Calibration for Weak Variance-Alpha-Gamma Processes
| Autor: | Dilip B. Madan, Kevin W. Lu, Boris Buchmann |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability 60G51 62F10 60E10 Subordinator Calibration (statistics) General Mathematics 010102 general mathematics Gamma process Method of moments (probability theory) Mathematical Finance (q-fin.MF) 01 natural sciences Lévy process Variance-gamma distribution Methodology (stat.ME) FOS: Economics and business Moment (mathematics) 010104 statistics & probability Quantitative Finance - Mathematical Finance Applied mathematics 0101 mathematics Brownian motion Statistics - Methodology Mathematics |
| Popis: | The weak variance-alpha-gamma process is a multivariate L��vy process constructed by weakly subordinating Brownian motion, possibly with correlated components with an alpha-gamma subordinator. It generalises the variance-alpha-gamma process of Semeraro constructed by traditional subordination. We compare three calibration methods for the weak variance-alpha-gamma process, method of moments, maximum likelihood estimation (MLE) and digital moment estimation (DME). We derive a condition for Fourier invertibility needed to apply MLE and show in our simulations that MLE produces a better fit when this condition holds, while DME produces a better fit when it is violated. We also find that the weak variance-alpha-gamma process exhibits a wider range of dependence and produces a significantly better fit than the variance-alpha-gamma process on an S&P500-FTSE100 data set, and that DME produces the best fit in this situation. |
| Databáze: | OpenAIRE |
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