跳分形过程下延展期权定价

华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (3): 30-40.

跳分形过程下延展期权定价

彭斌¹, 彭菲²

1. 中国人民大学商学院, 北京 100872; 2. 大不列颠哥伦比亚大学~~电子计算机学院, 温哥华~ V6T 1Z4, 加拿大

收稿日期:2010-12-01 修回日期:2011-03-01 出版日期:2012-05-25 发布日期:2012-05-22

Pricing extendible option under jump-fraction process

PENG Bin ¹, PENG Fei ²

1. School of Business, Renmin University, Beijing}100872, China; 2. Electrical & Computer Engineering, UBC, Vancouver B. C. V6T 1Z4, Canada

Received:2010-12-01 Revised:2011-03-01 Online:2012-05-25 Published:2012-05-22

摘要/Abstract

摘要： 当标的资产遵循跳分形过程时, 构建了延展期权的评估框架. 首先, 在风险中性环境里, 对标的资产发生跳跃次数的收益求条件期望现值, 导出了延展一期的看涨期权解析定价公式, 并探讨了公式的一些特殊情形. 然后, 将定价公式延展到\,$M$\,期, 该延展期权价值在\,$M$\,趋于无穷极限状态时, 将收敛于永久延展期权. 提出了一种简单有效的两点外推法求极限. 最后, 提供数值结果, 阐述了定价表达式的简单实用.

关键词: 跳分形过程, 延展期权, 两点外推技术

Abstract: A valuation framework for extendible options is constructed when the underlying asset obeys a fractional process with jump. Under the risk neutral environment, an analytic formula for the call option with one extendible maturity is derived by solving the expected present value of cashflow and conditioning jumps for the underlying asset. Moreover, some special cases of the formula are discussed. These results are generalized to the option with$ M $extendible maturity. Its value will converge in the limit to the value of perpetual extendible option as the number of extendible maturity increases to infinite. Extrapolated technique with two
points is presented to yield a simple and efficient computation procedure to calculate the limit. Numerical results are provided to illustrate provided that our pricing expressions are easy to implement.

Key words: jump fraction process, extendible option, extrapolated technique with two points

中图分类号:

O213

彭斌, 彭菲. 跳分形过程下延展期权定价[J]. 华东师范大学学报(自然科学版), 2012, 2012(3): 30-40.

PENG Bin, PENG Fei. Pricing extendible option under jump-fraction process[J]. Journal of East China Normal University(Natural Sc, 2012, 2012(3): 30-40.

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