Efficient computation of first passage times in Kou's jump-diffusion model (Belkaid & Utzet, 2016)

This work aims to improve the performance of the algorithms developed by Belkaid and Utzet by translating them to a pure C numerical execution from symbolic Maple scripts.

Speedup

Using Digits:=30; in Maple and 80-bit floats (long double) and 64-bit ints (int64_t) in C.

• 1st function (f1+euler+suma): x723 (from 868ms to 1.20ms)
• 2nd function (f2+euler+suma): x899 (from 1259ms to 1.40ms)

Using Digits:=500; in Maple and GNU GMP, MPFR and MPC multiprecision libraries in C.

• 3rd function (f1+gaver+fn): x14.2 (from 3364ms to 236.94ms)

Tested in an Intel(R) Core(TM)2 Duo CPU E8400 @ 3.00GHz with 6GB of ram and Linux OS (Xubuntu 16.10 64bit).

Order of accuracy

Computed comparing results for n=12 and n=50 for the two first functions:

• 1st function: result: 0.2558436487, order of accuracy: 10^(-8)
• 2nd function: result: 0.2236160448, order of accuracy: 10^(-7)
• 3rd function: results have all digits exactly computed.

Stability of Gaver with respect to n

Stability with respect to n and time of computation for Gaver algorithm: see results.md.