Regression Sensitivities for Initial Margin Calculations

Procyclicality of CCP Margin Models: Systemic Problems Need Systemic Approaches

Deep MVA: Deep Learning for Margin Valuation Adjustment of Callable Products

A bank’s capital charge computation is a widely discussed topic with new approaches emerging continuously. Each bank computes this figure using internal methodologies in order to reflect its capital adequacy; however, a more homogeneous model is recommended by the Basel committee to enable judging the situation of these financial institutions and relating different banks among each other.In this paper, we compare different numerical and econometric models to the Sensitivity Based Approach (SBA) implemented by the Basel Committee on Banking Supervision (BCBS) under Basel III in its December 2014 (rev. March 2015) publication in order to compute the capital charge in the trading book. We study the influence of having several currencies and maturities within the portfolio and try to define the time horizon and confidence level implied by Basel’s III approach through an application on bonds portfolios.By implementing several approaches, we are able to find equivalent VaRs to the one computed by the SBA on a pre-defined confidence level (97.5%). However, the time horizon differs according to the chosen methodology and ranges from 1 month up to 1 year.

The introduction of mandatory margining for non-cleared derivatives portfolios has major implications for the pricing and risk measurement of over-the-counter (OTC) derivatives. In particular, a model for estimating future initial margin requirements is necessary to enable the calculation of relevant pricing adjustments, net counterparty credit exposures and credit capital requirements. Existing literature on the topic suggests a model that makes use of regression techniques, but little detail is available on the predictive quality of these models within a Monte Carlo simulation framework. We review these regression-based initial margin models in detail and compare their output against the actual margin requirements measured by the International Swaps and Derivatives Association standard initial margin model (ISDA SIMM) methodology. We observe that the models generally perform well for single trades but show some degradation for larger diversified portfolios. We investigate potential extensions and improvements to the model, along with examining some additional ‘conservatism’ features that may have application in the context of credit exposure measurement. The initial margin modelling approaches discussed here are similarly applicable to centrally cleared or exchange-traded portfolios.

An Investigation into the Procyclicality of Risk-Based Initial Margin Models

We characterize the behavior of the Rough Heston model introduced by Jaisson and Rosenbaum (2016, Ann. Appl. Probab., 26, 2860–2882) in the small‐time, large‐time, and (i.e., ) limits. We show that the short‐maturity smile scales in qualitatively the same way as a general rough stochastic volatility model , and the rate function is equal to the Fenchel–Legendre transform of a simple transformation of the solution to the same Volterra integral equation (VIE) that appears in El Euch and Rosenbaum (2019, Math. Financ., 29, 3–38), but with the drift and mean reversion terms removed. The solution to this VIE satisfies a space–time scaling property which means we only need to solve this equation for the moment values of and so the rate function can be efficiently computed using an Adams scheme or a power series, and we compute a power series in the log‐moneyness variable for the asymptotic implied volatility which yields tractable expressions for the implied vol skew and convexity which is useful for calibration purposes. We later derive a formal saddle point approximation for call options in the Forde and Zhang (2017) large deviations regime which goes to higher order than previous works for rough models. Our higher‐order expansion captures the effect of both drift terms, and at leading order is of qualitatively the same form as the higher‐order expansion for a general model which appears in Friz et al. (2018, Math. Financ., 28, 962–988). The limiting asymptotic smile in the large‐maturity regime is obtained via a stability analysis of the fixed points of the VIE, and is the same as for the standard Heston model in Forde and Jacquier (2011, Finance Stoch., 15, 755–780). Finally, using Lévy's convergence theorem, we show that the log stock price tends weakly to a nonsymmetric random variable as (i.e., ) whose moment generating function (MGF) is also the solution to the Rough Heston VIE with , and we show that tends weakly to a nonsymmetric random variable as , which leads to a nonflat nonsymmetric asymptotic smile in the Edgeworth regime, where the log‐moneyness as , and we compute this asymptotic smile numerically. We also show that the third moment of the log stock price tends to a finite constant as (in contrast to the Rough Bergomi model discussed in Forde et al. (2020, Preprint) where the skew flattens or blows up) and the process converges on pathspace to a random tempered distribution which has the same law as the hyper‐rough Heston model, discussed in Jusselin and Rosenbaum (2020, Math. Finance, 30, 1309–1336) and Abi Jaber (2019, Ann. Appl. Probab., 29, 3155–3200).

