In this paper, we study data from financial markets, using the normalised Mutual Information Rate. We show how to use it to infer the underlying network structure of interrelations in the foreign currency exchange rates and stock indices of 15 currency areas. We first present the mathematical method and discuss its computational aspects, and apply it to artificial data from chaotic dynamics and to correlated normal-variates data. We then apply the method to infer the structure of the financial system from the time-series of currency exchange rates and stock indices. In particular, we study and reveal the interrelations among the various foreign currency exchange rates and stock indices in two separate networks, of which we also study their structural properties. Our results show that both inferred networks are small-world networks, sharing similar properties and having differences in terms of assortativity. Importantly, our work shows that global economies tend to connect with other economies world-wide, rather than creating small groups of local economies. Finally, the consistent interrelations depicted among the 15 currency areas are further supported by a discussion from the viewpoint of economics.

In this paper, we present a method to estimate the market parameters modelled by an asymmetric jump diffusion process. The method proposed is based on Kou’s jump diffusion model while the market parameters refer to the market drift, the market volatility, the jump intensity on market price, and the rate of jump occurrence in a consistent manner throughout the entire paper. The model captures the asymmetric nature of the price fluctuation during up trend markets and down trend markets. The results are compared to conventional options to observe the impact of jump effects. The results from simulation show that the asymmetric jump diffusion model can estimate the fair prices of European call options and annuity better than the Black-Scholes model and the symmetric jump diffusion model proposed by Kou and Merton.

The symmetric teleparallel theory offers an alternative gravitational formulation which can elucidate events in the early and late universe without requiring the physical existence of dark matter or dark energy. In this formalism, f ( Q,C ) gravity has been recently introduced by incorporating the boundary term C with the non-metricity scalar Q . In this paper, we develop the theory of cosmological scalar perturbation for f ( Q,C ) gravity, and retrieve that of f ( R̊ ) and f ( Q ) gravity from our result. The analysis assumes a model-independent approach within these theories that adheres to the conventional continuity equation at the background level. We derive the density contrast equation by employing some standard cosmological approximations, where the f ( Q,C ) theory is encoded in the effective Newtonian constant G _eff . Finally, we derive the evolution equation of density growth f _g .