Quadratic-Form Approximation of Conic Combinations of Correlated Lognormals with an Application to Arithmetic Asian Options

Information from the abstract

This paper develops a positive quadratic-form approximation for expectations of globally Lipschitz functionals of conic combinations of correlated lognormal random variables. The surrogate is constructed from the same Gaussian vector as the original combination, yielding an explicit functional approximation-error bound in the positive weights, Gaussian means, and full covariance matrix. A Laguerre-series representation characterizes the surrogate distribution and supports pricing approximations for discretely monitored fixed-strike arithmetic Asian options under deterministic time-dependent Black–Scholes parameters. The resulting bound provides a common absolute-error guarantee across strikes, while numerical series truncation and Monte Carlo uncertainty are assessed separately. Three numerical examples examine distributional and pricing accuracy, bound conservatism, scaling sensitivity, and comparison with a three-moment compound-gamma approximation. The quadratic construction remains available in the displayed configurations where compound-gamma calibration is inadmissible. Where both methods are admissible in the tested benchmarks, compound gamma has smaller observed pricing discrepancies and shorter computation times. Increased Gaussian dispersion reveals limitations of the second-order approximation, particularly in relative pricing accuracy. The contribution is the combined surrogate construction, analytical distributional evaluation, and explicit Lipschitz-functional error control.

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Related topics: Stochastic processes and financial applications · Risk and Portfolio Optimization · Capital Investment and Risk Analysis