Hedging nontradable risks with transaction costs and price impact
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 ob...
| Autores principales: | , , |
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| Formato: | Journal article |
| Lenguaje: | English |
| Publicado: |
Wiley
2020
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| _version_ | 1826311384575508480 |
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| author | Cartea, A Donnelly, RF Jaimungal, S |
| author_facet | Cartea, A Donnelly, RF Jaimungal, S |
| author_sort | Cartea, A |
| collection | OXFORD |
| description | 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(UT) 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(UT) 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. |
| first_indexed | 2024-03-07T08:07:35Z |
| format | Journal article |
| id | oxford-uuid:1396bbb0-4746-49b6-97c8-94a8b09b14cc |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:07:35Z |
| publishDate | 2020 |
| publisher | Wiley |
| record_format | dspace |
| spelling | oxford-uuid:1396bbb0-4746-49b6-97c8-94a8b09b14cc2023-11-13T11:28:46ZHedging nontradable risks with transaction costs and price impactJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1396bbb0-4746-49b6-97c8-94a8b09b14ccEnglishSymplectic ElementsWiley2020Cartea, ADonnelly, RFJaimungal, SA 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(UT) 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(UT) 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. |
| spellingShingle | Cartea, A Donnelly, RF Jaimungal, S Hedging nontradable risks with transaction costs and price impact |
| title | Hedging nontradable risks with transaction costs and price impact |
| title_full | Hedging nontradable risks with transaction costs and price impact |
| title_fullStr | Hedging nontradable risks with transaction costs and price impact |
| title_full_unstemmed | Hedging nontradable risks with transaction costs and price impact |
| title_short | Hedging nontradable risks with transaction costs and price impact |
| title_sort | hedging nontradable risks with transaction costs and price impact |
| work_keys_str_mv | AT carteaa hedgingnontradableriskswithtransactioncostsandpriceimpact AT donnellyrf hedgingnontradableriskswithtransactioncostsandpriceimpact AT jaimungals hedgingnontradableriskswithtransactioncostsandpriceimpact |