Maximal (Minimal) Conditional Expectation and European Option Pricing with Ambiguous Return Rate and Volatility

  • Authors:

  • Junfei Zhang;Shoumei Li

  • Affiliations:

  • College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, P.R. China;College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, P.R. China

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2013

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Abstract

In this paper, we consider the problem of option pricing when return rate and volatility are ambiguous. Firstly we illustrate how to describe this ambiguous option pricing model by using set-valued differential inclusion and how to change the discussion of pricing bound problems of options into that of maximal and minimal conditional expectations. Secondly we discuss the properties of maximal and minimal conditional expectations, especially the representation theorem of maximal and minimal expectations. Finally we give the bounds of the European option pricing by using above theorems.