Quantitative Finance

To the best of our knowledge, the application of deep learning in the field of quantitative risk management is still a relatively recent phenomenon. This article presents the key notions of Deep Asset Liability Management (Deep~ALM) for a technological transformation in the management of assets and liabilities along a whole term structure. The approach has a profound impact on a wide range of applications such as optimal decision making for treasurers, optimal procurement of commodities or the optimisation of hydroelectric power plants. As a by-product, intriguing aspects of goal-based investing or Asset Liability Management (ALM) in abstract terms concerning urgent challenges of our society are expected alongside. We illustrate the potential of the approach in a stylised case.

Building the future profit and loss (P&L) distribution of a portfolio holding, among other assets, highly non-linear and path-dependent derivatives is a challenging task. We provide a simple machinery where more and more assets could be accounted for in a simple and semi-automatic fashion. We resort to a variation of the Least Square Monte Carlo algorithm where interpolation of the continuation value of the portfolio is done with a feed forward neural network. This approach has several appealing features not all of them will be fully discussed in the paper. Neural networks are extremely flexible regressors. We do not need to worry about the fact that for multi assets payoff, the exercise surface could be non connected. Neither we have to search for smart regressors. The idea is to use, regardless of the complexity of the payoff, only the underlying processes. Neural networks with many outputs can interpolate every single assets in the portfolio generated by a single Monte Carlo simulation. This is an essential feature to account for the P&L distribution of the whole portfolio when the dependence structure between the different assets is very strong like the case where one has contingent claims written on the same underlying.

In this paper, we propose a neural network-based method for CVA computations of a portfolio of derivatives. In particular, we focus on portfolios consisting of a combination of derivatives, with and without true optionality, \textit{e.g.,} a portfolio of a mix of European- and Bermudan-type derivatives. CVA is computed, with and without netting, for different levels of WWR and for different levels of credit quality of the counterparty. We show that the CVA is overestimated with up to 25\% by using the standard procedure of not adjusting the exercise strategy for the default-risk of the counterparty. For the Expected Shortfall of the CVA dynamics, the overestimation was found to be more than 100\% in some non-extreme cases.

In this paper we introduce a new technique based on high-dimensional Chebyshev Tensors that we call \emph{Orthogonal Chebyshev Sliding Technique}. We implemented this technique inside the systems of a tier-one bank, and used it to approximate Front Office pricing functions in order to reduce the substantial computational burden associated with the capital calculation as specified by FRTB IMA. In all cases, the computational burden reductions obtained were of more than 90% , while keeping high degrees of accuracy, the latter obtained as a result of the mathematical properties enjoyed by Chebyshev Tensors.

Risk measure forecast and model have been developed in order to not only provide better forecast but also preserve its (empirical) property especially coherent property. Whilst the widely used risk measure of Value-at-Risk (VaR) has shown its performance and benefit in many applications, it is in fact not a coherent risk measure. Conditional VaR (CoVaR), defined as mean of losses beyond VaR, is one of alternative risk measures that satisfies coherent property. There has been several extensions of CoVaR such as Modified CoVaR (MCoVaR) and Copula CoVaR (CCoVaR). In this paper, we propose another risk measure, called Dependent CoVaR (DCoVaR), for a target loss that depends on another random loss, including model parameter treated as random loss. It is found that our DCoVaR outperforms than both MCoVaR and CCoVaR. Numerical simulation is carried out to illustrate the proposed DCoVaR. In addition, we do an empirical study of financial returns data to compute the DCoVaR forecast for heteroscedastic process.

Forecasting the CBOE volatility index (VIX) is a highly non-linear and memory-intensive task. In this paper, we use quantum reservoir computing to forecast the VIX using S&P500 (SPX) time-series. Our reservoir is a hybrid quantum-classical system executed on IBM's 53-qubit Rochester chip. We encode the SPX values in the rotation angles and linearly combine the average spin of the six-qubit register to predict the value of VIX at the next time step. Our results demonstrate a potential application of noisy intermediate scale quantum (NISQ) devices to complex, real world applications.

Stop-loss rules are often studied in the financial literature, but the stop-loss levels are seldom constructed systematically. In many papers, and indeed in practice as well, the level of the stops is too often set arbitrarily. Guided by the overarching goal in finance to maximize expected returns given available information, we propose a natural method by which to systematically select the stop-loss threshold by analyzing the distribution of maximum drawdowns. We present results for an hourly trading strategy with two variations on the construction.

We propose a method to assess the intrinsic risk carried by a financial position X when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex duality in a Knightian setting, where a family of probability measures replaces the single reference probability and is then applied to value financial positions. Diametrically, our construction of Value\&Risk measures is based on the selection of a basket of claims to test the reliability of models. We compare a random payoff X with a given class of derivatives written on X , and use these derivatives to \textquotedblleft test\textquotedblright\ the pricing measures. We further introduce and study a general class of Value\&Risk measures R(p,X,P) that describes the additional capital that is required to make X acceptable under a probability P and given the initial price p paid to acquire X .

We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013.

Any solvency regime for financial institutions should be aligned with the fundamental objectives of regulation: protecting liability holders and securing the stability of the financial system. The first objective leads to consider surplus-invariant capital adequacy tests, i.e. tests that do not depend on the surplus of a financial institution. We provide a complete characterization of closed, convex, surplus-invariant capital adequacy tests that highlights an inherent tension between surplus-invariance and the desire to give credit for diversification. The second objective leads to requiring consistency of capital adequacy tests across jurisdictions. Of particular importance in this respect are capital adequacy tests that remain invariant under a change of numéraire. We establish an intimate link between surplus- and numéraire invariant tests.