| Computer & Information Science |
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| A generalization of exotic options pricing formulae |
| Li Shu-jin, Li Sheng-hong |
| Department of Mathematics, Zhejiang University, Hangzhou 310027, China; Department of Foundation, Jiangsu Teachers University of Technology, Changzhou 213015, China |
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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.
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Received: 09 June 2005
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