标题： 一种最优传输方法用于套利校正：波动率压力测试的应用 显示英文标题

标题： An Optimal Transport approach to arbitrage correction: Application to volatility Stress-Tests

摘要： 我们提出一种基于最优传输的方法，以消除有限一组期权价格中的套利机会。 该方法特别用于监管压力测试，这要求对隐含波动率曲面施加重要的局部扭曲。 由此产生的压力期权价格自然与一组签名边缘测度相关联：我们将消除套利的过程表述为在签名测度空间中相对于Wasserstein度量的鞅测度子集上的投影。 我们展示了如何将此投影问题重新表述为最优传输问题；为了数值求解，我们应用了一种熵正则化技术。 对于正则化问题，我们推导出一个强对偶公式，展示了当正则化参数趋近于零时的收敛结果，并提出了一个多重约束的Sinkhorn算法，其中每次迭代最多涉及寻找显式标量函数的根。 还证明了该算法的收敛性。 我们通过[科恩、莱辛格和王，应用数学财务，2020]的现有方法，在各种场景和测试案例中进行了比较。 显示英文摘要

摘要： We present a method based on optimal transport to remove arbitrage opportunities within a finite set of option prices. The method is notably intended for regulatory stress-tests, which impose to apply important local distortions to implied volatility surfaces. The resulting stressed option prices are naturally associated to a family of signed marginal measures: we formulate the process of removing arbitrage as a projection onto the subset of martingale measures with respect to a Wasserstein metric in the space of signed measures. We show how this projection problem can be recast as an optimal transport problem; in view of the numerical solution, we apply an entropic regularization technique. For the regularized problem, we derive a strong duality formula, show convergence results as the regularization parameter approaches zero, and formulate a multi-constrained Sinkhorn algorithm, where each iteration involves, at worse, finding the root of an explicit scalar function. The convergence of this algorithm is also established. We compare our method with the existing approach by [Cohen, Reisinger and Wang, Appl.\ Math.\ Fin.\ 2020] across various scenarios and test cases.