A correction for the vertical gradient of air density has been incorporated into a skewed probability density function formulation for turbulence in the convective boundary layer. The related drift term for Lagrangian stochastic dispersion modelling has been derived based on the well-mixed condition. Furthermore, the formulation has been extended to include unsteady turbulence statistics and the related additional component of the drift term obtained. These formulations are an extension of the drift formulation reported by Luhar et al. (Atmos Environ 30:1407–1418, 1996) following the well-mixed condition proposed by Thomson (J Fluid Mech 180:529–556, 1987). Comprehensive tests were carried out to validate the formulations including consistency between forward and backward simulations and preservation of a well-mixed state with unsteady conditions. The stationary state CBL drift term with density correction was incorporated into the FLEXPART and FLEXPART-WRF Lagrangian models, and included the use of an ad hoc transition function that modulates the third moment of the vertical velocity based on stability parameters. Due to the current implementation of the FLEXPART models, only a steady-state horizontally homogeneous drift term could be included. To avoid numerical instability, in the presence of non-stationary and horizontally inhomogeneous conditions, a re-initialization procedure for particle velocity was used. The criteria for re-initialization and resulting errors were assessed for the case of non-stationary conditions by comparing a reference numerical solution in simplified unsteady conditions, obtained using the non-stationary drift term, and a solution based on the steady drift with re-initialization. Two examples of “real-world” numerical simulations were performed under different convective conditions to demonstrate the effect of the vertical gradient in density on the particle dispersion in the CBL.

CCP Clearing Demystified

Nonlinear breathing crack identification from time-domain sensitivity analysis

Asymptotic Approximations to CEV and SABR Models

Features of dynamic response sensitivity and its application in damage detection

This paper presents a stable method for the identification of sources located on the separation interface of two homogeneous media (where one of them is contained by the other one), from measurement yielded by those sources on the exterior boundary of the media. This is an ill-posed problem because numerical instability is presented, i.e., minimal errors in the measurement can result in significant changes in the solution. To obtain the proposed stable method the identification problem is categorized into three subproblems, two of which present numerical instability and regularization methods must be applied to obtain their solution in a stable form. To manage the numerical instability due to the ill-posedness of these subproblems, the Tikhonov regularization and sequential smoothing methods are used. We illustrate this methodology in a circular and irregular region to demonstrate the feasibility of the proposed method, which yields convergent and stable solutions for input data with and without noise.

—Numerical instability is an inherent issue with power system state estimation, and much effort has been made to overcome this issue using numerical techniques to ensure stability. This article proposes a regularization-based method for solving ill-conditioned hybrid state-estimation problems in the presence of equality constraints. The iterative linear state-estimation problem is solved by using Tikhonov regularization. The trade-off between the residual norm and the regularized norm is controlled by the regularization parameter in the regularization method. The regularization method employs an L-curve criterion for optimal selection of the regularization parameter. At the post-estimation stage, the correction in voltage phasor at the zero-injection bus is applied using Kirchhoff's current law. The proposed method is analyzed and tested for IEEE 14- and 118-bus test systems, as well as for a 13-bus ill-conditioned system.

