CVA with Wrong-Way Risk in the Presence of Early Exercise

Baviera, Roberto; Bua, Gaetano La; Pellicioli, Paolo

doi:10.1007/978-3-319-33446-2_5

Cited by 5 publications

(10 citation statements)

References 14 publications

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“…See for example [8] and [16]. The equivalence between Equation (5) and Equation (6) shows that the discount factor has the same function as the coefficients in front of V t . In particular we notice that in Equation (5) we are discounting at the rate r t + λ t and in the equivalent Equation ( 6) we eliminated the discount factors but we had to add the (r t + λ t )V t term.…”

Section: Theorem 45 (Solution To the Valuation Equation)mentioning

confidence: 99%

“…Notice that even if from Equation ( 6) it looks like V t depends on the future, it is just how the BSDE is formulated (see Section C). In the next section we will obtain an F t -adapted process as a solution to (6).…”

Section: Markovian Fbsde and Pdementioning

confidence: 99%

“…Remark 10. Note that assuming ε t = V t means that the term λ u ε u in θ u will cancel the term −λ t V t in Equation (6).…”

Section: Markovian Fbsde and Pdementioning

confidence: 99%

“…when the exposure to a counterparty is negatively correlated with the credit quality of the counterparty itself. Analyses of the dependence structure between exposure and default risk are treated for example in [6], while [12] and [17,18] specialise the problem to particular products: Longevity Swaps and Credit Default Swaps respectively.…”

Section: A Concise Introduction To Valuation Adjustmentsmentioning

confidence: 99%

“…6. He gives H t back to treasury, so the outstanding debt to the treasury is V t − C t since H t − C H t = 0 Time t + dt:…”

mentioning

confidence: 99%

See 4 more Smart Citations

Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement

Brigo

Francischello

Pallavicini

2019

European Journal of Operational Research

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2 The opinions here expressed are solely those of the authors and do not represent in any way those of their employers. Acknowledgments: we are grateful to Cristin Buescu, Jean-François Chassagneux, François Delarue, Federico Graceffa, and Marek Rutkowski for helfpul discussion and suggestions that helped us improve the paper. Marek Rutkowski and Andrea Pallavicini visits were funded via the EPSRC Mathematics Platform grant EP/I019111/1.

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Section: Theorem 45 (Solution To the Valuation Equation)mentioning

confidence: 99%

Section: Markovian Fbsde and Pdementioning

confidence: 99%

“…Remark 10. Note that assuming ε t = V t means that the term λ u ε u in θ u will cancel the term −λ t V t in Equation (6).…”

Section: Markovian Fbsde and Pdementioning

confidence: 99%

Section: A Concise Introduction To Valuation Adjustmentsmentioning

confidence: 99%

“…6. He gives H t back to treasury, so the outstanding debt to the treasury is V t − C t since H t − C H t = 0 Time t + dt:…”

mentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement

Brigo

Francischello

Pallavicini

2019

European Journal of Operational Research

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Model Independent WWR for Regulatory CVA and for Accounting CVA and FVA

Kenyon¹,

Berrahoui

Poncet

2020

SSRN Journal

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Wrong way risk (WWR) is a consideration for regulatory capital for credit valuation adjustment (CVA). WWR is also of interest for pricing and accounting and in these cases must include funding as well as exposure and default in CVA and FVA calculation. Here we introduce a model independent approach to WWR for regulatory CVA and also for accounting CVA and FVA. This model independent approach is extremely simple: we just re-write the CVA and FVA integral expressions in terms of their components and then calibrate these components. This provides transparency between component calibration and CVA/FVA effect because there is no model interpretation in between. Including funding in WWR means that there are now two WWR terms rather than the usual one. Using a regulatory inspired calibration from MAR50 we investigate WWR effects for vanilla interest rate swaps and show that the WWR effects for FVA are significantly more material than for CVA. This model independent approach can also be used to compare any WWR model by simply calibrating to it for a portfolio and counterparty, to demonstrate the effects of the model under investigation in terms of components of CVA/FVA calculations. arXiv:2003.03403v1 [q-fin.PR]

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Neural networks for stochastic control and decision making in mathematical finance

Andersson

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As the title suggests, this thesis is devoted to machine learning algorithms for stochastic control with applications in mathematical finance. In the first two chapters, we utilize neural networks to find the optimal exercise strategies of high-dimensional American options. Moreover, we compute option values along stochastic trajectories of the underlying assets, which is crucial in modern risk management. In Chapter 3, we approximate strongly coupled FBSDEs with a sequence of neural networks. More specifically, we are concerend with high-dimensional FBSDEs stemming from stochastic optimal control problems. These equations are inherently difficult to approximate due the coupling, and most classical methods as well as modern day machine learning algorithms break down. Our approach is novel in the sense that it combines mathematical structure from the initial control problem with the associate FBSDE which is shown to be both robust and accurate for a wide range of problems. In the final chapter, we consider time-inconsistent portfolio optimization problems. In general, for time-inconsistent problems the dynamic programming principle does not hold and in turn, the global problem cannot be divided into local sub-problems. Instead, we take on a fully data driven neural network-based approach to approximate the optimal allocation strategy directly. Beyond the classical instruments stocks and bonds, we also allow the investor to buy and sell options. In this way, we increase the flexibility in shaping the terminal wealth distribution.

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CVA with Wrong-Way Risk in the Presence of Early Exercise

Cited by 5 publications

References 14 publications

Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement

Nonlinear valuation under credit, funding, and margins: Existence, uniqueness, invariance, and disentanglement

Model Independent WWR for Regulatory CVA and for Accounting CVA and FVA

Neural networks for stochastic control and decision making in mathematical finance

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