A Review of Option Pricing Methods for Underlying Assets Modeled by ARIMA-GARCH Processes

A. R. Danilishin

Abstract


This paper surveys methods for valuing derivative financial instruments when underlying asset prices follow ARIMA-GARCH dynamics. Unlike geometric Brownian motion, these models capture volatility clustering, conditional heteroskedasticity, and heavy-tailed distributions. Hybrid ARIMA-GARCH specifications are examined, combining temporal dependence with time-varying volatility, and their implications for market incompleteness and the selection of an equivalent martingale measure are discussed. Extensions of Girsanov’s theorem and approaches for constructing measure changes in incomplete markets, including modifications for heavy-tailed distributions, receive particular attention. The review integrates analytical results with numerical option pricing algorithms under ARIMA-GARCH dynamics, assessing robustness of measure transformations, the influence of distributional assumptions, and sensitivity of schemes. Comparative analyses of option pricing methods, numerical examples, and practical recommendations for model choice and parameterization are presented. The conclusion highlights trade-offs among methods, limitations of current approaches, and prospects for further research in derivative valuation under non-Gaussian, heteroskedastic processes. Issues of numerical stability, risk assessment, and practical implementation are also considered.

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