TY - JOUR
T1 - On a positivity preserving numerical scheme for jump-extended CIR process
T2 - the alpha-stable case
AU - Li, Libo
AU - Taguchi, Dai
N1 - Funding Information:
The authors wish to thank the anonymous referees for their careful readings and valuable advices on the writing of this article. The first author also wishes to thank Allan Loi for interesting discussions. The second author was supported by JSPS KAKENHI Grant No. 17H066833.
Publisher Copyright:
© 2019, Springer Nature B.V.
PY - 2019/9/1
Y1 - 2019/9/1
N2 - We propose a positivity preserving implicit Euler–Maruyama scheme for a jump-extended Cox–Ingersoll–Ross (CIR) process where the jumps are governed by a compensated spectrally positive α-stable process for α∈ (1 , 2). Different to the existing positivity preserving numerical schemes for jump-extended CIR or constant elasticity variance process, the model considered here has infinite activity jumps. We calculate, in this specific model, the strong rate of convergence and give some numerical illustrations. Jump extended models of this type were initially studied in the context of branching processes and was recently introduced to the financial mathematics literature to model sovereign interest rates, power and energy markets.
AB - We propose a positivity preserving implicit Euler–Maruyama scheme for a jump-extended Cox–Ingersoll–Ross (CIR) process where the jumps are governed by a compensated spectrally positive α-stable process for α∈ (1 , 2). Different to the existing positivity preserving numerical schemes for jump-extended CIR or constant elasticity variance process, the model considered here has infinite activity jumps. We calculate, in this specific model, the strong rate of convergence and give some numerical illustrations. Jump extended models of this type were initially studied in the context of branching processes and was recently introduced to the financial mathematics literature to model sovereign interest rates, power and energy markets.
KW - Alpha-CIR models
KW - Euler–Maruyama scheme
KW - Hölder continuous coefficients
KW - Implicit scheme
KW - Lévy driven SDEs
KW - Spectrally positive Lévy process
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U2 - 10.1007/s10543-019-00753-8
DO - 10.1007/s10543-019-00753-8
M3 - Article
AN - SCOPUS:85065022443
SN - 0006-3835
VL - 59
SP - 747
EP - 774
JO - BIT Numerical Mathematics
JF - BIT Numerical Mathematics
IS - 3
ER -