Martingale approach in pricing and hedging European options under regime-switching

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2011-079

Classification and Topics

• Classification: Wirtschaft ; Financial Econometrics
• Subject: incomplete markets ; martingale measure ; generalized self-financing strategy ; attainability ; self-financing in mean ; Optionspreistheorie ; Martingale ; Markovscher Prozess ; Hedging ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Milstein, Grigori N. ; Spokoiny, Vladimir
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2011

Further information

• Handle: http://hdl.handle.net/10419/56750
• Last update: 10.03.2025, 11:43 AM CET