1,720,988 research outputs found
A change of measure formula for recursive conditional expectations
No full textWe derive a representation for the value process associated to the solutions of forward-backward stochastic differential equations in a jump-diffusion setting under multiple probability measures. Motivated by concrete financial problems, the latter representations are then applied to devise a generalization of the change of numéraire technique, allowing to obtain recursive pricing formulas in the presence of non-linear funding terms due to e.g. collateralization agreements
Option pricing in a sentiment-biased stochastic volatility model
No full textThis paper presents a Markov-modulated stochastic volatility model that captures the dependency of market regimes on investor sentiment. The main contribution lies in developing a modified version of the classical Heston model by allowing for a sentiment-driven bias in the volatility of the asset. Specifically, a two-factor Markov-modulated stochastic volatility model is proposed, integrating a diffusion coefficient in the risky asset dynamics and a correlation parameter influenced by both the volatility process and a continuous-time Markov chain accounting for the sentiment-bias. Diverging from conventional approaches in option pricing models, this framework operates under the real-world probability measure, necessitating considerations about the existence of an equivalent martingale pricing measure. The purpose of this paper is to derive a closed formula for the pricing of European-style derivatives and to fit the model on market data through a suitable calibration procedure. A comparison with the Heston benchmark model is provided for a sample of Apple, Amazon, and Bank of America stock options
Disentangling the relationship between Bitcoin and market attention measures
No full textIn the last few years Bitcoin price dynamics has been the subject of intense research. One of the main stream of investigation is the identification of relevant factors affecting its returns and volatility; empirical evidence suggests a positive association between returns and sentiment proxies about the Bitcoin network, such as Wikipedia inquiries, internet search intensity on the topic, trading volume in main exchanges or sentiment measures obtained via natural language processing algorithms applied on specialized forums comments or social media posts on the theme. In this paper we investigate the association of trading volume and internet search intensity with Bitcoin returns and volatility, complementing the outcomes in Figá-Talamanca and Patacca (Decis Econ Fin ISSN: 1129-6569, https ://doi.org/10.1007/s1020 3-019- 00258 -7, 2019) and Urquhart (Econ Lett 166:40–44, ISSN: 0165-1765, https ://doi.org/10.1016/j.econl et.2018.02.017, 2018): we find no direct relationship between the two market attention measures and returns while both the trading volume and the internet search intensity affect positively Bitcoin volatility. Conversely, an increase in Bitcoin returns does increase both trading volume and internet search intensity, evidencing an inverse relationship between returns and attention measures. As a byproduct, we also detect a positive association between trading volume and the internet search intensity and no reverse relationship. Since market attention, especially internet search volume, do increase around relevant events and corresponding news or announcements for the Bitcoin market, we also analyze whether and to which extent the above relationships change, after specific events are taken into account. Indeed, by applying two different approaches, we show that the relationships may change significantly
Does market attention affect Bitcoin returns and volatility?
No full textIn this paper, we analyze the relative impact of attention measures either on the mean or on the variance of Bitcoin returns by fitting nonlinear econometric models to historical data: Two non-overlapping subsamples are considered from January 1, 2012, to December 31, 2017. Outcomes confirm that market attention has an impact on Bitcoin returns and volatility, when measured by applying several transformations on time series for the trading volume or the SVI Google searches index. Specifically, best candidate models are selected via the so-called Box-Jenkins methodology and by maximizing out-of-sample forecasting performance. Overall, we can conclude that trading volume-related measures affect both the mean and the volatility of the cryptocurrency returns, while Internet searches volume mainly affects the volatility. An interesting side finding is that the inclusion of attention measures in model specification makes forecast estimates more accurate
Market attention and Bitcoin price modeling: theory, estimation and option pricing
No full textThe goal of this paper is to provide a novel quantitative framework to describe the Bitcoin price behavior, estimate model parameters and study the pricing problem for Bitcoin derivatives. To this end, we propose a continuous time model for Bitcoin price motivated by the findings in recent literature on Bitcoin, showing that price changes are affected by sentiment and attention of investors, see e.g., (Kristoufek in Sci Rep 3:3415, 2013, PLoS ONE 10(4):e0123923, 2015; Bukovina and Marticek in Sentiment and bitcoin volatility. Technical report, Mendel University in Brno, Faculty of Business and Economics 2016). Economic studies, such as Yermack (Handbook of Digital Currency, chapter second. Elsevier, Amsterdam, pp 31–43, 2015), have also classified Bitcoin as a speculative asset rather than a currency due to its high volatility. Building on these outcomes, the price dynamics in our suggestion is indeed affected by an exogenous factor which represents market attention in the Bitcoin system. We prove the model to be arbitrage-free under a mild condition and we fit the model to historical data for the Bitcoin price; after obtaining a approximate formula for the likelihood, parameter values are estimated by means of the profile likelihood method. In addition, we derive a closed pricing formula for European-style derivatives on Bitcoin, the performance of which is assessed on a panel of market prices for Plain Vanilla options quoted on www.deribit.com
A deep solver for BSDEs with jumps
Full text linkThe aim of this work is to propose an extension of the Deep BSDE solver by Han, E, Jentzen (2017) to the case of FBSDEs with jumps. As in the aforementioned solver, starting from a discretized version of the BSDE and parametrizing the (high dimensional) control processes by means of a family of artificial neural networks (ANNs), the BSDE is viewed as model-based reinforcement learning problem and the ANN parameters are fitted so as to minimize a prescribed loss function. We take into account both finite and infinite jump activity by introducing, in the latter case, an approximation with finitely many jumps of the forward process
Model-based arbitrage in multi-exchange models for Bitcoin price dynamics
No full textBitcoin is a digital currency started in early 2009 by its inventor under the pseudonym of Satoshi Nakamoto. In the last few years, Bitcoin has received much attention and has shown a surprising price increase. Bitcoin is currently traded on many webexchanges making it a rare example of a good for which different prices are readily available; this feature implies important issues about arbitrage opportunities since prices on different exchanges are shown to be driven by the same risk factor. In this paper, we show that simple strategies of strong arbitrage arise by trading across different Bitcoin exchanges taking advantage of the common risk factor. The suggested arbitrage strategies are based on two alternative model specifications. Precisely, we consider the multivariate versions of Black and Scholes model and of an attentionbased dynamics recently introduced in the literature
Common dynamic factors for cryptocurrencies and multiple pair-trading statistical arbitrages
Full text linkIn this paper, we apply dynamic factor analysis to model the joint behaviour of Bitcoin, Ethereum, Litecoin and Monero, as a representative basket of the cryptocurrencies asset class. The empirical results suggest that the basket price is suitably described by a model with two dynamic factors. More precisely, we detect one integrated and one stationary factor until the end of August 2019 and two integrated factors afterwards. Based on this evidence, we define a multiple long-short trading strategy which proves profitable when the second factor is stationary
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