基于Student t-分布的期权敏感性：Gosset公式的希腊族
Student's t-Distribution Based Option Sensitivities: Greeks for the Gosset Formulae
摘要：
欧式期权可以在收益服从Student t分布时定价，前提是资产的价值有上限或分布被截断。为了纪念W. S.戈塞特在本文中，我们比较了Gosset和Black-Scholes公式的希腊语，并讨论了实现。t分布需要一个形状参数ν来匹配观察到的收益的“厚尾”。对于大的ν，Gosset和Black-Scholes公式是等价的。戈塞特公式去除了波动率已知的要求，在这个意义上可以被视为布莱克-斯科尔斯公式的扩展。
英文摘要：
European options can be priced when returns follow a Student's t-distribution, provided that the asset is capped in value or the distribution is truncated. We call pricing of options using a log Student's t-distribution a Gosset approach, in honour of W.S. Gosset. In this paper, we compare the greeks for Gosset and Black-Scholes formulae and we discuss implementation. The t-distribution requires a shape parameter νto match the "fat tails" of the observed returns. For large ν, the Gosset and Black-Scholes formulae are equivalent. The Gosset formulae removes the requirement that the volatility be known, and in this sense can be viewed as an extension of the Black-Scholes formula.
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