TY - JOUR
T1 - Erlangization/Canadization of Phase-Type Jump Diffusions, with Applications to Barrier Options
AU - Asmussen, Søren
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/12
Y1 - 2024/12
N2 - For a jump diffusion with upward phase-type jumps with p phases, the maximum before an independent Erlang time eηq with q stages and rate parameter η is again phase-type with q(p+1) phases. An iterative scheme for computing the phase generator is presented and applied to representing the price of a barrier option with time horizon eηq as a single ordinary integral. Canadization then means to approximate a fixed horizon T with an eηq satisying Eeηq=T for a sufficiently large q. Similar results holds for Greeks like the delta and the gamma. A numerical example is given for a down-and-in call option and the Canadization is combined with Richardson extrapolation. Finally, a recursion is developed that only requires the iteration to be performed in p+1 dimensions.
AB - For a jump diffusion with upward phase-type jumps with p phases, the maximum before an independent Erlang time eηq with q stages and rate parameter η is again phase-type with q(p+1) phases. An iterative scheme for computing the phase generator is presented and applied to representing the price of a barrier option with time horizon eηq as a single ordinary integral. Canadization then means to approximate a fixed horizon T with an eηq satisying Eeηq=T for a sufficiently large q. Similar results holds for Greeks like the delta and the gamma. A numerical example is given for a down-and-in call option and the Canadization is combined with Richardson extrapolation. Finally, a recursion is developed that only requires the iteration to be performed in p+1 dimensions.
KW - Block Toeplitz matrix
KW - Fixed point equation
KW - Greeks
KW - Iteration
KW - Lévy process
KW - Phase-type distribution
KW - Richardson extrapolation
KW - Romberg integration
KW - Upper triangular block matrix
KW - Wiener-Hopf factorization
UR - http://www.scopus.com/inward/record.url?scp=85203685240&partnerID=8YFLogxK
U2 - 10.1007/s41096-024-00209-5
DO - 10.1007/s41096-024-00209-5
M3 - Journal article
AN - SCOPUS:85203685240
SN - 2364-9569
VL - 25
SP - 575
EP - 596
JO - Journal of the Indian Society for Probability and Statistics
JF - Journal of the Indian Society for Probability and Statistics
IS - 2
ER -