On the Evaluation of Compound Options
Michael J. P. Selby, Stewart D. Hodges
Management Science · 1987 · Volume 33 · Issue 3
Abstract
Compound option valuation formulae give rise to the summation of a series of multinormal distribution functions. This paper presents an identity on sums of nested multinormal distributions of arbitrary dimension. We show that this identity generalizes some well-known low order identities for the multinormal distribution. We present three applications of the new identity to contingent claims valuation problems. The first and second applications show that by reducing significantly the number of integrals to be evaluated, faster and more accurate algorithms can be developed for implementing the Geske-Johnson American put valuation formula and the Roll-Geske-Whaley American call formula; the third gives new economic insights into the valuation of disaggregated coupon bonds.
Keywords
American call, American put, computational efficiency, contingent claims, coupon bonds, identity, multinormal, nested
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