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Rural subjects, the agricultural industrial structure, public services and rural governance are fully empowered by digital villages. This empowerment effectively compensates for the urban-rural digital divide and promotes the equalization of urban-rural income, consumption, education, medical care, and governance. Based on the three-stage data envelopment analysis (DEA) model and Malmquist index, this article conducts an in-depth study of the static and dynamic efficiency trends of digital villages that empower urban-rural balanced development in 31 provinces in China from 2015 to 2020. The results show that comprehensive technical efficiency of 31 provinces is weak DEA effective, and that the scale efficiency is the main factor affecting comprehensive technical efficiency. The educational level, local finance and industrial structure optimization have a significant positive impact on efficiency evaluation, but technological innovation and the urbanization level have a significant negative impact. Total factor productivity shows diminishing marginal utility based on the Malmquist index and its decomposition change. Restricted by the change in technological progress, the efficiency of digital villages in China in enabling urban-rural equilibrium needs to be further improved.

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This paper investigates the valuation of vulnerable European options considering the market prices of common systematic jump risks under regime-switching jump-diffusion models. The way of regime-switching Esscher transform is adopted to identify an equivalent martingale measure for pricing vulnerable European options. Explicit analytical pricing formulae for vulnerable European options are derived by risk-neutral pricing theory. For comparison, the other two cases are also considered separately. The first case considers all jump risks as unsystematic risks while the second one assumes all jumps risks to be systematic risks. Numerical examples for the valuation of vulnerable European options are provided to illustrate our results and indicate the influence of the market prices of jump risks on the valuation of vulnerable European options.

In this paper, we study the equilibrium valuation for currency options in a setting of the two-country Lucas-type economy. Different from the continuous model in Bakshi and Chen [1], we propose a discontinuous model with jump processes. Empirical findings reveal that the jump components in each country's money supply can be decomposed into the simultaneous co-jump component and the country-specific jump component. Each of the jump components is modeled with a Poisson process whose jump intensity follows a mean reversion stochastic process. By solving a partial integro-differential equation (PIDE), we get a closed-form solution to the PIDE for a European call currency option. The numerical results show that the derived option pricing formula is efficient for practical use. Importantly, we find that the co-jump has a significant impact on option price and implied volatility.

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To achieve China’s new development pattern and the “dual carbon” goals, it is necessary to boost emission reduction and high-quality economic development simultaneously. Green credit (GC), consisting of environmental regulation and economic leverage, has a profound impact on improving total factor carbon emission performance (TFCEP). By selecting the panel data of 30 provinces and municipalities in China from 2001 to 2020, this paper constructs a series of panel models to analyze the transmission path of GC to TFCEP. The results indicate that the relationship between GC and TFCEP showed an “inverted-U-shaped” relationship. This is mainly because “energy-saving and emission reduction” first appeared in the government planning outline in 2006, and transition-friendly enterprises successfully transformed with low-interest green credit, thereby effectively improving their TFCEP. However, as environmental regulations continue to increase and the scale of green credit continues to expand, the efficiency of green credit allocation and internal conflicts with other environmental regulation policies are also emerging. At the same time, the advancement of industrial structure and green technology innovation had a significant mediating effect between GC and TFCEP; government quality has a strong moderating effect on the second stage of the mediating process. When GC reaches a certain scale, it tends to restrain TFCEP more in central and western China than in eastern China. Therefore, it is of great significance to continuously increase the scale of GC, promote the advancement of clean energy industrial structure, and improve green technology innovation.