Black-Scholes option pricing strategy and risk-averse coordination for designing vehicle-to-grid reserve contracts

Abstract

Based on the conditional value-at-risk criterion and trading characteristics of the vehicle-to-grid reserve market, this paper establishes an option pricing strategy for a risk-neutral grid company, and builds two electricity reserve models for a risk-averse electric vehicle user before and after options implementation. Then, the impact of options, electricity selling price and risk aversion changes on feedback equilibrium strategies and optimal profits are comparatively analyzed between a Stackelberg game and a cooperative game. The results demonstrate that simply using protective market pricing mechanism to determine the contract price places all of the vehicle-to-grid market's trading risk onto the grid company, so that opportunistic behavior cannot be prevented in bad market conditions. To address this, the grid company can buy options to mitigate the risk of price fluctuations; the cooperation system can be further enhanced through a “Black-Scholes option pricing + reserve cooperation + deposit” joint contract, which achieves Pareto improvements of the optimal profits on both sides of the channel. Finally, the analytical relations among the vehicle-to-grid reserve's cooperation coefficient, trade deposit, and electricity contract price in equilibrium are derived, and the feasibility of the proposed models and theoretical analyses is verified by three numerical examples.