Study of Last Passage Times up to a Finite Horizon

Christophe Profeta (), Bernard Roynette () and Marc Yor
Additional contact information
Christophe Profeta: Université Nancy I
Bernard Roynette: Université Nancy I
Marc Yor: Université Paris VI

Chapter Chapter 5 in Option Prices as Probabilities, 2010, pp 115-141 from Springer

Abstract: 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: $$\mathcal {G}_K^{(\mathcal{E})}(t)=\sup\{s\leq t;\;\mathcal{E}_s=K\}$$ 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.

Keywords: Brownian Motion; Passage Time; Markov Property; Brownian Bridge; Finite Horizon (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-642-10395-7_5

Ordering information: This item can be ordered from
http://www.springer.com/9783642103957

DOI: 10.1007/978-3-642-10395-7_5

Access Statistics for this chapter

More chapters in Springer Finance from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().