Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2202.02708 |
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Inhaltsangabe:
- We extend the information-based asset-pricing framework by Brody, Hughston \& Macrina to incorporate a stochastic bankruptcy time for the writer of the asset. Our model introduces a non-defaultable cash flow $Z_T$ to be made at time $T$, alongside the time $τ$ of a possible bankruptcy of the writer of the asset are in line with the filtration generated by a Brownian random bridge with length $ν=τ\wedge T$ and pinning point $σZ_T$, where $σ$ is a constant. Quantities $Z_T$ and $τ$ are not necessarily independent. The model does not depend crucially on the interpretation of $τ$ as a bankruptcy time. We derived the price process of the asset and compute the prices of associated options. The dynamics of the price process satisfy a diffusion equation. Employing the approach of P.-A.~ Meyer, we provide the explicit computation of the compensator of $ν$. Leveraging special properties of the bridge process, we also provide the explicit expression of the compensator of $Z_T\,\mathbb{I}_{[ν,+\infty)}$. The resulting conclusion highlights the totally inaccessible property of the stopping time $ν$. This characteristic is particularly suitable for financial markets where the time of default of a writer cannot be predictable from any other signal in the system until default happens.