Static Replication of Barrier Options: Some General Results

2000 ◽  
Author(s):  
Leif B.G. Andersen ◽  
Jesper Andreasen ◽  
David A. Eliezer
Keyword(s):  
Barrier Options

Discrete Asian barrier options

1999 ◽  
Vol 3 (1) ◽  
pp. 41-67 ◽  
Author(s):  
R Zvan ◽  
P Forsyth ◽  
K Vetzal
Keyword(s):  
Barrier Options

THE FEYNMAN–KAC FORMULA AND PRICING OCCUPATION TIME DERIVATIVES

1999 ◽  
Vol 02 (02) ◽  
pp. 153-178 ◽  
Author(s):  
JULIEN-N. HUGONNIER
Keyword(s):  
Brownian Motion ◽  
Time Derivative ◽  
Occupation Time ◽  
Barrier Options ◽  
Occupation Times

In this paper, we undertake a study of occupation time derivatives that is derivatives for which the pay-off is contingent on both the terminal asset's price and one of its occupation times. To this end we use a formula of M. Kac to compute the joint law of Brownian motion and one of its occupation times. General pricing formulas for occupation time derivatives are established and it is shown that any occupation time derivative can be continuously hedged by a controlled portfolio of the basic securities. We further study some examples of interest including cumulative barrier options and discuss some numerical implementations.

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