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.

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关于不确定波动率和亚洲期权定价的随机多项式混沌扩展的说明

摘要 本文关注具有不确定波动性的亚洲期权定价的准确有效的多项式混沌展开 (PCE)。虽然波动率参数的任意分布用于估计现实世界的期权价格，但任意多项式混沌 (aPC) 被合并用于近似历史波动率分布的原始数据。进行了严格的分析，以确保所完成的紧凑型 aPC Crank-Nicolson 有限差分方法的数值稳定性。将获得的数值结果与通过标准蒙特卡罗方案 (MCS) 和具有不同随机波动率的广义多项式混沌 (gPC) 的解决方案进行比较。使用来自亚洲金融业的股票数据。