumed here, owing to the famous no-speculation, no-trade results

A Novel Methodology to Calculate the Probability of Volatility Clusters in Financial Series: An Application to Cryptocurrency Markets

One of the main characteristics of cryptocurrencies is the high volatility of their exchange rates. In a previous work, the authors found that a process with volatility clusters displays a volatility series with a high Hurst exponent. In this paper, we provide a novel methodology to calculate the probability of volatility clusters with a special emphasis on cryptocurrencies. With this aim, we calculate the Hurst exponent of a volatility series by means of the FD4 approach. An explicit criterion to computationally determine whether there exist volatility clusters of a fixed size is described. We found that the probabilities of volatility clusters of an index (S&P500) and a stock (Apple) showed a similar profile, whereas the probability of volatility clusters of a forex pair (Euro/USD) became quite lower. On the other hand, a similar profile appeared for Bitcoin/USD, Ethereum/USD, and Ripple/USD cryptocurrencies, with the probabilities of volatility clusters of all such cryptocurrencies being much greater than the ones of the three traditional assets. Our results suggest that the volatility in cryptocurrencies changes faster than in traditional assets, and much faster than in forex pairs

An Agent-Based Model of a Pricing Process with Power Law, Volatility Clustering, and Jumps

In this paper, we propose a new model of security price dynamics in order to explain the stylized facts of the pricing process such as power law distribution, volatility clustering, jumps, and structural changes. We assume that there are two types of agents in the financial market: speculators and fundamental investors. Speculators use past prices to predict future prices and only buy assets whose prices are expected to rise. Fundamental investors attach a certain value to each asset and buy when the asset is undervalued by the market. When the expectations of agents are exogenously driven, that is, entirely shaped by exogenous news, then they can be modeled as following a random walk. We assume that the information related to the two types of agents in the model will arrive randomly with a certain probability distribution and change the viewpoint of the agents according to a certain percentage. Our simulated results show that this model can simulate well the random walk of asset prices and explain the power-law tail distribution of returns, volatility clustering, jumps, and structural changes of asset prices

Quantitative Methods for Economics and Finance

This book is a collection of papers for the Special Issue “Quantitative Methods for Economics and Finance” of the journal Mathematics. This Special Issue reflects on the latest developments in different fields of economics and finance where mathematics plays a significant role. The book gathers 19 papers on topics such as volatility clusters and volatility dynamic, forecasting, stocks, indexes, cryptocurrencies and commodities, trade agreements, the relationship between volume and price, trading strategies, efficiency, regression, utility models, fraud prediction, or intertemporal choice