Bilateral gamma distributions and processes in financial mathematics. (English) Zbl 1133.62089
The authors propose a new interesting family of Lévy processes: bilateral processes, which are defined as the difference of two independent gamma processes. This four-parameter class of processes is more flexible than variance gamma processes and is analytically tractable; in particular, these processes have a simple cumulant generating function. The aim of the paper is twofold. First, the properties of these processes are investigated as well as their generating distributions and it is shown how they are related to the other distributions considered in the literature. The second goal is to apply bilateral gamma processes to modeling financial market fluctuations. Exponential Lévy stock market models are treated and a closed formula for pricing European Call Options is derived.
Reviewer: Yuliya S. Mishura (Kyïv)
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 60G51 | Processes with independent increments; Lévy processes |
| 91B28 | Finance etc. (MSC2000) |
| 60E10 | Characteristic functions; other transforms |
| 62M05 | Markov processes: estimation; hidden Markov models |
Keywords:
bilateral gamma processes; measure transformations; stock models; option pricing; term structure modelsReferences:
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