Optimal foreign exchange rate intervention in lévy markets
This paper considers an exchange rate problem in Lévy markets, where the Central Bank has to intervene. We assume that, in the absence of control, the exchange rate evolves according to Brownian motion with a jump component. The Central Bank is allowed to intervene in order to keep the exchange rate...
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| Format: | Article |
| Language: | English |
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Hindawi
2021
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| Online Access: | https://doi.org/10.1155/2014/746815 http://hdl.handle.net/11408/4608 |
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| author | Mutakaya, Masimba Aspinas Chikodza, Eriyoti Chiyaka, Edward T. |
| author_facet | Mutakaya, Masimba Aspinas Chikodza, Eriyoti Chiyaka, Edward T. |
| author_sort | Mutakaya, Masimba Aspinas |
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| description | This paper considers an exchange rate problem in Lévy markets, where the Central Bank has to intervene. We assume that, in the absence of control, the exchange rate evolves according to Brownian motion with a jump component. The Central Bank is allowed to intervene in order to keep the exchange rate as close as possible to a prespecified target value. The interventions by the Central Bank are associated with costs. We present the situation as an impulse control problem, where the objective of the bank is to minimize the intervention costs. In particular, the paper extends the model by Huang, 2009, to incorporate a jump component. We formulate and prove an optimal verification theorem for the impulse control. We then propose an impulse control and construct a value function and then verify that they solve the quasivariational inequalities. Our results suggest that if the expected number of jumps is high the Central Bank will intervene more frequently and with large intervention amounts hence the intervention costs will be high. |
| format | Article |
| id | ir-11408-4608 |
| institution | My University |
| language | English |
| publishDate | 2021 |
| publisher | Hindawi |
| record_format | dspace |
| spelling | ir-11408-46082022-06-27T13:49:06Z Optimal foreign exchange rate intervention in lévy markets Mutakaya, Masimba Aspinas Chikodza, Eriyoti Chiyaka, Edward T. Exchange rate Central Bank This paper considers an exchange rate problem in Lévy markets, where the Central Bank has to intervene. We assume that, in the absence of control, the exchange rate evolves according to Brownian motion with a jump component. The Central Bank is allowed to intervene in order to keep the exchange rate as close as possible to a prespecified target value. The interventions by the Central Bank are associated with costs. We present the situation as an impulse control problem, where the objective of the bank is to minimize the intervention costs. In particular, the paper extends the model by Huang, 2009, to incorporate a jump component. We formulate and prove an optimal verification theorem for the impulse control. We then propose an impulse control and construct a value function and then verify that they solve the quasivariational inequalities. Our results suggest that if the expected number of jumps is high the Central Bank will intervene more frequently and with large intervention amounts hence the intervention costs will be high. 2021-11-25T12:21:48Z 2021-11-25T12:21:48Z 2014 Article https://doi.org/10.1155/2014/746815 http://hdl.handle.net/11408/4608 en International Journal of Stochastic Analysis;Vol. 2014: p. 1-9 open Hindawi |
| spellingShingle | Exchange rate Central Bank Mutakaya, Masimba Aspinas Chikodza, Eriyoti Chiyaka, Edward T. Optimal foreign exchange rate intervention in lévy markets |
| title | Optimal foreign exchange rate intervention in lévy markets |
| title_full | Optimal foreign exchange rate intervention in lévy markets |
| title_fullStr | Optimal foreign exchange rate intervention in lévy markets |
| title_full_unstemmed | Optimal foreign exchange rate intervention in lévy markets |
| title_short | Optimal foreign exchange rate intervention in lévy markets |
| title_sort | optimal foreign exchange rate intervention in lévy markets |
| topic | Exchange rate Central Bank |
| url | https://doi.org/10.1155/2014/746815 http://hdl.handle.net/11408/4608 |
| work_keys_str_mv | AT mutakayamasimbaaspinas optimalforeignexchangerateinterventioninlevymarkets AT chikodzaeriyoti optimalforeignexchangerateinterventioninlevymarkets AT chiyakaedwardt optimalforeignexchangerateinterventioninlevymarkets |