Application of Malliavin Calculus in Mean-Variance Hedging Strategy
This paper considers an approach of Malliavin calculus to obtain the hedging ratio for mean-variance hedging (MVH) strategy under the stochastic volatility model with pure jump Lévy process (SVJ). Specifically speaking, there exists a correspondence between the martingale representation theorem and...
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| Veröffentlicht in: | Mathematical problems in engineering 2022-12, Vol.2022, p.1-17 |
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| creator | Liu, Kefan Chen, Jingyao Zhang, Jichao Tan, Xili |
| description | This paper considers an approach of Malliavin calculus to obtain the hedging ratio for mean-variance hedging (MVH) strategy under the stochastic volatility model with pure jump Lévy process (SVJ). Specifically speaking, there exists a correspondence between the martingale representation theorem and the Clark-Ocone formula for a square integrable contingent claim. Therefore, we can replace the diffusion term coefficients with the functions containing Malliavin derivatives to get a closed-form representation for the MVH strategy. By fast Fourier transform (FFT) algorithm, some numerical examples are performed to analyze the sensitivity of MVH strategy concerning strike price and current time. |
| doi_str_mv | 10.1155/2022/3096866 |
| format | Article |
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Specifically speaking, there exists a correspondence between the martingale representation theorem and the Clark-Ocone formula for a square integrable contingent claim. Therefore, we can replace the diffusion term coefficients with the functions containing Malliavin derivatives to get a closed-form representation for the MVH strategy. 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Specifically speaking, there exists a correspondence between the martingale representation theorem and the Clark-Ocone formula for a square integrable contingent claim. Therefore, we can replace the diffusion term coefficients with the functions containing Malliavin derivatives to get a closed-form representation for the MVH strategy. By fast Fourier transform (FFT) algorithm, some numerical examples are performed to analyze the sensitivity of MVH strategy concerning strike price and current time.</description><subject>Algorithms</subject><subject>Decomposition</subject><subject>Fast Fourier transformations</subject><subject>Hedging</subject><subject>Interest rates</subject><subject>Martingales</subject><subject>Representations</subject><subject>Stochastic models</subject><subject>Stochastic processes</subject><subject>Volatility</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>BENPR</sourceid><recordid>eNp9kD1PwzAURS0EEqWw8QMiMUKo_RI7zlhFQJGoGPgQm_Xq2MVVcIKdgPrvSdXOTPcOR_dKh5BLRm8Z43wGFGCW0VJIIY7IhHGRpZzlxfHYKeQpg-zjlJzFuKEUGGdyQqp51zVOY-9an7Q2WWLTOPxxPqmw0UMzxGTsS4M-fcfg0GuTLEy9dn6dvPQBe7PenpMTi000F4eckrf7u9dqkT49PzxW86dUA-R9aoRkXIuS13KlJXAJYHld53ZlmbQ01wIML21ZQK1XBgAyaTmyUjJRotUym5Kr_W4X2u_BxF5t2iH48VJBwXmWF-PmSN3sKR3aGIOxqgvuC8NWMap2mtROkzpoGvHrPf7pfI2_7n_6DyWlZfw</recordid><startdate>20221205</startdate><enddate>20221205</enddate><creator>Liu, Kefan</creator><creator>Chen, Jingyao</creator><creator>Zhang, Jichao</creator><creator>Tan, Xili</creator><general>Hindawi</general><general>Hindawi Limited</general><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0001-6778-5306</orcidid><orcidid>https://orcid.org/0000-0002-2036-2274</orcidid></search><sort><creationdate>20221205</creationdate><title>Application of Malliavin Calculus in Mean-Variance Hedging Strategy</title><author>Liu, Kefan ; 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| source | Wiley Online Library Open Access; EZB-FREE-00999 freely available EZB journals; Alma/SFX Local Collection |
| subjects | Algorithms Decomposition Fast Fourier transformations Hedging Interest rates Martingales Representations Stochastic models Stochastic processes Volatility |
| title | Application of Malliavin Calculus in Mean-Variance Hedging Strategy |
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