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Received: 2005-06-09

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Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.4 P.584-590

http://doi.org/10.1631/jzus.2006.A0584


A generalization of exotic options pricing formulae


Author(s):  Li Shu-jin, Li Sheng-hong

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   jslsj@163.com

Key Words:  Risk-neutral measure, Compound options, Change of probability measure, Numeraire, Girsanov&rsquo, s theorem


Li Shu-jin, Li Sheng-hong. A generalization of exotic options pricing formulae[J]. Journal of Zhejiang University Science A, 2006, 7(4): 584-590.

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Abstract: 
Exotic options, or “path-dependent” options are options whose payoff depends on the behavior of the price of the underlying between 0 and the maturity, rather than merely on the final price of the underlying, such as compound options, reset options and so on. In this paper, a generalization of the Geske formula for compound call options is obtained in the case of time-dependent volatility and time-dependent interest rate by applying martingale methods and the change of numeraire or the change of probability measure. An analytic formula for the reset call options with predetermined dates is also derived in the case by using the same approach. In contrast to partial differential equation (PDE) approach, our approach is simpler.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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