What is it about?
Perpetual American option price is a solution of multidimensional obstacle problem. Sensitivity of the price and its partial derivatives with respect to volatilities of the underlying assets is an important practical issue. We establish the latter sensitivity results based on the thorough study of the multidimensional elliptic obstacle problem.
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Why is it important?
The stability result with respect to payoff functions, which was proved by J.-F. Rodrigues under the non-degeneracy condition, is generalized to the case of arbitrary payoff functions belonging to the space Lp(D), pā„2.
Perspectives
Sensitivity results are important from the practical point of view for both finite and infinite time intervals.
Professor Malkhaz Shashiashvili
Ivane Javakhishvili Tbilisi State University
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This page is a summary of: Stability estimates for the multidimensional elliptic obstacle problem, Georgian Mathematical Journal, January 2012, De Gruyter,
DOI: 10.1515/gmj-2012-0007.
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