Option pricing in the presence of random arbitrage return

  • Authors:

  • Jungmin Choi;Max Gunzburger

  • Affiliations:

  • Department of Mathematics, Florida State University, Tallahassee, FL, USA;Department of Scientific Computing, Florida State University, Tallahassee, FL, USA

  • Venue:
  • International Journal of Computer Mathematics - SPECIAL ISSUE ON FINANCIAL DERIVATIVES
  • Year:
  • 2009

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Abstract

We consider option pricing problems when we relax the condition of no arbitrage in the Black-Scholes model. Assuming random noise in the interest rate process, the derived pricing equation is in the form of stochastic partial differential equation. We used Karhunen-Loeve expansion to approximate the stochastic term and a combined finite difference/finite element method to effect temporal and “spatial” discretization. Computational examples in which the noise is assumed to be a Ornstein-Uhlenbeck process are provided that illustrate not only the discretization methods used, but the type of results relevant to option pricing that can be obtained from the model.