Option Pricing under the Subordinated Market Models

This paper aims to study option pricing problem under the subordinated Brownian motion. Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity, leptokurtic, and long memory, which indicate that the fractional calculus can describe the financial data well. Then, we investigate the option pricing under the assumption that the stock price is driven by the subordinated Brownian motion. The closed-form pricing formula for European options is derived. In the comparison with the classic Black–Sholes model, we find the option prices become higher, and the “volatility smiles” phenomenon happens in the proposed model. Finally, an empirical analysis is performed to show the validity of these results.

Analyzing Electricity Markets with Increasing Penetration of Large-Scale Renewable Power Generation

Global electricity markets are undergoing a rapid transformation in their energy mix to meet commitments towards sustainable electric grids. This change in energy mix engenders significant challenges, specifically concerning the management of non-dispatchable energy resources. System and market operators are required to meet power system security and reliability requirements whilst providing electricity at competitive prices. An overview of electricity markets is provided in this paper with a critical appraisal of each market’s ability to manage the large-scale energy mix transition. This paper provides a commentary on the distinct features of electricity market models implemented around the world and highlights the barriers within these market models that are hindering the energy mix transition. Various researchers and policymakers are proposing solutions and market reforms for the smooth transitioning of the energy mix. This paper presents a systematic review of the proposed solutions in the literature and critiques the effectiveness and ease of implementation of the reviewed solutions. Research gaps and future research directions are indicated to promote further exploration towards the effective integration of large-scale renewable energy technologies.