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Hedging nontradable risks with transaction costs and price impact
Author(s) -
Cartea Álvaro,
Donnelly Ryan,
Jaimungal Sebastian
Publication year - 2020
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12259
Subject(s) - position (finance) , economics , asset (computer security) , econometrics , transaction cost , nonlinear system , risk aversion (psychology) , value (mathematics) , function (biology) , database transaction , mathematical optimization , mathematics , microeconomics , expected utility hypothesis , computer science , mathematical economics , statistics , finance , computer security , evolutionary biology , biology , physics , quantum mechanics , programming language
Abstract A risk‐averse agent hedges her exposure to a nontradable risk factor U using a correlated traded asset S and accounts for the impact of her trades on both factors. The effect of the agent's trades on U is referred to as cross‐impact. By solving the agent's stochastic control problem, we obtain a closed‐form expression for the optimal strategy when the agent holds a linear position in U . When the exposure to the nontradable risk factor ψ ( U T ) is nonlinear, we provide an approximation to the optimal strategy in closed‐form, and prove that the value function is correctly approximated by this strategy when cross‐impact and risk‐aversion are small. We further prove that when ψ ( U T ) is nonlinear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's “Delta” under a particular probability measure.