LONG RANGE DEPENDENCE, NO ARBITRAGE AND THE BLACK–SCHOLES FORMULA
2002 ◽
Vol 02
(02)
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pp. 265-280
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Keyword(s):
A bond and stock model is considered where the driving process is the sum of a Wiener process W and a continuous process Z with zero generalized quadratic variation. By means of forward integrals a hedge against Markov-type claims is constructed. If Z is independent of W under some natural assumptions on Z and the admissible portfolio processes the model is shown to be arbitrage free. The fair price of the above claims agrees with that in the classical case Z ≡ 0. In particular, the Black–Scholes formula remains valid for non-semimartingale models with long range dependence.
2010 ◽
Vol 389
(3)
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pp. 438-444
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Keyword(s):
2011 ◽
Vol 390
(9)
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pp. 1623-1634
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Keyword(s):
2010 ◽
Vol 389
(4)
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pp. 789-796
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Keyword(s):
2011 ◽
Vol 4
(8)
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pp. 345-348
Keyword(s):
2006 ◽
Vol 16
(18)
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pp. 1331-1338
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Keyword(s):
2012 ◽
Vol 105
(1)
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pp. 322-347
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