Researchers are applying advanced mathematical modeling to the volatile world of cryptocurrency markets, aiming to better understand and manage financial risks. A new study details the use of a subordinated Lévy process, driven by a univariate integrated square-root Cox–Ingersoll–Ross (CIR) process, to capture the complex behavior of crypto asset prices.
The resulting stochastic volatility normal tempered stable (SVNTS) process, according to the research, effectively models key characteristics of cryptocurrency data, including the tendency for large price swings – known as heavy tails – asymmetry in price movements, and volatility clustering. The CIR model, originally developed in 1985 by John C. Cox, Jonathan E. Ingersoll, and Stephen A. Ross, describes the evolution of interest rates and has been adapted for use in financial markets beyond traditional finance.
A core component of the study involves a novel approach to calculating the probability of different return outcomes. Researchers employed the rapid Fourier transform (FFT) to numerically approximate the return probability density, which then facilitates the computation of tail risk measures – critical for assessing potential losses. This builds on existing work demonstrating the CIR process’s ability to model interest rate dynamics, as outlined in quantitative finance literature.
The SVNTS model was tested against a variety of cryptocurrency datasets, and its accuracy was rigorously evaluated. The researchers similarly proposed a new framework for estimating the model’s parameters. This framework combines maximum likelihood estimation, based on the FFT-derived density, with a Bayesian optimization scheme utilizing Gaussian regression and expected improvement for initial parameter selection. Particle swarm optimization, a technique less commonly used in similar studies, was then employed for final refinement.
Recognizing that cryptocurrencies don’t operate in isolation, the study also addresses the relationships between different assets. A Student t-copula was used to model these dependencies, allowing researchers to separate the marginal distributions of individual cryptocurrencies from their joint dependency structure. This separation is particularly important for accurately modeling tail dependence – the tendency for assets to move together during periods of market stress.
To assess the practical application of the model, portfolio optimization was performed using a robust multivariate simulation framework. The goal was to minimize conditional value-at-risk (CVaR) – a measure of potential losses – across a selection of cryptocurrencies. The accuracy of the resulting value-at-risk (VaR) and CVaR estimates was then validated through extensive backtesting procedures.
The research highlights the increasing sophistication of risk management techniques being applied to the cryptocurrency space. As blockchain and artificial intelligence converge, models like the SVNTS process are becoming increasingly important for predicting borrowing costs and constructing yield curves, according to industry analysts. The study’s findings could inform the development of autonomous trading bots and risk engines in decentralized finance (DeFi) platforms.
