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Mean-variance hedging in an illiquid market
Consider a market consisting of two correlated assets: one liquidly traded asset and one illiquid asset that can only be traded at time 0. For a European derivative written on the illiquid asset, we find a hedging strategy consisting of a constant (time 0) holding in the illiquid asset and dynamic t...
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| Format: | Thesis |
| Language: | English |
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Division of Actuarial Science
2015
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| _version_ | 1867613236623310849 |
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| access_status_str | Open Access |
| author | Mavuso, Melusi Manqoba |
| author2 | Ebobisse Bille, Francois |
| author_browse | Ebobisse Bille, Francois Mavuso, Melusi Manqoba |
| author_facet | Ebobisse Bille, Francois Mavuso, Melusi Manqoba |
| author_sort | Mavuso, Melusi Manqoba |
| collection | Thesis |
| description | Consider a market consisting of two correlated assets: one liquidly traded asset and one illiquid asset that can only be traded at time 0. For a European derivative written on the illiquid asset, we find a hedging strategy consisting of a constant (time 0) holding in the illiquid asset and dynamic trading strategies in the liquid asset and a riskless bank account that minimizes the expected square replication error at maturity. This mean-variance optimal strategy is first found when the liquidly traded asset is a local martingale under the real world probability measure through an application of the Kunita-Watanabe projection onto the space of attainable claims. The result is then extended to the case where the liquidly traded asset is a continuous square integrable semimartingale, and we again use the Kunita-Watanabe decomposition, now under the variance optimal martingale measure, to find the mean-variance optimal strategy in feedback form. In an example, we consider the case where the two assets are driven by correlated Brownian motions and the derivative is a call option on the illiquid asset. We use this example to compare the terminal hedging profit and loss of the optimal strategy to a corresponding strategy that does not use the static hedge in the illiquid asset and conclude that the use of the static hedge reduces the expected square replication error significantly (by up to 90% in some cases). We also give closed form expressions for the expected square replication error in terms of integrals of well-known special functions. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/15595 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:56.154Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Division of Actuarial Science |
| publisherStr | Division of Actuarial Science |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/15595 Mean-variance hedging in an illiquid market Mavuso, Melusi Manqoba Ebobisse Bille, Francois Mathematical Finance Consider a market consisting of two correlated assets: one liquidly traded asset and one illiquid asset that can only be traded at time 0. For a European derivative written on the illiquid asset, we find a hedging strategy consisting of a constant (time 0) holding in the illiquid asset and dynamic trading strategies in the liquid asset and a riskless bank account that minimizes the expected square replication error at maturity. This mean-variance optimal strategy is first found when the liquidly traded asset is a local martingale under the real world probability measure through an application of the Kunita-Watanabe projection onto the space of attainable claims. The result is then extended to the case where the liquidly traded asset is a continuous square integrable semimartingale, and we again use the Kunita-Watanabe decomposition, now under the variance optimal martingale measure, to find the mean-variance optimal strategy in feedback form. In an example, we consider the case where the two assets are driven by correlated Brownian motions and the derivative is a call option on the illiquid asset. We use this example to compare the terminal hedging profit and loss of the optimal strategy to a corresponding strategy that does not use the static hedge in the illiquid asset and conclude that the use of the static hedge reduces the expected square replication error significantly (by up to 90% in some cases). We also give closed form expressions for the expected square replication error in terms of integrals of well-known special functions. 2015-12-04T18:06:52Z 2015-12-04T18:06:52Z 2015 Master Thesis Masters MPhil http://hdl.handle.net/11427/15595 eng application/pdf Division of Actuarial Science Faculty of Commerce University of Cape Town |
| spellingShingle | Mathematical Finance Mavuso, Melusi Manqoba Mean-variance hedging in an illiquid market |
| thesis_degree_str | Master's |
| title | Mean-variance hedging in an illiquid market |
| title_full | Mean-variance hedging in an illiquid market |
| title_fullStr | Mean-variance hedging in an illiquid market |
| title_full_unstemmed | Mean-variance hedging in an illiquid market |
| title_short | Mean-variance hedging in an illiquid market |
| title_sort | mean variance hedging in an illiquid market |
| topic | Mathematical Finance |
| url | http://hdl.handle.net/11427/15595 |
| work_keys_str_mv | AT mavusomelusimanqoba meanvariancehedginginanilliquidmarket |