Sources and further reading
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The volume combines the quadratic-form engine, query-adaptive packet theory, and streaming polyphase analysis. Their source correspondence and reproducible records accompany the editable book. The works below provide the classical inversion, COS, and statistical foundations. Section 12.2 distinguishes those foundations from the contribution developed here.
References
[1] Imhof1961
J. P. Imhof, Computing the distribution of quadratic forms in normal variables, Biometrika 48(3–4) (1961), 419–426. doi:10.1093/biomet/48.3-4.419.
[2] Davies1980
R. B. Davies, Algorithm AS 155: The distribution of a linear combination of \(\chi^2\) random variables, Applied Statistics 29(3) (1980), 323–333. doi:10.2307/2346911.
[3] FangOosterlee2008
F. Fang and C. W. Oosterlee, A novel pricing method for European options based on Fourier-cosine series expansions, SIAM Journal on Scientific Computing 31(2) (2008–2009), 826–848. Published online in 2008. doi:10.1137/080718061.
[4] JunikePankrashkin2022
G. Junike and K. Pankrashkin, Precise option pricing by the COS method—How to choose the truncation range, Applied Mathematics and Computation 421 (2022), 126935. doi:10.1016/j.amc.2022.126935.
[5] Junike2024
G. Junike, On the number of terms in the COS method for European option pricing, Numerische Mathematik 156 (2024), 533–564. doi:10.1007/s00211-024-01402-1.
[6] JunikeStier2025
G. Junike and H. Stier, From characteristic functions to multivariate distribution functions and European option prices by the (damped) COS method, SIAM Journal on Numerical Analysis 63(6) (2025), 2421–2453. doi:10.1137/24M1666240.
[7] Wu2011
M. C. Wu, S. Lee, T. Cai, Y. Li, M. Boehnke, and X. Lin, Rare-variant association testing for sequencing data with the sequence kernel association test, American Journal of Human Genetics 89(1) (2011), 82–93. doi:10.1016/j.ajhg.2011.05.029.