Mild to classical solutions for XVA equations under stochastic volatility
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914728457011200 |
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| author | Brigo, Damiano Graceffa, Federico Kalinin, Alexander |
| author_facet | Brigo, Damiano Graceffa, Federico Kalinin, Alexander |
| contents | We extend the valuation of contingent claims in presence of default, collateral and funding to a random functional setting and characterise pre-default value processes by martingales. Pre-default value semimartingales can also be described by BSDEs with random path-dependent coefficients and martingales as drivers. En route, we generalise previous settings by relaxing conditions on the available market information, allowing for an arbitrary default-free filtration and constructing a broad class of default times. Moreover, under stochastic volatility, we characterise pre-default value processes via mild solutions to parabolic semilinear PDEs and give sufficient conditions for mild solutions to exist uniquely and to be classical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_11808 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Mild to classical solutions for XVA equations under stochastic volatility Brigo, Damiano Graceffa, Federico Kalinin, Alexander Probability Pricing of Securities 91G20, 91G80, 60G40, 60H20, 60H30, 35K58 We extend the valuation of contingent claims in presence of default, collateral and funding to a random functional setting and characterise pre-default value processes by martingales. Pre-default value semimartingales can also be described by BSDEs with random path-dependent coefficients and martingales as drivers. En route, we generalise previous settings by relaxing conditions on the available market information, allowing for an arbitrary default-free filtration and constructing a broad class of default times. Moreover, under stochastic volatility, we characterise pre-default value processes via mild solutions to parabolic semilinear PDEs and give sufficient conditions for mild solutions to exist uniquely and to be classical. |
| title | Mild to classical solutions for XVA equations under stochastic volatility |
| topic | Probability Pricing of Securities 91G20, 91G80, 60G40, 60H20, 60H30, 35K58 |
| url | https://arxiv.org/abs/2112.11808 |