Green hydrogen in fuel cell vehicles (FCVs) is a promising alternative in the transportation sector. However, high hydrogen costs hinder progress. An on-site hydrogen refueling station (OHRS) can avoid hydrogen transportation and participate in the market to reduce costs. In the forward market, it can lock in inexpensive electricity in advance; meanwhile, lower prices can be attained in the spot market. However, due to the operational constraints of OHRS, allocating electricity between the forward and spot markets is a multi-time scale optimization problem. This paper establishes electricity transaction models and a state equation of the OHRS. A two-stage stochastic optimization model is then proposed to address the allocation problem. Actual market data are used in numerical studies. The results show that storage tanks and electrolysers capacity are critical to arbitrage. Moreover, participating in both the forward and spot markets can usually achieve the lowest levelized cost of hydrogen(LCOH).