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...

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...

Bienaymé-Galton-Watson branching processes subordinated to a continuous time random index are considered. The branching processes are assumed to be critical with finite or infinite offspring variance. The indexing process is assumed to be a renewal one with finite or infinite mean of the...

For the renewal counting process M(t)=min{k:Skt} and the independent of it nonnegative random variable T, we investigate the asymptotic behaviour of P(M(t)T) and P(M(t)=K(t)x|M(t)T) in cases when the interarrival times have an infinite mean. These quantities appear in a natural way when...