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Robustness of the Black-Scholes approach in the case of options on several assets

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Author Info

  • Tiziano Vargiolu

    ()
    (Dipartimento di Matematica Pura ed Applicata, Universit√° di Padova, Via Belzoni 7, 35131 Padova, Italy Manuscript)

  • Silvia Romagnoli

    ()
    (Istituto di Matematica Generale e Finanziaria, Universit√° di Bologna, Piazza Scaravilli 2, 40139 Bologna, Italy)

Abstract

In 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 Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 4 (2000)
Issue (Month): 3 ()
Pages: 325-341

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Handle: RePEc:spr:finsto:v:4:y:2000:i:3:p:325-341

Note: received: April 1998; final revision received: May 1999
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Related research

Keywords: stochastic volatility; superreplication; stochastic optimal control; Hamilton-Jacobi-Bellman equations;

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Cited by:
  1. Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999, arXiv.org.
  2. 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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