Infinitesimal sensitivities, computed as derivatives of pricing functions, are often used to comp... more Infinitesimal sensitivities, computed as derivatives of pricing functions, are often used to compute hedge ratios for high frequency rebalancing strategies executed by front desk trading operations. However, for the purpose of risk calculations requiring a 2-week VaR metric with shocks of size typical of stress periods, infinitesimal sensitivities are arguably unfit for purpose. In this article, we propose to quantify a metric for Risk-Not-In-VAR (RniVAR) by computing upper bounds on the errors in the sensitivities expansion. We find that regression based sensitivities can be substantially compressed and made more robust by means of Krylov regularisation. They also have a better quality P\&L explain than infinitesimal sensitivities computed by taking infinitesimal derivatives. There is a trade-off between compression ratios for regularised sensitivities and the size of RniVAR. The latter is added as a conservative adjustment to the IM formula to make it consistent with back-testing ...
Close-coupling in quantum systems induces cascade transitions that are not captured by simple per... more Close-coupling in quantum systems induces cascade transitions that are not captured by simple perturbation theories and hence more relevant and complex methods are needed. However, the analytic tractability of the latter is limited to just a few highly stylized models, e.g. equidistant infinite systems. Showing that properly adjusted key modeling parameters enable an extension of analytic solutions across more realistic cases (e.g. non-uniform level spacing and finite and asymmetric boundary conditions) arising in various experimental set-ups. Also demonstrating that the Fokker-Planck approach applied to probability amplitudes rather than to probabilities themselves – the latter being a traditional kinetics approach – produces coarse-grained amplitudes “smoothed” over the fine structure of an exact solution and driven by lower order terms in the generating function. Models and results presented here naturally overlap with algorithms of Quantum Walks related to quantum computing stud...
Infinitesimal sensitivities, computed as derivatives of pricing functions, are often used to comp... more Infinitesimal sensitivities, computed as derivatives of pricing functions, are often used to compute hedge ratios for high frequency rebalancing strategies executed by front desk trading operations. However, for the purpose of risk calculations requiring a 2-week VaR metric with shocks of size typical of stress periods, infinitesimal sensitivities are arguably unfit for purpose. In this article, we propose to quantify a metric for Risk-Not-In-VAR (RniVAR) by computing upper bounds on the errors in the sensitivities expansion. We find that regression based sensitivities can be substantially compressed and made more robust by means of Krylov regularisation. They also have a better quality P\&L explain than infinitesimal sensitivities computed by taking infinitesimal derivatives. There is a trade-off between compression ratios for regularised sensitivities and the size of RniVAR. The latter is added as a conservative adjustment to the IM formula to make it consistent with back-testing benchmarks, while regularisation de-noises dynamic rebalancing by avoiding over-fitting and makes hedging more robust.
The ongoing controversy about whether or not the FVA and KVA should be an adjustment to fair valu... more The ongoing controversy about whether or not the FVA and KVA should be an adjustment to fair valuation originates from the attempt to shoehorn metrics quantifying market incompleteness into the traditional valuation paradigm based on complete markets. After reviewing the concept of fair valuation, we introduce the concept of prudent valuation in incomplete markets and review what went lost in translation in the FVA/KVA debate.
Practical aspects of single- and doubled-random WWR models for CVA are reviewed. Discussing the s... more Practical aspects of single- and doubled-random WWR models for CVA are reviewed. Discussing the single-random WWR model conditioning the exposure on the random default time and suggesting modifications which help a) isolate WWR effect from RWR, and b) specify expectations about WWR trends with changing default rate. Further, overviewing the general CVA dependence on the default rate via developing clarifying approximations and analyzing conditions when CVA declines with growing default rate. Demonstrating then that although technically double-random WWR can reduce CVA in that area, the needed parameters are long maturities combined with atypically high default rates so that the effect is rather of an academic than practical interest.
Developing analytic techniques for potential future exposure (PFE) of a general type transaction ... more Developing analytic techniques for potential future exposure (PFE) of a general type transaction and applying it to credit value adjustment (CVA) and wrong way risk (WWR). The solutions provide a transparent and computationally friendly analytic formulas and good quality analytic estimates of CVA and WWR prior to conducting systematic simulations.
Comparing alternatives for a simultaneous incorporation of intra and inter correlations into the ... more Comparing alternatives for a simultaneous incorporation of intra and inter correlations into the credit portfolio loss distribution within the asymptotic single risk factor (ASRF) model and showing that the resulting distribution depends on the type of a dominant correlation: whether it is of intra d-d/lgd-lgd or inter d-lgd type. Showing that the classic Vasicek distribution (derived originally for intra d-d correlations only), modified to embrace both intra and inter correlation types by properly constructing composite mean and correlation parameters, offers an analytic solution which covers an entire range of correlations and is easy to use as opposed to a more formal approach of a bivariate joint default probability density which requires numerical averaging over the underlying latent factors and applies only when intra correlations dominate.
