Robustness of the Black-Scholes Approach in the Case of Options on Several Assets

Posted: 22 Aug 2000

See all articles by Silvia Romagnoli

Silvia Romagnoli

University of Bologna - Department of Statistics

Tiziano Vargiolu

Department of Mathematics

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

JEL Classification: G13

Suggested Citation

Romagnoli, Silvia and Vargiolu, Tiziano, Robustness of the Black-Scholes Approach in the Case of Options on Several Assets. Available at SSRN: https://ssrn.com/abstract=228728

Silvia Romagnoli (Contact Author)

University of Bologna - Department of Statistics ( email )

Tiziano Vargiolu

Department of Mathematics ( email )

Italy
+390498271383 (Phone)

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