Abstract
In Chapter 1, we have expressed the European put and call quantities in terms of the last passage time \(\mathcal {G}_{K}^{(\mathcal{E})}\). However, since \(\mathcal {G}_{K}^{(\mathcal{E})}\) is not a stopping time, formulae (1.20) and (1.21) are not very convenient for simulation purposes. To counter this drawback, we introduce in Section 5.1 of the present Chapter the ℱ t -measurable random time:
and write the analogues of formulae (1.20) and (1.21) for these times \(\mathcal {G}_{K}^{(\mathcal{E})}(t)\). This will lead us to the interesting notion of past-future martingales, which we shall study in details in Section 5.2.
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© 2010 Springer-Verlag Berlin Heidelberg
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Profeta, C., Roynette, B., Yor, M. (2010). Study of Last Passage Times up to a Finite Horizon. In: Option Prices as Probabilities. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10395-7_5
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DOI: https://doi.org/10.1007/978-3-642-10395-7_5
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Publisher Name: Springer, Berlin, Heidelberg
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