Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the subsequent local volatility surface is never considered. In this article, we develop a deep learning approach for interpolation of European vanilla option prices which jointly yields the full surface of local volatilities. We demonstrate the modification of the loss function or the feed forward network architecture to enforce (hard constraints approach) or favor (soft constraints approach) the no-arbitrage conditions and we specify the experimental design parameters that are needed for adequate performance. A novel component is the use of the Dupire formula to enforce bounds on the local volatility associated with option prices, during the network fitting. Our methodology is benchmarked numerically on real datasets of DAX vanilla options.
Since the 2008-09 financial crisis, banks have introduced a family of XVA metrics to quantify the cost of counterparty risk and of its capital and funding implications: the credit/debt valuation adjustment (CVA and DVA), the costs of funding variation margin (FVA) and initial margin (MVA), and the capital valuation adjustment (KVA).We revisit from a wealth conservation and wealth transfer perspective at the incremental trade level the cost-of-capital XVA approach developed at the level of the balance sheet of the bank in Albanese, Crépey, Hoskinson, and Saadeddine (2019). Trade incremental XVAs reflect the wealth transfers triggered by the deals due to the incompleteness of counterparty risk. XVA-inclusive trading strategies achieve a given hurdle rate to shareholders in the conservative limit case that no new trades occur.XVAs represent a switch of paradigm in derivative management, from hedging to balance sheet optimization. This is illustrated by a review of possible applications of the XVA metrics.
Since the 2008–2009 financial crisis, banks have introduced a family of X-valuation adjustments (XVAs) to quantify the cost of counterparty risk and of its capital and funding implications. XVAs represent a switch of paradigm in derivative management, from hedging to balance sheet optimization. They reflect market inefficiencies that should be compressed as much as possible. In this work, we present a genetic algorithm applied to the compression of credit valuation adjustment (CVA), the expected cost of client defaults to a bank. The design of the algorithm is fine-tuned to the hybrid structure, both discrete and continuous parameter, of the corresponding high-dimensional and nonconvex optimization problem. To make intensive trade incremental XVA computations practical in real-time as required for XVA compression purposes, we propose an approach that circumvents portfolio revaluation at the cost of disk memory, storing the portfolio exposure of the night so that the exposure of the portfolio augmented by a new deal can be obtained at the cost of computing the exposure of the new deal only. This is illustrated by a CVA compression case study on real swap portfolios.
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