A note on stochastic polynomial chaos expansions for uncertain volatility and Asian option pricing

Y.-T. Lin, Y.-T. Shih, C.-S. Chien and Q. Sheng

Applied Mathematics and Computation, 2021, vol. 393, issue C

Abstract: This paper concerns accurate and efficient polynomial chaos expansions (PCEs) for Asian option pricing with uncertain volatilities. While arbitrary distributions of the volatility parameter are applied for estimating real-world option prices, arbitrary polynomial chaos (aPC) are incorporated for approximating raw data of the historical volatility distributions. Rigorous analysis is carried out to ensure the numerical stability of the compact aPC Crank-Nicolson finite difference method accomplished. Numerical results acquired are compared with solutions via standard Monte Carlo schemes (MCSs) and generalized polynomial chaos (gPC) with different random volatilities. Stock data from Asian financial industry are used. It is evident that the novel schemes derived are highly accurate and efficient for evaluating means and variances of uncertain volatility and stochastic Asian option pricing.

Keywords: Uncertain volatility; Asian option; Statistical moments; Generalized polynomial chaos; Arbitrary polynomial chaos (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:393:y:2021:i:c:s0096300320307177

DOI: 10.1016/j.amc.2020.125764

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