Affine models with path-dependence under parameter uncertainty and their application in finance

Benedikt Geuchen, Katharina Oberpriller and Thorsten Schmidt

Papers from arXiv.org

Abstract: In this work we consider one-dimensional generalized affine processes under the paradigm of Knightian uncertainty (so-called non-linear generalized affine models). This extends and generalizes previous results in Fadina et al. (2019) and L\"utkebohmert et al. (2022). In particular, we study the case when the payoff is allowed to depend on the path, like it is the case for barrier options or Asian options. To this end, we develop the path-dependent setting for the value function which we do by relying on functional It\^o calculus. We establish a dynamic programming principle which then leads to a functional non-linear Kolmogorov equation describing the evolution of the value function. While for Asian options, the valuation can be traced back to PDE methods, this is no longer possible for more complicated payoffs like barrier options. To handle such payoffs in an efficient manner, we approximate the functional derivatives with deep neural networks and show that the numerical valuation under parameter uncertainty is highly tractable. Finally, we consider the application to structural modelling of credit and counterparty risk, where both parameter uncertainty and path-dependence are crucial and the approach proposed here opens the door to efficient numerical methods in this field.

Date: 2022-07, Revised 2024-06
New Economics Papers: this item is included in nep-cmp
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2207.13350 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2207.13350

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().