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Title: Computation of three discrete mixtures of continuous distributions: Stability analysis Authors:  Joana Leite - Coimbra Business School | ISCAC - IPC and CMUC (Portugal) [presenting]
Jose Carlos Dias - ISCTE-IUL and UNIDE-IUL (Portugal)
Joao Pedro Nunes - ISCTE-IUL and UNIDE-IUL (Portugal)
Abstract: The distributions of the squared sample multiple correlation coefficient, noncentral $t$, and noncentral chi-square are critical in many fields, including Finance. For example, the latter has applications in the context of interest rate modelling, valuation of financial and real options, and the simulation of stochastic volatility processes. Previous algorithms for computing these distributions achieved significant gains in efficiency when compared to the previous ones, and, nowadays, are considered the benchmark. In their core are recurrence relations of special functions, applied in both the forward and in the backward directions. Recently, stability issues have been raised regarding the algorithm for the noncentral chi-square distribution. In this setting, all three algorithms are analysed, with particular attention paid to the stability of the recurrence relations. Necessary modifications are implemented in the algorithms and comparison studies carried out.