TY - JOUR
T1 - Barrier option pricing by branching processes
AU - Mitov, Georgi K.
AU - Rachev, Svetlozar T.
AU - Kim, Young Shin
AU - Fabozzi, Frank J.
N1 - Funding Information:
Georgi Mitov is supported by the German Academic Exchange Service (DAAD) and in part by NSF-Bulgaria (grant VU-MI-105/20-05). Svetlozar Rachev gratefully acknowledges research support by grants from Division of Mathematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara, the Deutschen Forschungsgemeinschaft, and the Deutscher Akademischer Austausch Dienst.
PY - 2009/11
Y1 - 2009/11
N2 - This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options. Our results show that the prices of barrier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small.
AB - This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options. Our results show that the prices of barrier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small.
KW - Barrier option
KW - Bienayme-Galton-Watson branching process
KW - Branching process in a random environment
KW - Up-and-out call option
UR - http://www.scopus.com/inward/record.url?scp=71249086386&partnerID=8YFLogxK
U2 - 10.1142/S0219024909005555
DO - 10.1142/S0219024909005555
M3 - Article
AN - SCOPUS:71249086386
SN - 0219-0249
VL - 12
SP - 1055
EP - 1073
JO - International Journal of Theoretical and Applied Finance
JF - International Journal of Theoretical and Applied Finance
IS - 7
ER -