Hedge and speculate: replicating option payoffs with limit and market orders
We consider an agent who takes a short position in a contingent claim and employs limit orders (LOs) and market orders (MOs) to trade in the underlying asset to maximize expected utility of terminal wealth. The agent solves a combined optimal stopping and control problem where trading has frictions:...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2019
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| _version_ | 1797064676038672384 |
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| author | Cartea, A Gan, L Jaimungal, S |
| author_facet | Cartea, A Gan, L Jaimungal, S |
| author_sort | Cartea, A |
| collection | OXFORD |
| description | We consider an agent who takes a short position in a contingent claim and employs limit orders (LOs) and market orders (MOs) to trade in the underlying asset to maximize expected utility of terminal wealth. The agent solves a combined optimal stopping and control problem where trading has frictions: MOs (executed by the agent and other traders) have permanent price impact and pay exchange fees, and LOs earn the spread (relative to the midprice of the asset) and pay no exchange fees. We show how the agent replicates the payoff of the claim and also speculates in the asset to maximize expected utility of terminal wealth. In the strategy, MOs are used to keep the inventory on target, to replicate the payoff, and LOs are employed to build the inventory at favorable prices and boost expected terminal wealth by executing roundtrip trades that earn the spread. We calibrate the model to the E-mini contract that tracks the S&P 500 index, provide numerical examples of the performance of the strategy, and prove that our scheme converges to the viscosity solution of the dynamic programming equation. |
| first_indexed | 2024-03-06T21:17:44Z |
| format | Journal article |
| id | oxford-uuid:405c3eb3-130f-4e67-bff0-223c4f6e980a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:17:44Z |
| publishDate | 2019 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:405c3eb3-130f-4e67-bff0-223c4f6e980a2022-03-26T14:37:26ZHedge and speculate: replicating option payoffs with limit and market ordersJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:405c3eb3-130f-4e67-bff0-223c4f6e980aEnglishSymplectic Elements at OxfordSociety for Industrial and Applied Mathematics2019Cartea, AGan, LJaimungal, SWe consider an agent who takes a short position in a contingent claim and employs limit orders (LOs) and market orders (MOs) to trade in the underlying asset to maximize expected utility of terminal wealth. The agent solves a combined optimal stopping and control problem where trading has frictions: MOs (executed by the agent and other traders) have permanent price impact and pay exchange fees, and LOs earn the spread (relative to the midprice of the asset) and pay no exchange fees. We show how the agent replicates the payoff of the claim and also speculates in the asset to maximize expected utility of terminal wealth. In the strategy, MOs are used to keep the inventory on target, to replicate the payoff, and LOs are employed to build the inventory at favorable prices and boost expected terminal wealth by executing roundtrip trades that earn the spread. We calibrate the model to the E-mini contract that tracks the S&P 500 index, provide numerical examples of the performance of the strategy, and prove that our scheme converges to the viscosity solution of the dynamic programming equation. |
| spellingShingle | Cartea, A Gan, L Jaimungal, S Hedge and speculate: replicating option payoffs with limit and market orders |
| title | Hedge and speculate: replicating option payoffs with limit and market orders |
| title_full | Hedge and speculate: replicating option payoffs with limit and market orders |
| title_fullStr | Hedge and speculate: replicating option payoffs with limit and market orders |
| title_full_unstemmed | Hedge and speculate: replicating option payoffs with limit and market orders |
| title_short | Hedge and speculate: replicating option payoffs with limit and market orders |
| title_sort | hedge and speculate replicating option payoffs with limit and market orders |
| work_keys_str_mv | AT carteaa hedgeandspeculatereplicatingoptionpayoffswithlimitandmarketorders AT ganl hedgeandspeculatereplicatingoptionpayoffswithlimitandmarketorders AT jaimungals hedgeandspeculatereplicatingoptionpayoffswithlimitandmarketorders |