Cross hedging with stochastic correlation
This paper is concerned with the study of quadratic hedging of contingent claims with basis risk. We extend existing results by allowing the correlation between the hedging instrument and the underlying of the contingent claim to be random itself. We assume that the correlation process ρ evolves acc...
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| Veröffentlicht in: | Finance and stochastics 2012, Vol.16 (1), p.17-43 |
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| creator | Ankirchner, Stefan Heyne, Gregor |
| description | This paper is concerned with the study of quadratic hedging of contingent claims with basis risk. We extend existing results by allowing the correlation between the hedging instrument and the underlying of the contingent claim to be random itself. We assume that the correlation process
ρ
evolves according to a stochastic differential equation with values between the boundaries −1 and 1. We keep the correlation dynamics general and derive an integrability condition on the correlation process that allows to describe and compute the quadratic hedge by means of a simple hedging formula that can be directly implemented. Furthermore, we show that the conditions on
ρ
are fulfilled by a large class of dynamics. The theory is exemplified by various explicitly given correlation dynamics. |
| doi_str_mv | 10.1007/s00780-010-0148-2 |
| format | Article |
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ρ
evolves according to a stochastic differential equation with values between the boundaries −1 and 1. We keep the correlation dynamics general and derive an integrability condition on the correlation process that allows to describe and compute the quadratic hedge by means of a simple hedging formula that can be directly implemented. Furthermore, we show that the conditions on
ρ
are fulfilled by a large class of dynamics. The theory is exemplified by various explicitly given correlation dynamics.</description><identifier>ISSN: 0949-2984</identifier><identifier>EISSN: 1432-1122</identifier><identifier>DOI: 10.1007/s00780-010-0148-2</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Correlation ; Differential analysis ; Economic Theory/Quantitative Economics/Mathematical Methods ; Economics ; Expected values ; Finance ; Futures ; Hedging ; Insurance ; Management ; Market ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Money markets ; Prices ; Probability Theory and Stochastic Processes ; Quantitative Finance ; Reductionism ; Risk ; Statistics for Business ; Stochastic models ; Stock exchanges ; Studies</subject><ispartof>Finance and stochastics, 2012, Vol.16 (1), p.17-43</ispartof><rights>Springer-Verlag 2010</rights><rights>Springer-Verlag 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c380t-25e63b7b7fc0ef42a0cf9c3edb93113a836be4351fb1acb154da1f5b689f29ec3</citedby><cites>FETCH-LOGICAL-c380t-25e63b7b7fc0ef42a0cf9c3edb93113a836be4351fb1acb154da1f5b689f29ec3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00780-010-0148-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00780-010-0148-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Ankirchner, Stefan</creatorcontrib><creatorcontrib>Heyne, Gregor</creatorcontrib><title>Cross hedging with stochastic correlation</title><title>Finance and stochastics</title><addtitle>Finance Stoch</addtitle><description>This paper is concerned with the study of quadratic hedging of contingent claims with basis risk. We extend existing results by allowing the correlation between the hedging instrument and the underlying of the contingent claim to be random itself. We assume that the correlation process
ρ
evolves according to a stochastic differential equation with values between the boundaries −1 and 1. We keep the correlation dynamics general and derive an integrability condition on the correlation process that allows to describe and compute the quadratic hedge by means of a simple hedging formula that can be directly implemented. Furthermore, we show that the conditions on
ρ
are fulfilled by a large class of dynamics. 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We extend existing results by allowing the correlation between the hedging instrument and the underlying of the contingent claim to be random itself. We assume that the correlation process
ρ
evolves according to a stochastic differential equation with values between the boundaries −1 and 1. We keep the correlation dynamics general and derive an integrability condition on the correlation process that allows to describe and compute the quadratic hedge by means of a simple hedging formula that can be directly implemented. Furthermore, we show that the conditions on
ρ
are fulfilled by a large class of dynamics. The theory is exemplified by various explicitly given correlation dynamics.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s00780-010-0148-2</doi><tpages>27</tpages></addata></record> |
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| ispartof | Finance and stochastics, 2012, Vol.16 (1), p.17-43 |
| issn | 0949-2984 1432-1122 |
| language | eng |
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| source | Business Source Complete; SpringerLink Journals - AutoHoldings |
| subjects | Correlation Differential analysis Economic Theory/Quantitative Economics/Mathematical Methods Economics Expected values Finance Futures Hedging Insurance Management Market Mathematical analysis Mathematics Mathematics and Statistics Money markets Prices Probability Theory and Stochastic Processes Quantitative Finance Reductionism Risk Statistics for Business Stochastic models Stock exchanges Studies |
| title | Cross hedging with stochastic correlation |
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