分形Hurst指数在彩虹期权定价中的应用(英文)

Applying Fractal Hurst Exponent to Pricing Rainbow Option

1991年Rubinstein把“彩虹”这个标签引入期权当中,他强调基于多种资产组合起来的期权就像五颜六色的彩虹一样,期权中的每一种标的资产可以用彩虹中的一种颜色来表示,即彩虹期权不但是一种基于多种标的资产的期权,而且也被当作是一种关联期权.交割时期权交割价格依赖于这些资产的综合表现.在讨论股票对数价格的动力学行为时引入分形中Hurst指数,并当Hurst指数取值于区间(1/2,1)时推导出相应的彩虹期权的定价公式.

The Label rainbow was coined by Rubinstefin（ 1991 ）, who emphasizes that this option was based on a combination of various assets like a rainbow is a combination of various colors. More generally, rainbow options are multi-asset options, also referred to as correlation options. Rainbow can take various other forms but the combining idea is to have a pay-off that is depending on the assets sorted by their performance at maturity. Hurst exponents into the dynamics of stock log-price are introduced, and the corresponding rainbow option pricing formulas with Hurst exponents being in （1/2, 1） are deduced.