Abstract
We introduce a new stochastic tree representation of a strictly stationary submartingale process for modelling, forecasting, and pricing speculative bubbles on commodity and cryptocurrency markets. The model is compared to other trees proposed in the literature on bubble asset modelling and stochastic volatility approximation. We show that the proposed model is an extension of the well-known Blanchard-Watson bubble. The model provides (quasi) closed-form pricing formulas for European options, which are derived and illustrated.
| Original language | English |
|---|---|
| Pages (from-to) | 932-944 |
| Number of pages | 13 |
| Journal | Journal of Time Series Analysis |
| Volume | 46 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 1 Sept 2025 |
| Externally published | Yes |
Keywords
- European option
- bubble asset
- bubble pattern
- local trends
- stationary submartingale
- stochastic intensity
- stochastic tree
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