A Spanning Series Approach to Options
本文证明期权定价的Edgeworth展开等价于用Hermite多项式逼近期权收益，从而将期权价值表示为无穷级数，并针对厚尾模型提供收敛的矩方法，可高效替代傅里叶变换，应用于Hull-White随机波动率模型。
This paper shows that Edgeworth expansions for option valuation are equivalent to approximating option payoffs using Hermite polynomials. Consequently, the value of an option is the value of an infinite series of replicating polynomials. The resultant formulas express option values in terms of skewness, kurtosis, and higher moments. Unfortunately, the Hermite series diverges for fat-tailed models, so we provide alternative moment-based formulas. These formulas are a computationally efficient alternative to Fourier transform valuation and can value options even when the characteristic function is unknown. Applications include the first convergent solution for Hull and White’s stochastic volatility model.Received February 1, 2016; accepted June 27, 2016 by Editor Wayne Ferson.