Quantitative Finance

Di Nunno, Giulia;Yurchenko-Tytarenko, Anton

doi: 10.48550/arxiv.2209.13054pmid: N/A

Abstract:We consider stochastic volatility dynamics driven by a general Hölder continuous Volterra-type noise and with unbounded drift. For these so-called SVV-models, we consider the explicit computation of quadratic hedging strategies. While the theoretical hedge is well-known in terms of the non-anticipating derivative for all square integrable claims, the fact that these models are typically non-Markovian provides is a challenge in the direct computation of conditional expectations at the core of the explicit hedging strategy. To overcome this difficulty, we propose a Markovian approximation of the model which stems from an adequate approximation of the kernel in the Volterra noise. We study the approximation of the volatility, of the prices and of the optimal mean-square hedge. We provide the corresponding error estimates. The work is completed with numerical simulations.

Acciaio, Beatrice;Backhoff, Julio;Pammer, Gudmund

doi: 10.48550/arxiv.2209.15037pmid: N/A

Abstract:In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the problems of pricing and hedging. The pricing measures here will be such that asset price processes are close to being martingales, and the hedging strategies will need to cover some additional cost. We show a quantitative version of the Fundamental Theorem of Asset Pricing and of the Super-Replication Theorem. Finally, we study robustness of the amount of arbitrage and existence of respective pricing measures, showing stability of these concepts with respect to a strong adapted Wasserstein distance.

Gong, Chen Chris;Ueckerdt, Falko;Pietzcker, Robert;Odenweller, Adrian;Schill, Wolf-Peter;Kittel, Martin;Luderer, Gunnar

doi: 10.5194/gmd-16-4977-2023pmid: N/A

Abstract:Integrated assessment models (IAMs) are a central tool for the quantitative analysis of climate change mitigation strategies. However, due to their global, cross-sectoral and centennial scope, IAMs cannot explicitly represent the spatio-temporal detail required to properly analyze the key role of variable renewable electricity (VRE) for decarbonizing the power sector and end-use electrification. In contrast, power sector models (PSMs) incorporate high spatio-temporal resolutions, but tend to have narrower scopes and shorter time horizons. To overcome these limitations, we present a novel methodology: an iterative and fully automated soft-coupling framework that combines the strengths of a IAM and a PSM. This framework uses the market values of power generation as well as the capture prices of demand in the PSM as price signals that change the capacity and power mix of the IAM. Hence, both models make endogenous investment decisions, leading to a joint solution. We apply the method to Germany in a proof-of-concept study using the IAM REMIND and the PSM DIETER, and confirm the theoretical prediction of almost-full convergence both in terms of decision variables and (shadow) prices. At the end of the iterative process, the absolute model difference between the generation shares of any generator type for any year is <5% for a simple configuration (no storage, no flexible demand), and 6-7% for a more realistic and detailed configuration (with storage and flexible demand). For the simple configuration, we mathematically show that this coupling scheme corresponds uniquely to an iterative mapping of the Lagrangians of two power sector optimization problems of different time resolutions, which can lead to a comprehensive model convergence of both decision variables and (shadow) prices. Since our approach is based on fundamental economic principles, it is applicable also to other IAM-PSM pairs.

Lu, Yutong;Reinert, Gesine;Cucuringu, Mihai

doi: 10.48550/arxiv.2209.10334pmid: N/A

Abstract:The time proximity of high-frequency trades can contain a salient signal. In this paper, we propose a method to classify every trade, based on its proximity with other trades in the market within a short period of time, into five types. By means of a suitably defined normalized order imbalance associated to each type of trade, which we denote as conditional order imbalance (COI), we investigate the price impact of the decomposed trade flows. Our empirical findings indicate strong positive correlations between contemporaneous returns and COIs. In terms of predictability, we document that associations with future returns are positive for COIs of trades which are isolated from trades of stocks other than themselves, and negative otherwise. Furthermore, trading strategies which we develop using COIs achieve conspicuous returns and Sharpe ratios, in an extensive experimental setup on a universe of 457 stocks using daily data for a period of four years.

Rizzato, Matteo;Wallart, Julien;Geissler, Christophe;Morizet, Nicolas;Boumlaik, Noureddine

doi: 10.1016/j.physa.2023.128899pmid: N/A

Abstract:The finance industry is producing an increasing amount of datasets that investment professionals can consider to be influential on the price of financial assets. These datasets were initially mainly limited to exchange data, namely price, capitalization and volume. Their coverage has now considerably expanded to include, for example, macroeconomic data, supply and demand of commodities, balance sheet data and more recently extra-financial data such as ESG scores. This broadening of the factors retained as influential constitutes a serious challenge for statistical modeling. Indeed, the instability of the correlations between these factors makes it practically impossible to identify the joint laws needed to construct scenarios. Fortunately, spectacular advances in Deep Learning field in recent years have given rise to GANs. GANs are a type of generative machine learning models that produce new data samples with the same characteristics as a training data distribution in an unsupervised way, avoiding data assumptions and human induced biases. In this work, we are exploring the use of GANs for synthetic financial scenarios generation. This pilot study is the result of a collaboration between Fujitsu and Advestis and it will be followed by a thorough exploration of the use cases that can benefit from the proposed solution. We propose a GANs-based algorithm that allows the replication of multivariate data representing several properties (including, but not limited to, price, market capitalization, ESG score, controversy score,. . .) of a set of stocks. This approach differs from examples in the financial literature, which are mainly focused on the reproduction of temporal asset price scenarios. We also propose several metrics to evaluate the quality of the data generated by the GANs. This approach is well fit for the generation of scenarios, the time direction simply arising as a subsequent (eventually conditioned) generation of data points drawn from the learned distribution. Our method will allow to simulate high dimensional scenarios (compared to $\lesssim10$ features currently employed in most recent use cases) where network complexity is reduced thanks to a wisely performed feature engineering and selection. Complete results will be presented in a forthcoming study.

van der Zwaard, T.;Grzelak, L. A.;Oosterlee, C. W.

doi: 10.1142/s0219024924500109pmid: N/A

Abstract:Wrong-Way Risk (WWR) is an important component in Funding Valuation Adjustment (FVA) modelling. Yet, the standard assumption is independence between market risks and the counterparty defaults and funding costs. This typical industrial setting is our point of departure, where we aim to assess the impact of WWR without running a full Monte Carlo simulation with all credit and funding processes. We propose to split the exposure profile into two parts: an independent and a WWR-driven part. For the former, exposures can be re-used from the standard xVA calculation. We express the second part of the exposure profile in terms of the stochastic drivers and approximate these by a common Gaussian stochastic factor. Within the affine setting, the proposed approximation is generic, is an add-on to the existing xVA calculations and provides an efficient and robust way to include WWR in FVA modelling. Case studies for an interest rate swap and a representative multi-currency portfolio of swaps illustrate that the approximation method is applicable in a practical setting. We analyze the approximation error and use the approximation to compute WWR sensitivities, which are needed for risk management. The approach is equally applicable to other metrics such as Credit Valuation Adjustment.