Journal of Mathematical Finance
Volume 6, Issue 1 (February 2016)
ISSN Print: 2162-2434 ISSN Online: 2162-2442
Google-based Impact Factor: 0.87 Citations h5-index & Ranking
Uncertain Volatility Derivative Model Based on the Polynomial Chaos ()
Affiliation(s)
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.
KEYWORDS
Share and Cite:
Cited by
Copyright © 2024 by authors and Scientific Research Publishing Inc.
This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.