This paper studies the heterogeneous effects of exchange rate and stock market on carbon emission allowance price in four emissions trading scheme pilots in China. We employ a panel quantile regression model, which can describe both individual and distributional heterogeneity. The empirical results illustrate that the effects of explanatory variables on carbon emission allowance price is heterogeneous along the whole quantiles. Specifically, exchange rate has a negative effect on carbon emission allowance price at lower quantiles, while becomes a positive effect at higher quantiles. In addition, a negative effect exists between domestic stock market and carbon emission allowance price, and the intensity decreasing along with the increase of quantile. By contrast, an increasing positive effect is discovered between European stock market and domestic carbon emission allowance prices. Finally, heterogeneous effects on carbon emission allowance price can also be proved in European Union Emission Trading Scheme (EU-ETS).

This paper investigates the pricing issue of power exchange options with default risk, in which the dynamics of the underlying assets and the counterparty asset follow three correlated stochastic volatility models with stochastic interest rate. We assume that the volatility risk is decomposed into short-term and long-term volatility. The stochastic interest rate is driven by the CIR (Cox-Ingersoll-Ross) process. Based on the proposed model, we derive a closed-form solution for the price of power exchange option with default risk by means of Fourier transform. Besides, the price of power exchange option with default risk can be quickly computed by employing the fast Fourier transform (FFT) algorithm. The results of Monte Carlo simulations demonstrate that the FFT is fast and accurate. More importantly, the pricing model also shows that: (i) a higher long-run mean of the underlying asset price's instantaneous variance induces a higher value of power exchange option with default risk; (ii) the long-run mean of instantaneous variance in counterparty's asset value has a negative impact on the price of power exchange option with default risk; and (iii) the higher the long-run mean of stochastic interest rate, the higher the power exchange option price.

We study the optimal proportional reinsurance and investment problem in a general jump-diffusion financial market. Assuming that the insurer’s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer and invest in a risk-free asset and a risky asset, whose price is modelled by a general jump-diffusion process. The insurance company wishes to maximize the expected exponential utility of the terminal wealth. By using techniques of stochastic control theory, closed-form expressions for the value function and optimal strategy are obtained. A Monte Carlo simulation is conducted to illustrate that the closed-form expressions we derived are indeed the optimal strategies, and some numerical examples are presented to analyse the impact of model parameters on the optimal strategies.