Ítem
Acceso Abierto
Optimal liquidation with temporary and permanent price impact, an application to cryptocurrencies
| dc.contributor.gruplac | Grupo de investigaciones. Facultad de Economía. Universidad del Rosario | |
| dc.creator | Hugo E. Ramírez | |
| dc.creator | Sánchez López, Julián Fernando | |
| dc.date.accessioned | 2023-03-17T19:41:01Z | |
| dc.date.available | 2023-03-17T19:41:01Z | |
| dc.date.created | 2023-03-17 | |
| dc.date.issued | 2023-02-17 | |
| dc.description | Este artículo estudia la liquidación óptima de activos financieros en la presencia de impactos de precio temporales y permanentes. Empezamos presentando soluciones analíticas al problema con impacto temporal lineal, y impacto permantente lineal y cuadrático. Luego, usando información del libro de ordenes para la criptomoneda BNB, estimamos la forma funcional del los impactos permanente y temporal bajo tres escenarios diferentes: subestimado, sobrestimado y estimado promedio, encontrando diferentes formas funcionales para cada escenario. Usando diferencias finitas e iteración de política óptima resolvemos el problema de forma numerica y observamos cambios interesantes en la política óptima cuando aplicamos las formas funcionales calibradas lineal y potencia para los impactos temporal y permanente. Luego con estas políticas óptimas, identificamos la trayectoria de liquidación óptima y con objeto de comparar, simulamos liquidaciones entre las diferentes estrategias óptimas bajo las diferentes parametrizaciones y contra una estrategia ingenua. finalmente, caracterizanos las políticas óptimas basados en la forma funcional del inventario y encontramos que las políticas que generan mayor ganacia son aquellas que empiezan con baja taza de liquidación que aumenta con el tiempo. | |
| dc.description.abstract | This paper studies the optimal liquidation of stocks in the presence of temporary and permanent price impacts, and we focus in the case of cryptocurrencies. We start by presenting analytical solutions to the problem with linear temporary impact, and linear and quadratic permanent impact. Then, using data from the order book of the BNB cryptocurrency, we estimate the functional form of the temporary and permanent price impact in three different scenarios: underestimation, overestimation and average estimation, finding different functional forms for each scenario. Using finite differences and optimal policy iteration, we solve the problem numerically and observe interesting changes in the optimal liquidation policy when applying calibrated linear and power forms for the temporary and permanent price impacts. Then, with these optimal policies, we identify optimal liquidation trajectories and simulate the liquidation of initial inventories to compare the performance among the optimal strategies under different parametrizations and against a naive strategy. Finally, we characterize the optimal policies based on the functional form of the inventory and find that policies generating the highest revenue are those starting with a low trading rate and increasing it as time passes. | |
| dc.format.extent | 20 pp | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.doi | https://doi.org/10.48713/10336_38259 | |
| dc.identifier.uri | https://repository.urosario.edu.co/handle/10336/38259 | |
| dc.language.iso | spa | |
| dc.publisher | Universidad del Rosario | |
| dc.publisher.department | Facultad de Economía | |
| dc.relation.uri | https://ideas.repec.org/p/col/000092/020669.html | |
| dc.rights | Attribution-NonCommercial-ShareAlike 4.0 International | * |
| dc.rights.accesRights | info:eu-repo/semantics/openAccess | |
| dc.rights.acceso | Abierto (Texto Completo) | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | * |
| dc.source.bibliographicCitation | Alfonsi, A. F. A. and Schied, A. (2010). Optimal execution strategies in limit order books with general shape functions. Quantitative Finance, Taylor. | |
| dc.source.bibliographicCitation | Almgren, R. and Chriss, N. (2000). Optimal execution of portfolio transactions. J. Risk, 3:5–39. | |
| dc.source.bibliographicCitation | Almgren, R., Thum, C., Hauptmann, E., and Li, H. (2005). Direct estimation of equity market impact. | |
| dc.source.bibliographicCitation | Barger, W. and Lorig, M. (2018). Optimal liquidation under stochastic price impact. International Journal of Theoretical and Applied Finance. | |
| dc.source.bibliographicCitation | Barles, G. and Souganidis, P. E. (1991). Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Analysis, 4(3):271–283. | |
| dc.source.bibliographicCitation | Bellman, R. and Dreyfus, S. (1962). Applied dynamic programming. A report kprepared for United States Air Force project RAND. | |
| dc.source.bibliographicCitation | Bershova, N. and Rakhlin, D. (2013). The non-linear market impact of large trades: Evidence from buy-side order flow. Quantitative Finance, 13(11):1759–1778. | |
| dc.source.bibliographicCitation | Blanco Encinosa, L. J. (2021). Criptomonedas. Breve an´alisis desde la perspectiva econ´omica y financiera. Cofin Habana, 15. | |
| dc.source.bibliographicCitation | Brunovsk´y, P., Cern´y, A., and Komadel, J. (2018). Optimal trade execution under endogenous pressure to ˇ liquidate: Theory and numerical solutions. European Journal of Operational Research, 264(3):1159–1171. | |
| dc.source.bibliographicCitation | Cartea, A. and Jaimungal, S. (2016a). A closed-form execution strategy to target. SIAM Journal on Financial Mathematics, 7(1):760–785. | |
| dc.source.bibliographicCitation | Cartea, A. and Jaimungal, S. (2016b). Incorporating order-flow into optimal execution. Mathematics and Financial Economics, 10(3):339–364. | |
| dc.source.bibliographicCitation | Cartea, A., Jaimungal, S., and Penalva, J. (2015). Algorithmic and high-frequency trading. Cambridge University Press. | |
| dc.source.bibliographicCitation | Curato, G., Gatheral, J., and Lillo, F. (2017). Optimal execution with nonlinear transient market impact. Quantitative Finance, 17(1):41–54. | |
| dc.source.bibliographicCitation | Duffy, D. J. (2006). Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach. John Wiley. | |
| dc.source.bibliographicCitation | Gatheral, J. (2010). No-dynamic-arbitrage and market impact. Quantitative Finance, 10(7):749–759. | |
| dc.source.bibliographicCitation | Gueant, O. (2014). Permanent market impact can be nonlinear. Preprint. | |
| dc.source.bibliographicCitation | Huberman, G. and Stanzl, W. (2004). Price manipulation and quasi-arbitrage. Econometrica, 72(4):1247– 1275. | |
| dc.source.instname | instname:Universidad del Rosario | |
| dc.source.reponame | reponame:Repositorio Institucional EdocUR | |
| dc.subject.keyword | Optimal liquidation, price impact, finite differences, Stochastic Control, cryptocurrencies | |
| dc.subject.keyword | Price impact | |
| dc.subject.keyword | Finite differences | |
| dc.subject.keyword | Stochastic control | |
| dc.subject.keyword | Cryptocurrencies | |
| dc.title | Optimal liquidation with temporary and permanent price impact, an application to cryptocurrencies | |
| dc.type | workingPaper | |
| dc.type.hasVersion | info:eu-repo/semantics/draft | |
| dc.type.spa | Documento de Trabajo |
