The evaluation of an Asian option formula is the problem discussed in this paper. An algorithm for the evaluation, constructed by mathematical derivations from the formula, is presented.

The paper has five sections. The first section, an introduction, begins by defining the problem. A brief survey of various solutions is given. The solution proposed uses a Hermitian quadrature formula. It contains evaluations of a hyperbolic integral and a trigonometric integral. The second section is on the hyperbolic integral. The proposed evaluation applies Leibniz’s rule on Taylor’s coefficients. Theorems describing the bounds are derived. Section 3 covers the trigonometric integral. An algorithm based on the discussion in the first three sections is presented in section 4, and an example is described in section 5. The performance data is provided in tables on the loss of digits and timings.

This paper requires readers to have an understanding of basic mathematical symbols and notations, such as integrals, functions, and intervals. A background in the basic theories of integrals and series is also required.