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.

By using the Black-Derman-Toy (BDT) model, we predict the future trend of the riskless rate, and then we build an equation that relates the market price of zero-coupon bonds and the theoretical price of zero-coupon bonds calculated using a binomial option pricing model. Based on this, we can find the implied daily return μ, implied natural upturn probability p, and implied daily volatility σ with respect to different time-to-maturity values of zero-coupon bonds. With these results, we can give some suggestions to bond traders.

Liquid crystal elastomers (LCEs) are shape morphing materials whose large and reversible shape transformation results from the coupling between the mobile anisotropic properties of liquid crystal (LC) units and the rubber elastic of polymer networks. Their shape changing behaviors under the stimuli are largely directed by LC orientations, and therefore various strategies have been developed to spatially modulate the LC alignments. But most of the methods suffer from complex fabrication technologies or intrinsic limitations in applicability. To address this issue, programmable complex shape changes in some types of LCEs, such as polysiloxane side-chain LCEs or thiol-acrylate main-chain LCEs, etc, have been achieved by using a mechanical alignment programming process coupled with two-step crosslinking. Here, we report a polysiloxane main-chain LCE with programmable 2D and 3D shape changing performances achieved by mechanically programming the polydomain LCE between the two crosslinking steps. The resulting LCEs exhibited reversible thermal induced shape transformation between the initial and programmed shapes due to the two-way memory between the first network structure and the second network structure. Our work would be potential for expanding the applications of LCE materials in actuators, soft robotics and smart structures where arbitrary and easily programmed shape morphings are needed.