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

Tiziano Vargiolu and Silvia Romagnoli ()
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Silvia Romagnoli: Istituto di Matematica Generale e Finanziaria, Universitá di Bologna, Piazza Scaravilli 2, 40139 Bologna, Italy

Finance and Stochastics, 2000, vol. 4, issue 3, 325-341

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.

Keywords: stochastic volatility; superreplication; stochastic optimal control; Hamilton-Jacobi-Bellman equations (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2000-05-09
Note: received: April 1998; final revision received: May 1999
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Citations: View citations in EconPapers (6)

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