Article1993

The Valuation of Path Dependent Contracts on the Average

Peter H. Ritchken · L. Sankarasubramanian · Anand M. Vijh

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Stochastic processes and financial applications Financial Markets and Investment Strategies Capital Investment and Risk Analysis

Abstract

This article values option contracts based on the average price realized over a finite time horizon. Such contracts are of importance to traders who periodically transact in spot markets and who require protection from adverse moves in their total accrued costs realized over their trading horizons. Explicit valuation models for pricing a variety of path dependent contracts based on geometric and arithmetic averages are developed. The early exercise features of American contracts are investigated, and it is shown that this feature has significant value.

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References

1979Option pricing: A simplified approach 1981Martingales and stochastic integrals in the theory of continuous trading 1978THE VALUE OF AN OPTION TO EXCHANGE ONE ASSET FOR ANOTHER 1977Options: A Monte Carlo approach 1987Efficient Analytic Approximation of American Option Values 1990A pricing method for options based on average asset values 1979Path Dependent Options: "Buy at the Low, Sell at the High"

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1999Jump Processes in Commodity Futures Prices and Options Pricing 1995Lattice Models for Pricing American Interest Rate Claims 2000Analytical Valuation of American-Style Asian Options 2002Convergence of numerical methods for valuing path-dependent options using interpolation 2002On the equivalence of floating- and fixed-strike Asian options 2006Extending quadrature methods to value multi-asset and complex path dependent options 2001Pricing Algorithms for Options with Exotic Path-Dependence

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