Speedy developments in Quantum Technologies and Computing with far reaching potential application... more Speedy developments in Quantum Technologies and Computing with far reaching potential applications in non-traditional fields of finance, bio-medical, biochemistry , etc., make it imperative that fundamentals of Quantum Technologies are well explained and understood. Meanwhile, paradigms of so-called quantum non-locality, wave function (WF) "collapse", "Schrödinger cat" and some other historically popular misconceptions continue to stir controversies, feed mysteries around quantum phenomena and confuse prospective users. In this regard we argue that above misinterpretations stem essentially from classically minded and experimentally unverifiable perceptions, recasting and fitting the Principle of Superposition and key experimental details into classical terms and logic. Further, we revisit key components of general quantum measurement protocols-analyzers and detectors-and explain in this context paradoxes of WF collapse and Schrödinger cat. Then to demystify and clarify the concept of entanglement in multi-component systems (comprised of photons, electrons, atoms and even small macro-objects) and longdistance correlations, we remind that quantum measurements routinely reveal correlations mandated by conservation laws in each individual realization. Remarkably, this "correlation-by-initial conditions" (in addition to traditional "correlation-byinteractions") is by no means an exclusive quantum feature, but also has it analogiesin simplified form though-in Classical Mechanics (CM). However, an appearance and understanding of those correlations in Quantum Mechanics (QM) is governed by the wave-particle duality, forgetting of which leads to endless line of paradoxes. We keep reiterating that QM is not a dynamical theory in the same sense the CM is-it is a statistical theory, as established in 1926 by Born's postulate. That is, while QM enforces conservations laws and ensuing correlations in each individual outcome, it does not indicate how exactly a specific outcome is selected. This selection remains fundamentally random and represents true randomness of QM, the latter being a statistical paradigm with a WF standing for a complex-valued amplitude of a distribution function. We note in conclusion that, although a quantum logic is admittedly a challenge for classical imagination, mechanistically complementing quantum foundations by classically minded expectations trivializes true quantum effects to primitive classical constructions and gives rise to a mysteriously omnipresent non-locality.
Infinitesimal sensitivities, computed as derivatives of pricing functions, are often used to comp... more Infinitesimal sensitivities, computed as derivatives of pricing functions, are often used to compute hedge ratios for high frequency rebalancing strategies executed by front desk trading operations. However, for the purpose of risk calculations requiring a 2-week VaR metric with shocks of size typical of stress periods, infinitesimal sensitivities are arguably unfit for purpose. In this article, we propose to quantify a metric for Risk-Not-In-VAR (RniVAR) by computing upper bounds on the errors in the sensitivities expansion. We find that regression based sensitivities can be substantially compressed and made more robust by means of Krylov regularisation. They also have a better quality P\&L explain than infinitesimal sensitivities computed by taking infinitesimal derivatives. There is a trade-off between compression ratios for regularised sensitivities and the size of RniVAR. The latter is added as a conservative adjustment to the IM formula to make it consistent with back-testing ...
Close-coupling in quantum systems induces cascade transitions that are not captured by simple per... more Close-coupling in quantum systems induces cascade transitions that are not captured by simple perturbation theories and hence more relevant and complex methods are needed. However, the analytic tractability of the latter is limited to just a few highly stylized models, e.g. equidistant infinite systems. Showing that properly adjusted key modeling parameters enable an extension of analytic solutions across more realistic cases (e.g. non-uniform level spacing and finite and asymmetric boundary conditions) arising in various experimental set-ups. Also demonstrating that the Fokker-Planck approach applied to probability amplitudes rather than to probabilities themselves – the latter being a traditional kinetics approach – produces coarse-grained amplitudes “smoothed” over the fine structure of an exact solution and driven by lower order terms in the generating function. Models and results presented here naturally overlap with algorithms of Quantum Walks related to quantum computing stud...
Infinitesimal sensitivities, computed as derivatives of pricing functions, are often used to comp... more Infinitesimal sensitivities, computed as derivatives of pricing functions, are often used to compute hedge ratios for high frequency rebalancing strategies executed by front desk trading operations. However, for the purpose of risk calculations requiring a 2-week VaR metric with shocks of size typical of stress periods, infinitesimal sensitivities are arguably unfit for purpose. In this article, we propose to quantify a metric for Risk-Not-In-VAR (RniVAR) by computing upper bounds on the errors in the sensitivities expansion. We find that regression based sensitivities can be substantially compressed and made more robust by means of Krylov regularisation. They also have a better quality P\&L explain than infinitesimal sensitivities computed by taking infinitesimal derivatives. There is a trade-off between compression ratios for regularised sensitivities and the size of RniVAR. The latter is added as a conservative adjustment to the IM formula to make it consistent with back-testing benchmarks, while regularisation de-noises dynamic rebalancing by avoiding over-fitting and makes hedging more robust.
