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Avellaneda, M., Levy, A. and Para, A. (1995) Pricing and Hedging Derivative Securities in Markets with Uncertain Volatilities. Applied Mathematical Finance, 2, 73-88.
http://dx.doi.org/10.1080/13504869500000005

has been cited by the following article:

• TITLE: Uncertain Volatility Derivative Model Based on the Polynomial Chaos

  AUTHORS: Stefanos Drakos

  KEYWORDS: Uncertain Volatility Model, Polynomial Chaos, Quantification of Uncertainty, Stochastic Finite Element Method

  JOURNAL NAME: Journal of Mathematical Finance, Vol.6 No.1, February 19, 2016

  ABSTRACT: In the modern financial market the derivative pricing considers the use of historical or implied volatility which is actually the forward expectation of uncertainty. The common way of derivative pricing is to use the volatility as constant value in the well known Black Sholes equation. The aim of the current work was to develop a model where the uncertainty of volatility propagates to the derivative pricing and hedging according to the Black-Sholes PDE considering the volatility as stochastic process rather as a constant. A stochastic finite element method using generalized polynomial chaos was used to develop an algorithm of uncertainty propagation solving finally a deterministic problem for derivative pricing. The output of the method leads to derivative price distribution and the results of Monte Carlo Method for the derivative’s distribution were used as the exact solution against those rose from the new algorithm.