Analytic Formulae for Basket Options with Stochastic Volatility

• Main Authors: Ren - wei Chen, 陳仁維
• Other Authors: Chung-Gee Lin
• Format: Others
• Language: en_US
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/02533487452718045753

碩士 === 東吳大學 === 商用數學系 === 95 === The valuation of basket options is complex since the weighted average of lognormal random variables is no longer lognormal. Moreover, as the stochastic volatility inherent in the financial asset prices are extensively observed, however, few academic works pay attention to the pricing and hedging of basket options with stochastic volatility, despite the popularity of basket options in practical application. This paper derives the analytic solution for pricing and hedging basket option with stochastic volatility by integrating Taylor series expansions. Numerical experiments show that our analytic solution performs very well and is computationally efficient as benchmarked with large sample Monte Carlo simulations. Our analytic solution can also be treated as a practical tool for pricing and hedging stochastic volatility basket options, since it is easy to implement and is more desirable as the computing speed is an important consideration.