COS Method

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1 \backmatter
2 \chapter{Sources and further reading}
3 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~\ref{sec:prior-work} distinguishes those foundations from the contribution developed here.
4 
5 \begingroup\small
6 \patchcmd{\thebibliography}{\chapter*{\bibname}}{\section*{\bibname}}{}{}
7 \begin{thebibliography}{9}
8 \bibitem{Imhof1961} J.~P. Imhof, Computing the distribution of quadratic forms
9 in normal variables, \emph{Biometrika} 48(3--4) (1961), 419--426.
10 \href{https://doi.org/10.1093/biomet/48.3-4.419}{doi:10.1093/biomet/48.3-4.419}.
11 \bibitem{Davies1980} R.~B. Davies, Algorithm AS~155: The distribution of a
12 linear combination of $\chi^2$ random variables,
13 \emph{Applied Statistics} 29(3) (1980), 323--333.
14 \href{https://doi.org/10.2307/2346911}{doi:10.2307/2346911}.
15 \bibitem{FangOosterlee2008} F. Fang and C.~W. Oosterlee, A novel pricing
16 method for European options based on Fourier-cosine series expansions,
17 \emph{SIAM Journal on Scientific Computing} 31(2) (2008--2009), 826--848.
18 Published online in 2008.
19 \href{https://doi.org/10.1137/080718061}{doi:10.1137/080718061}.
20 \bibitem{JunikePankrashkin2022} G. Junike and K. Pankrashkin,
21 Precise option pricing by the COS method---How to choose the truncation range,
22 \emph{Applied Mathematics and Computation} 421 (2022), 126935.
23 \href{https://doi.org/10.1016/j.amc.2022.126935}{doi:10.1016/j.amc.2022.126935}.
24 \bibitem{Junike2024} G. Junike, On the number of terms in the COS method
25 for European option pricing, \emph{Numerische Mathematik} 156 (2024), 533--564.
26 \href{https://doi.org/10.1007/s00211-024-01402-1}{doi:10.1007/s00211-024-01402-1}.
27 \bibitem{JunikeStier2025} G. Junike and H. Stier, From characteristic
28 functions to multivariate distribution functions and European option prices
29 by the (damped) COS method, \emph{SIAM Journal on Numerical Analysis}
30 63(6) (2025), 2421--2453.
31 \href{https://doi.org/10.1137/24M1666240}{doi:10.1137/24M1666240}.
32 \bibitem{Wu2011} M.~C. Wu, S. Lee, T. Cai, Y. Li, M. Boehnke, and X. Lin,
33 Rare-variant association testing for sequencing data with the sequence
34 kernel association test, \emph{American Journal of Human Genetics}
35 89(1) (2011), 82--93.
36 \href{https://doi.org/10.1016/j.ajhg.2011.05.029}{doi:10.1016/j.ajhg.2011.05.029}.
37 \end{thebibliography}
38 \endgroup

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