Hedging Non-Tradable Risks with Transaction Costs and Price Impact

An agent hedges exposure to a non-tradable risk factor U using a correlated traded asset S and accounts for the impact of trades on both factors. We obtain in closed-form the optimal strategy when the agent holds a linear... [ view full abstract ]

An agent hedges exposure to a non-tradable risk factor U using a correlated traded asset S and accounts for the impact of trades on both factors. We obtain in closed-form the optimal strategy when the agent holds a linear position in U. With non-linear exposure to U, we provide an approximation to the optimal strategy in closed-form, and prove that the value function is correctly approximated when cross-impact and risk-aversion are small. With non-linear exposure, the approximate optimal strategy can be written in terms of the optimal strategy for linear exposure with the size of the position changing dynamically according to the exposure's "Delta" under a particular probability measure.