A Variable Reduction Technique for Pricing Average‐rate Options

Average-rate options, commonly known as Asian options, are contingent claims whose payoffs depend on the arithmetic average of some underlying index over a fixed time horizon. This paper proposes a new valuation technique, called the variable reduction technique, for average rate options. This method transforms the valuation problem of an average-rate option into an evaluation of a conditional expectation that is determined by a one-dimensional Markov process (as opposed to a two-dimensional Markov process). This variable reduction technique works directly with the arithmetic average and does not encounter approximation errors when volatility of the underlying is relatively large. Further, reducing the dimensionality by one makes pricing more efficient in terms of computing time. The variable reduction technique is applied in a simple Black-Scholes' economy in which there is one risky asset and one riskless bond. The paper also discusses application of the technique to average-rate options where the underlying index is an interest rate. Numerical comparisons of different methods are also presented.