Bismut–Elworthy–Li formula for subordinated Brownian motion applied to hedging financial derivatives
| dc.contributor.author | Kateregga, Michael | |
| dc.contributor.author | Mataramvura, Sure | |
| dc.contributor.author | Taylor, David | |
| dc.date.accessioned | 2018-02-15T13:18:23Z | |
| dc.date.available | 2017-09-17 | |
| dc.date.available | 2018-02-15T13:18:23Z | |
| dc.date.issued | 2017-09-27 | |
| dc.description.abstract | he objective of the paper is to extend the results in Fournié, Lasry, Lions, Lebuchoux, and Touzi (1999), Cass and Fritz (2007) for continuous processes to jump processes based on the Bismut–Elworthy–Li (BEL) formula in Elworthy and Li (1994). We construct a jump process using a subordinated Brownian motion where the subordinator is an inverse 훼-stable process (Lt )t≥0 with (0, 1]. The results are derived using Malliavin integration by parts formula. We derive representation formulas for computing financial Greeks and show that in the event when Lt ≡ t, we retrieve the results in Fournié et al. (1999). The purpose is to by-pass the derivative of an (irregular) pay-off function in a jump-type market by introducing a weight term in form of an integral with respect to subordinated Brownian motion. Using MonteCarlo techniques, we estimate financial Greeks for a digital option and show that the BEL formula still performs better for a discontinuous pay-off in a jump asset model setting and that the finite-difference methods are better for continuous pay-offs in a similar setting. In summary, the motivation and contribution of this paper demonstrates that the Malliavin integration by parts representation formula holds for subordinated Brownian motion and, this representation is useful in developing simple and tractable hedging strategies (the Greeks) in jump-type derivatives market as opposed to more complex jump models. | en_ZA |
| dc.identifier.apacitation | Kateregga, M., Mataramvura, S., & Taylor, D. (2017). Bismut–Elworthy–Li formula for subordinated Brownian motion applied to hedging financial derivatives. <i>Cogent-Economics and Finance</i>, http://hdl.handle.net/11427/27585 | en_ZA |
| dc.identifier.chicagocitation | Kateregga, Michael, Sure Mataramvura, and David Taylor "Bismut–Elworthy–Li formula for subordinated Brownian motion applied to hedging financial derivatives." <i>Cogent-Economics and Finance</i> (2017) http://hdl.handle.net/11427/27585 | en_ZA |
| dc.identifier.citation | Kateregga et al (2017b) | en_ZA |
| dc.identifier.issn | 2332-2039 | en_ZA |
| dc.identifier.ris | TY - Journal Article AU - Kateregga, Michael AU - Mataramvura, Sure AU - Taylor, David AB - he objective of the paper is to extend the results in Fournié, Lasry, Lions, Lebuchoux, and Touzi (1999), Cass and Fritz (2007) for continuous processes to jump processes based on the Bismut–Elworthy–Li (BEL) formula in Elworthy and Li (1994). We construct a jump process using a subordinated Brownian motion where the subordinator is an inverse 훼-stable process (Lt )t≥0 with (0, 1]. The results are derived using Malliavin integration by parts formula. We derive representation formulas for computing financial Greeks and show that in the event when Lt ≡ t, we retrieve the results in Fournié et al. (1999). The purpose is to by-pass the derivative of an (irregular) pay-off function in a jump-type market by introducing a weight term in form of an integral with respect to subordinated Brownian motion. Using MonteCarlo techniques, we estimate financial Greeks for a digital option and show that the BEL formula still performs better for a discontinuous pay-off in a jump asset model setting and that the finite-difference methods are better for continuous pay-offs in a similar setting. In summary, the motivation and contribution of this paper demonstrates that the Malliavin integration by parts representation formula holds for subordinated Brownian motion and, this representation is useful in developing simple and tractable hedging strategies (the Greeks) in jump-type derivatives market as opposed to more complex jump models. DA - 2017-09-27 DB - OpenUCT DP - University of Cape Town J1 - Cogent-Economics and Finance LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 SM - 2332-2039 T1 - Bismut–Elworthy–Li formula for subordinated Brownian motion applied to hedging financial derivatives TI - Bismut–Elworthy–Li formula for subordinated Brownian motion applied to hedging financial derivatives UR - http://hdl.handle.net/11427/27585 ER - | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/11427/27585 | |
| dc.identifier.vancouvercitation | Kateregga M, Mataramvura S, Taylor D. Bismut–Elworthy–Li formula for subordinated Brownian motion applied to hedging financial derivatives. Cogent-Economics and Finance. 2017; http://hdl.handle.net/11427/27585. | en_ZA |
| dc.language | eng | en_ZA |
| dc.publisher | Taylor and Francis | en_ZA |
| dc.publisher.department | Division of Actuarial Science | en_ZA |
| dc.publisher.faculty | Faculty of Commerce | en_ZA |
| dc.publisher.institution | University of Cape Town | |
| dc.relation.ispartofseries | Research papers | en_ZA |
| dc.rights | Creative Commons Attribution 4.0 International (CC BY 4.0) | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | en_ZA |
| dc.source | Cogent-Economics and Finance | en_ZA |
| dc.source.uri | https://www.cogentoa.com/journal/economics-and-finance | |
| dc.subject.other | Stable distribution | |
| dc.subject.other | Malliavin calculus | |
| dc.subject.other | subordinated Brownian motion | |
| dc.subject.other | Bismut–Elworthy–Li formula | |
| dc.title | Bismut–Elworthy–Li formula for subordinated Brownian motion applied to hedging financial derivatives | en_ZA |
| dc.type | Journal Article | en_ZA |
| uct.type.filetype | Text | |
| uct.type.filetype | Image | |
| uct.type.publication | Teaching and Learning | en_ZA |
| uct.type.resource | Article | en_ZA |