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This paper considers the pricing issue of vulnerable European option when the dynamics of the underlying asset value and counterparty’s asset value follow two correlated exponential Lévy processes with stochastic volatility, and the stochastic volatility is divided into the long-term and short-term volatility. A mean-reverting process is introduced to describe the common long-term volatility risk in underlying asset price and counterparty’s asset value. The short-term fluctuation of stochastic volatility is governed by a mean-reverting process. Based on the proposed model, the joint moment generating function of underlying log-asset price and counterparty’s log-asset value is explicitly derived. We derive a closed-form solution for the vulnerable European option price by using the Fourier inversion formula for distribution functions. Finally, numerical simulations are provided to illustrate the effects of stochastic volatility, jump risk, and counterparty credit risk on the vulnerable option price.

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Based on textual data mining methods and global English articles, we develop an index for measuring the uncertainty of international trade rules and evaluating the role of trade rule uncertainty in the relationship between international trade and carbon emissions, via a mediating effect model. The empirical results show that: (1) Increasing trade volume in developing countries contributes to a rise in trade rule uncertainty, which in turn triggers trade conflicts and even trade wars between countries. (2) There are significant correlations between international trade and carbon emissions, and international trade impacts carbon emissions in both direct and indirect ways. (3) Trade rule uncertainty plays a mediating role in the relationship between international trade and carbon emissions. (4) Trade rule uncertainty significantly impacts carbon emissions in most developed and developing countries, but the impact is not significant in the USA. Our work not only contributes to extending measurements of uncertainty but also helps to quantify the impacts of trade rule uncertainty on carbon emissions.