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Symbolic-numeric option valuation

Peter Mitic
Organization: Positive Corporation Limited
Journal / Anthology

Innovation in Mathematics: Proceedings of the Second International Mathematica Symposium
Year: 1997
Page range: 337-344

Techniques for option valuation, both analytic and numeric, are well-estblished. Many of them cannot be used if the nature of the option is such that knowledge of the future is a prerequisite for valuation. For example, the value when the option expires may depend on the price of the underlying asset during the lifetime of the option. This paper describes a method of overcoming this problem by manipulating a symbolic parameter in a numeric scheme. This parameter characterizes the option price at any stage in its lifetime as a function of the price history of the underlying asset. Certain options may then be valued by symbolic manipulations involving this parameter, such that it is not necessary to know a numerical value for a parameter in advance. This enables a limited amount of path-dependency' to be introduced into option valuation when using established numerical techniques, which has hitherto been very difficult or impossible.

*Business and Economics

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