In real financial markets, the certainty equivalent rate is an important factor for investors to consider. From the value of a specific company’s certainty equivalent rate, investors can judge if this company is worth investing in. In this paper, we will explore how to obtain the value of the certainty equivalent rate so that we can evaluate a given company. First, we will introduce the theoretical support of this paper, which is put-call parity. From put-call parity, we will derive the mathematical expression for the certainty equivalent rate. Second, we will use the mathematical expression for the certainty equivalent rate to perform an empirical study. We will consider some extreme examples, including some of the best- and worst-performing stocks up to this point in 2023. Based on these stocks’ data, we will visualize the performance of these stocks and explain the meaning of the data. Finally, we will apply the results to a very popular industry—the electric vehicle industry—to explore the current electric vehicle market situation in the U.S.A.

We give two examples of the appearance of heavy-tailed distributions in applications to social sciences. Among these distributions are the laws of Pareto, Lotka, and some new ones. The examples are illustrated by constructing suitable toy models.

This paper delves into the dynamics of asset pricing within Bachelier’s market model (BMM), elucidating the representation of risky asset price dynamics and the definition of riskless assets. It highlights the fundamental differences between BMM and the Black-Scholes-Merton market model (BSMMM), including the extension of BMM to handle assets yielding a simple dividend. Our investigation further explores Bachelier’s term structure of interest rates (BTSIR), introducing a novel version of Bachelier’s Heath-Jarrow-Morton model and adapting the Hull-White interest rate model to fit BMM. The study concludes by examining the applicability of BMM in real-world scenarios, such as those involving environmental, social, and governance (ESG)-adjusted stock prices and commodity spreads.