Valuation of power option for uncertain financial market

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• 作者：Zhiqiang Zhang ; ^a ; ^b ; ^{sjzhangzhiqiang@sxdtdx.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Weiqi Liu^c ; ^{liuwq@sxu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yuhong Sheng^d ; ^{shengyuhong1@sina.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Uncertainty theory ; Uncertain differential equation ; Uncertain stock model ; Power option
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 August 2016
• 年：2016
• 卷：286
• 期：Complete
• 页码：257-264
• 全文大小：342 K

文摘

Power option is such an option whose payoff is based on the price of the underlying asset raised to some power. Unlike Black–Scholes setting, we investigate the valuation of power options under the assumption that the underlying stock price is assumed to follow an uncertain differential equation, and derive the pricing formulas of power options for Liu’s uncertain stock model with the method of uncertain calculus based on uncertainty theory. Some numerical examples are given to illustrate the pricing formulas.