Malliavin Calculus and the Optimal Weighting Function in a Pure Jump Lévy Setting
2021 ◽
Vol 55
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pp. 66-81
Keyword(s):
The paper is devoted to the problem of obtaining weighting functions for the Greeks of an option price written on a stock whose dynamics are of pure jump type. The problem is motivated by the work of Fourni\'e et al. [8, 9], who considered the price sensitivities of a frictionless market and proved that Greeks can be computed as the expectation of the product of the discounted payoff $\Phi$ and a suitable weighted function, i.e.Greek = E[Φ(XT)weight]. Since the weighting functions are random variables that need to be explicitly computed on each specific case, we establish necessary and sufficient conditions to be satisfied. The method used relied on the Malliavin calculus for Levy processes.
1980 ◽
Vol 30
(1)
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pp. 5-14
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2010 ◽
Vol 53
(6)
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pp. 1421-1434
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1995 ◽
Vol 18
(2)
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pp. 391-396
1986 ◽
Vol 18
(04)
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pp. 865-879
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1999 ◽
Vol 36
(1)
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pp. 78-85
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2010 ◽
Vol 2010
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pp. 1-17
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1972 ◽
Vol 4
(02)
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pp. 285-295
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1974 ◽
Vol 11
(04)
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pp. 836-841
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