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.

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.

The Solvency II regulatory framework specifies procedures and parameters for determining solvency capital requirements (SCRs) for insurance companies. The proposed standard SCR calculations involve two steps. The Value–at–Risk (VaR) of each risk driver is measured and, in a second step, all components are aggregated to the company’s overall SCR, using the Standard Formula. This formula has two inputs: the VaRs of the individual risk drivers and their correlations. The appropriate calibration of these input parameters has been the purpose of various Quantitative Impact Studies that have been conducted during recent years. This paper demonstrates that the parameter calibration for the equity–risk module—overall, with about 25%, the most significant risk component—is seriously flawed, giving rise to spurious and highly erratic parameter values. As a consequence, an implementation of the Standard Formula with the currently proposed calibration settings for equity–risk is likely to produce inaccurate, biased and, over time, highly erratic capital requirements.