The Pricing of Power Options under the GeneralizedBlack-Scholes Model

• Main Authors: Yi-Yun Wu, 吳宜紜
• Other Authors: Hong-Kun Xu
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/33542906004673746475

碩士 === 國立中山大學 === 應用數學系研究所 === 99 === A closed-form pricing formula of European options is obtained by Fischer Black and Myron Scholes (1973). In such a European option, the payoff depends `linearly'' on the underlying asset price at the expiration time. An power option has a payoff which depends nonlinearly on the underlying asset price at the expiration time by raising a certain exponent. In the Black-Scholes model, a closed-form formula of a power option is obtained by Esser (2004). This paper extends Esser''s result to the generalized Black- Scholes model. That is, we derive a closed-form pricing formula of a power option in the case when both the interest rate and the stock volatility are time-dependent.