Limit results for discretely observed stochastic volatility models with leverage e¤ect

In this note we generalize the limit results in [Genon-Catalot, Jeantheau, Laredo, 2000, Bernoulli ] for simple stochastic volatility models to the case where a non zero correlation is allowed between the Brownian mo- tion driving the main di¤usion process and the Brownian motion driving the dymaics of the instantaneous variance. We also extend the results to the case where the main di¤usion admits a non zero drift which is linear in the variance process. The main motivation for such an extension is the application of these limit results in order to perform statistical infer- ence in some of the stochastic volatility models introduced in the ?nancial mathematics literature. In this framework it is of relevance the so called "leverage e¤ect" between the stock log-price and its volatility, which is indeed explained by a negative correlation between the Brownian motions driving the log-price process and its instantaneous variance. Moreover a linear term in the variance appears in the drift of the log-price diffusion.

Path properties of simulation schemes for the Heston stochastic volatility model.

The aim of this study is to evaluate some simulation schemes recently suggested for the Heston model by examining their ability in reproducing, on the simulated paths, the autocovariance function of the generated model, when discretely observed. This is done by applying the outcomes of previous research where, based on discrete equi-spaced observations of the log-price, we determined an approximate confidence band for the theoretical autocovariance function of the mean variance process.

Modeling Bitcoin Price and Bubbles

The goal of this chapter is to present recent developments about Bitcoin1 price modeling and related applications. Precisely, we consider a bivariate model in continuous time to describe the behavior of Bitcoin price and of the investors’ attention on the overall network. The attention index affects Bitcoin price through a suitable dependence on the drift and diffusion coefficients and a possible correlation between the sources of randomness represented by the driving Brownian motions. The model is fitted on historical data of Bitcoin prices, by considering the total trading volume and the Google Search Volume Index as proxies for the attention measure. Moreover, a closed formula is computed for European-style derivatives on Bitcoin. Finally, we discuss two possible extensions of the model. Precisely, we investigate the relation between the correlation parameter and possible bubble effects in the asset price; further, we consider a multivariate framework to represent the special feature of Bitcoin being traded on several exchanges and we discuss conditions to rule out arbitrage opportunities in this setting

Il Futuro della Cybersecurity in Italia: Ambiti Progettuali Strategici

Il presente volume nasce come continuazione del precedente, con l’obiettivo di delineare un insieme di ambiti progettuali e di azioni che la comunità nazionale della ricerca ritiene essenziali a complemento e a supporto di quelli previsti nel DPCM Gentiloni in materia di sicurezza cibernetica, pubblicato nel febbraio del 2017. La lettura non richiede particolari conoscenze tecniche; il testo è fruibile da chiunque utilizzi strumenti informatici o navighi in rete. Nel volume vengono considerati molteplici aspetti della cybersecurity, che vanno dalla definizione di infrastrutture e centri necessari a organizzare la difesa alle azioni e alle tecnologie da sviluppare per essere protetti al meglio, dall’individuazione delle principali tecnologie da difendere alla proposta di un insieme di azioni orizzontali per la formazione, la sensibilizzazione e la gestione dei rischi. Gli ambiti progettuali e le azioni, che noi speriamo possano svilupparsi nei prossimi anni in Italia, sono poi accompagnate da una serie di raccomandazioni agli organi preposti per affrontare al meglio, e da Paese consapevole, la sfida della trasformazione digitale. Le raccomandazioni non intendono essere esaustive, ma vanno a toccare dei punti che riteniamo essenziali per una corretta implementazione di una politica di sicurezza cibernetica a livello nazionale. Politica che, per sua natura, dovrà necessariamente essere dinamica e in continua evoluzione in base ai cambiamenti tecnologici, normativi, sociali e geopolitici. All’interno del volume, sono riportati dei riquadri con sfondo violetto o grigio; i primi sono usati nel capitolo introduttivo e nelle conclusioni per mettere in evidenza alcuni concetti ritenuti importanti, i secondi sono usati negli altri capitoli per spiegare il significato di alcuni termini tecnici comunemente utilizzati dagli addetti ai lavori. In conclusione, ringraziamo tutti i colleghi che hanno contribuito a questo volume: un gruppo di oltre 120 ricercatori, provenienti da circa 40 tra Enti di Ricerca e Università, unico per numerosità ed eccellenza, che rappresenta il meglio della ricerca in Italia nel settore della cybersecurity. Un grazie speciale va a Gabriella Caramagno e ad Angela Miola che hanno contribuito a tutte le fasi di produzione del libro. Tra i ringraziamenti ci fa piacere aggiungere il supporto ottenuto dai partecipanti al progetto FILIERASICURA

An explorative analysis of sentiment impact on S&P 500 components returns, volatility and downside risk

The main contribution of this study is to assess whether investor sentiment, as measured through textual analysis of newspaper articles or social media posts, does have an effect on the mean returns and on the variance of financial stocks. The analysis is carried on a basket of the S &P 500 components where stock returns and volatility are modeled within the GARCH family augmented, both in the mean and the variance equation, with an exogenous variable representing the investor sentiment; the latter is measured through specific Bloomberg proprietary scores based on News or Twitter feeds. Empirical results support the hypothesis that these indicators do have a positive impact on stock prices: the Twitter based index positively affects the components returns, confirming the outcomes of existing studies, whereas the news based index has a significant impact on their volatility. We also contribute the literature by performing the same analysis across the 11 sectors of the index, evidencing that investor sentiment has a significant impact on Industrials, Health Care, Consumer Discretionary, Consumer Staples, Information Technology and Communication Services. As a further contribution, we perform an out-of-sample analysis to assess the potential effect of Bloomberg sentiment scores on downside risk measures, such as Value at Risk and Expected Shortfall. This subject is relevant to regulators in order to conceive suitable policy interventions during turmoil periods around specific market sectors or stocks

Sentiment-driven mean reversion in the 4/2 stochastic volatility model with jumps

With the availability of social networks, specialized forums, and online news, sentiment analysis has become a common and useful technique for the analysis of economic and financial scenarios. Several data-providers have also started computing proprietary sentiment indexes on financial assets to be delivered together with market price and trading volume. We develop a modified version of themean-reverting 4/2 stochastic volatility model introduced in Escobar-Anel & Gong (2020) to describe the dynamics of commodities. In our specification, jumps are allowed in the asset price dynamics, and the drift coefficientmay also switch between regimes related to a sentiment indicator. In this framework, we discuss the distributional characteristics of asset returns, provide a numerical procedure for model estimation, and give some preliminary results on the pricing of European-style derivatives. Finally, the model is fitted to the market data for Gold and Crude Oil

Cryptocurrencies as a driver of innovation for the monetary system

In this paper we outline a theory of cryptocurrencies that parallels the standard theory of money. We evidence that cryptocurrencies satisfy some but not all conditions that qualify a medium of exchange as money. Specifically, the process of creation and distribution of cryptocurrencies significantly differs from that of money impacting trust and value creation. New form of cryptocurrencies, such as central bank digital currencies, are considered. We outline scenarios of future evolution of cryptocurrencies and how they might be adopted by central banks to replace cash and/or to have direct interaction with the public