The ongoing controversy about whether or not the FVA and KVA should be an adjustment to fair valu... more The ongoing controversy about whether or not the FVA and KVA should be an adjustment to fair valuation originates from the attempt to shoehorn metrics quantifying market incompleteness into the traditional valuation paradigm based on complete markets. After reviewing the concept of fair valuation, we introduce the concept of prudent valuation in incomplete markets and review what went lost in translation in the FVA/KVA debate.
Practical aspects of single- and doubled-random WWR models for CVA are reviewed. Discussing the s... more Practical aspects of single- and doubled-random WWR models for CVA are reviewed. Discussing the single-random WWR model conditioning the exposure on the random default time and suggesting modifications which help a) isolate WWR effect from RWR, and b) specify expectations about WWR trends with changing default rate. Further, overviewing the general CVA dependence on the default rate via developing clarifying approximations and analyzing conditions when CVA declines with growing default rate. Demonstrating then that although technically double-random WWR can reduce CVA in that area, the needed parameters are long maturities combined with atypically high default rates so that the effect is rather of an academic than practical interest.
Developing analytic techniques for potential future exposure (PFE) of a general type transaction ... more Developing analytic techniques for potential future exposure (PFE) of a general type transaction and applying it to credit value adjustment (CVA) and wrong way risk (WWR). The solutions provide a transparent and computationally friendly analytic formulas and good quality analytic estimates of CVA and WWR prior to conducting systematic simulations.
Comparing alternatives for a simultaneous incorporation of intra and inter correlations into the ... more Comparing alternatives for a simultaneous incorporation of intra and inter correlations into the credit portfolio loss distribution within the asymptotic single risk factor (ASRF) model and showing that the resulting distribution depends on the type of a dominant correlation: whether it is of intra d-d/lgd-lgd or inter d-lgd type. Showing that the classic Vasicek distribution (derived originally for intra d-d correlations only), modified to embrace both intra and inter correlation types by properly constructing composite mean and correlation parameters, offers an analytic solution which covers an entire range of correlations and is easy to use as opposed to a more formal approach of a bivariate joint default probability density which requires numerical averaging over the underlying latent factors and applies only when intra correlations dominate.
Speedy developments in Quantum Technologies and Computing with far reaching potential application... more Speedy developments in Quantum Technologies and Computing with far reaching potential applications in non-traditional fields of finance, bio-medical, biochemistry , etc., make it imperative that fundamentals of Quantum Technologies are well explained and understood. Meanwhile, paradigms of so-called quantum non-locality, wave function (WF) "collapse", "Schrödinger cat" and some other historically popular misconceptions continue to stir controversies, feed mysteries around quantum phenomena and confuse prospective users. In this regard we argue that above misinterpretations stem essentially from classically minded and experimentally unverifiable perceptions, recasting and fitting the Principle of Superposition and key experimental details into classical terms and logic. Further, we revisit key components of general quantum measurement protocols-analyzers and detectors-and explain in this context paradoxes of WF collapse and Schrödinger cat. Then to demystify and clarify the concept of entanglement in multi-component systems (comprised of photons, electrons, atoms and even small macro-objects) and longdistance correlations, we remind that quantum measurements routinely reveal correlations mandated by conservation laws in each individual realization. Remarkably, this "correlation-by-initial conditions" (in addition to traditional "correlation-byinteractions") is by no means an exclusive quantum feature, but also has it analogiesin simplified form though-in Classical Mechanics (CM). However, an appearance and understanding of those correlations in Quantum Mechanics (QM) is governed by the wave-particle duality, forgetting of which leads to endless line of paradoxes. We keep reiterating that QM is not a dynamical theory in the same sense the CM is-it is a statistical theory, as established in 1926 by Born's postulate. That is, while QM enforces conservations laws and ensuing correlations in each individual outcome, it does not indicate how exactly a specific outcome is selected. This selection remains fundamentally random and represents true randomness of QM, the latter being a statistical paradigm with a WF standing for a complex-valued amplitude of a distribution function. We note in conclusion that, although a quantum logic is admittedly a challenge for classical imagination, mechanistically complementing quantum foundations by classically minded expectations trivializes true quantum effects to primitive classical constructions and gives rise to a mysteriously omnipresent non-locality.
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