Robustness of the Black-Scholes approach in the case of options on several assets
AbstractIn this paper we analyse a stochastic volatility model that is an extension of the traditional Black-Scholes one. We price European options on several assets by using a superstrategy approach. We characterize the Markov superstrategies, and show that they are linked to a nonlinear PDE, called the Black-Scholes-Barenblatt (BSB) equation. This equation is the Hamilton-Jacobi-Bellman equation of an optimal control problem, which has a nice financial interpretation. Then we analyse the optimization problem included in the BSB equation and give some sufficient conditions for reduction of the BSB equation to a linear Black-Scholes equation. Some examples are given.
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Bibliographic InfoArticle provided by Springer in its journal Finance and Stochastics.
Volume (Year): 4 (2000)
Issue (Month): 3 ()
Note: received: April 1998; final revision received: May 1999
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Web page: http://www.springerlink.com/content/101164/
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- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999, arXiv.org.
- Joel Vanden, 2006. "Exact Superreplication Strategies for a Class of Derivative Assets," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 13(1), pages 61-87.
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