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A Note on Pricing Asian Derivatives with Continuous Geometric Averaging

Summary: A Note on Pricing Asian Derivatives with
Continuous Geometric Averaging
John E. Angus
Claremont Graduate University
April 1, 1999
A general expression is derived for the price of a European-style Asian con-
tingent claim whose terminal value depends on both the underlying asset price
and the continuous geometric average of the price of the underlying asset over
the life of the claim. SpeciŽc formulas are derived for Asian call, put, and binary
options, as well as for the average strike binary options.
Key words: mathematical Žnance, options, average, contingent claims.
1. Introduction
Assume that trading is done in a perfect continuous security market with no transac-
tion costs. Consider a security (e.g. a stock) whose share price is governed by the Ito
stochastic differential equation
dS = (µ - D)Sdt + SdX (1.1)
where µ and are positive constants, {X(t), t 0} is a standard Brownian motion,
and D represents a constant rate of continuous dividend payment. Assume all risk-
free investments earn the same Žxed constant rate of continuously compounded return


Source: Angus, John - School of Mathematical Sciences, Claremont Graduate University


Collections: Mathematics