A Novel Extension of Entropy Measures in Quantifying Financial Markets Uncertainty:

Theory and Applications

Abstract

The global financial market is characterized by inherent and evolving uncertainty. Measuring this uncertainty plays a crucial role in managing risk associated with financial derivatives. Various mathematical models, including robust risk measures, model risk measures, and locally risk-minimizing strategies, have been employed to quantify this uncertainty. This paper contributes to this ongoing research by proposing novel approaches to quantify uncertainty in financial derivatives, specifically by leveraging entropy measures with stochastic probability density functions. Traditionally, entropy models have relied on Gaussian probability density functions. This paper proposes an alternative approach using stochastic probability density functions, to capture the inherent randomness of uncertainty in financial markets. Furthermore, the use of this developed stochastic density function will achieve linear and sub-linear scaling without relying on the sparsity of the density matrix nor on the design of the subsystem interaction in embedding schemes. We demonstrate that this approach adheres to key entropy properties and can be extended to various entropy families. Empirical results show that the proposed model using stochastic probabilities outperforms models using normal probabilities, potentially representing a significant advancement in quantifying uncertainty with entropy measures.