Laser peen forming (LPF) is a novel flexible forming process with remarkable advantages in complex shape forming. The distributed process planning model, which applies eigen-moment as the intermediate design variable, is an effective way to realize the process planning for complex shape forming. Due to the immaturity of the model, numerical instabilities such as checkerboards and intermediate densities commonly occurring in process planning. Therefore, it is difficult to apply the planning results as a forming scheme directly. This study utilizes the perimeter constraint method, re-drives the process planning model's mathematical expression to realize the aggregation control of the eigen-moment field. Effects of perimeter constraint and Tikhonov regularization term are verified and compared through the numerical method. Results show that perimeter constraint is more effective in preventing numerical instabilities. Then the improved model is applied to the LPF process planning of cylinder, saddle, and wave surface. LPF experiments are carried out based on the process planning results. Experimental surfaces are measured and compared with objective surfaces to verified the improved model. Because there still exists a specific error between the experimental surfaces and the objective surfaces. Reasons for the error are analyzed and discussed, and methods to improve the precision of LPF technology are further proposed.

NUMBER of methods have been developed for damage detection in the last two decades. Many of the methods are based on the observation of dynamic behavior of a structure (Doebling et al. [1], Brincker et al. [2], Maeck and DeRoeck [3]), among which the sensitivity approach via a model-updating technique is commonly accepted and applied extensively in the engineering industry because of its clear mathematical background andquantitativeindications.However,thistypeofmethodisweakat accommodating the influence of measurement errors, leading to illconditioned problems, as demonstrated by Friswell et al. [4] and Humar et al. [5]. This shortcoming means that the existence and uniqueness of the solution is not ensured and numerical instability is likely to take place in the course of the solution process [6,7]. Investigations have since been conducted to deal with the illconditioned problems in model updating. Hansen [8,9] and Vogel [10] proposed regularization methods for obtaining a solution of the inverse problem. It is recognized in regularization theory that the conventional output error, which is usually the vector of differences between thecomputedandmeasuredresponses,canbemadeunrealistically small if the process of damage identification is allowed to behave badly, such that the variable has arbitrarily large deviations from the true set of parameter change, or there may be infinite sets of ill-posed solutions. A stable solution scheme can be achieved by imposing certain constraints in the form of added penalty terms with adjustable weighting parameters based on posterior knowledge. Recently,TiturusandFriswell[11]presentedthesensitivity-based model-updating method with an additional regularization criterion and computed the solutions based on the generalized singular value decomposition.Specificfeaturesoftheparameterandresponsepaths were explored when the regularization parameter varies. The four different types of spaces that arise in the solution were discussed, together with the characteristics of the families of the regularized solution. Weber et al. [12] applied the Tikhonov regularization and truncated singular value decomposition consistently to a nonlinear updating problem. Line-search and stopping criteria known from numericaloptimizationwereadaptedtotheregularizedproblem.The optimal regularization parameter was determined by generalized cross-validation. From experiences gained in model updating with laboratory test structures, the authors found that Tikhonov regularization can give the optimal solution when there is no noise or very small noise in the measurement. But in the updating procedure for a nonlinear inverse problem with the inclusion of noise and model error, the signal-tonoise ratio is getting smaller [13,14] with each iteration, and the solution obtained from a poor regularization parameter is usually unacceptable. The algorithm does not accurately converge, and the results depend strongly on the convergence criteria and tolerances. In this paper, two techniques are proposed in a new regularization method for the identification of local damages in a structure. One technique proposed a new side condition that classified the elements aspossiblydamagedandundamagedelements,whichwillbetreated differently later. The other technique restricts the range of variation of the regularization parameter, such that the regularization solution will be in a realistic range, and the correct optimal point from the curvature of the L-curve is consistently chosen to ensure a continuousconvergingprocess.Bothtechniquesmakefulluseofthe information from results obtained in previous iteration steps. A plane frame structure is studied with two damaged elements and different levels of noise and model errors to illustrate the application of the proposed method. Numerical results show that the proposed consistent regularization method is very effective at improving the results in the inverse problem with ill-conditioning, compared with the conventional Tikhonov regularization.