Abstract This paper develops an integrated optimisation model for pricing and hedging oil derivatives in incomplete markets where available market quotes and the trader’s views, inventory and risk aversion may affect the pricing. The model is well suited for practical applications such as the design of optimal cross-hedging strategies and the market-maker problem of pricing derivatives while managing inventory risk in illiquid market conditions. We use numerical experiments to illustrate the model features. First, by computing optimal hedge ratios, we show that the hedge effectiveness of using all available market quotes is significantly higher than that of conventional strategies using only one hedging instrument. Second, we find that the indifference prices of spread derivative contracts are often more competitive than the available market quotes. Third, we study the sensitivities of indifference prices with respect to a market-maker’s risk aversion, views and inventory.
Pennanen et al. (2026) studied this question.