Related papers: A Multivariate Hawkes Process Model for Stablecoin…
Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this…
We present a tractable non-independent increment process which provides a high modeling flexibility. The process lies on an extension of the so-called Harris chains to continuous time being stationary and Feller. We exhibit constructions,…
Stablecoins represent a critical bridge between cryptocurrency and traditional finance, with Tether (USDT) dominating the sector as the largest stablecoin by market capitalization. By Q1 2025, Tether directly held approximately $98.5…
Correlations in complex systems are often obscured by nonstationarity, long-range memory, and heavy-tailed fluctuations, which limit the usefulness of traditional covariance-based analyses. To address these challenges, we construct scale…
Given a stationary point process, an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate. It might signal a local non-stationarity or the presence of an external…
We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In…
Existence and stability properties are studied for Hawkes process, i.e. point process $S$ that has long-memory and intensity $r(t)=\lambda \big(g_0(t)+ \sum_{\tau<t, \tau \in S} h(t-\tau) \big)$. The approach to Hawkes process presented in…
In decentralized finance (DeFi), stablecoins like DAI are designed to offer a stable value amidst the fluctuating nature of cryptocurrencies. We examine the class of crypto-backed stable derivatives, with a focus on mechanisms for price…
BitCoin transactions are malleable in a sense that given a transaction an adversary can easily construct an equivalent transaction which has a different hash. This can pose a serious problem in some BitCoin distributed contracts in which…
Hawkes processes have seen a number of applications in finance, due to their ability to capture event clustering behaviour typically observed in financial systems. Given a calibrated Hawkes process, of concern is the statistical fit to…
HYGARCH process is the commonly used long memory process in modeling the long-rang dependence in volatility. Financial time series are characterized by transition between phases of different volatility levels. The smooth transition HYGARCH…
Extreme volatility, nonlinear dependencies, and systemic fragility are characteristics of cryptocurrency markets. The assumptions of normality and centralized control in traditional financial risk models frequently cause them to miss these…
This work builds upon the long-standing conjecture that linear diffusion models are inadequate for complex market dynamics. Specifically, it provides experimental validation for the author's prior arguments that realistic market dynamics…
The process algebra HYPE was recently proposed as a fine-grained modelling approach for capturing the behaviour of hybrid systems. In the original proposal, each flow or influence affecting a variable is modelled separately and the overall…
Dynamically distributed inflation is a common mechanism used to guide a blockchain's staking rate towards a desired equilibrium between network security and token liquidity. However, the high sensitivity of the annual percentage yield to…
The event sequence of many diverse systems is represented as a sequence of discrete events in a continuous space. Examples of such an event sequence are earthquake aftershock events, financial transactions, e-commerce transactions, social…
Identifying the structural dependence between the cryptocurrencies and predicting market trend are fundamental for effective portfolio management in cryptocurrency trading. In this paper, we present a unified Bayesian framework based on…
In a discrete-time setting, we consider an arrival process $\left\{\xi_n \, \middle| \, n = 1, 2, \ldots \right\}$, which models the occurrence of events, and a corresponding point process $\left\{H_n \, \middle| \, n = 1, 2, \ldots…
We formulate and solve stochastic control problems that model the core yield-generating strategy of the Ethena protocol, a decentralized finance (DeFi) stablecoin that earns yield by combining a long position in staked Ethereum (stETH) with…
This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $ S=(S_{t})_{t\geq0} $ is given by \[…