Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/56750 
Year of Publication: 
2011
Series/Report no.: 
SFB 649 Discussion Paper No. 2011-079
Publisher: 
Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk, Berlin
Abstract: 
The paper focuses on the problem of pricing and hedging a European contingent claim for an incomplete market model, in which evolution of price processes for a saving account and stocks depends on an observable Markov chain. The pricing function is evaluated using the martingale approach. The equivalent martingale measure is introduced in a way that the Markov chain remains the historical one, and the pricing function satisfies the Cauchy problem for a system of linear parabolic equations. It is shown that any European contingent claim is attainable using a generalized self-financing replicating strategy. For such a strategy, apart from the initial endowment, some additional funds are required both step-wise at the jump moments of the Markov chain and continuously between the jump moments. It is proved that the additional funds (the additional investments and consumptions) are present in the proposed strategy in a risk-neutral manner, hence the generalized self-financing strategy is self-financing in mean. A payment for the considered option should consist of two parts: the initial endowment and a fair insurance premium in order to compensate for contributions and consumptions arising in future.
Subjects: 
incomplete markets
martingale measure
generalized self-financing strategy
attainability
self-financing in mean
JEL: 
C58
Document Type: 
Working Paper

Files in This Item:
File
Size
592.77 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.