Mitic, P; (1997) Symbolic-Numeric Option Valuation. In: Keranen, V and Mitic, P and Heitamaki, A, (eds.) Innovation in Mathematics. (pp. pp. 337-344). WIT Press: Southampton, England.

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Abstract

Techniques for option valuation, both analytic and numeric, are well-established. 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 characterises 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.

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