Abstract In this article we propose a new more general calibration of the Heston Stochastic-Local Volatility (HSLV) model. More precisely, the main contribution is to perform the direct calibration of the whole set of parameters at the same time instead of the usual two steps procedure. Moreover, the proposed approach allows to use exotic options to calibrate the HSLV model, thus making it more flexible and general. However, as there are no analytical formulas available to price exotic options to calibrate the model, the cost function (the HSLV pricer) involved in the calibration process must be computed using Monte Carlo methods, thus leading to a highly demanding computational problem. Therefore, we also propose efficient parallel GPU implementations of Monte Carlo techniques for the pricers. Furthermore, for solving the resulting global optimization problem, we develop customized parallel multi-CPU implementations of two of the most common stochastic metaheuristic global optimization algorithms: Differential Evolution and Simulated Annealing. A comparison between both algorithms has been made. This second level of parallelization has been carried out by the implementation of the cost function as a single GPU kernel and keeping the OpenMP parallelization for the optimization algorithm, thus leading to a hybrid multi-GPU implementation of the calibrator. All these implementations have been tested with real market data for European and barrier options in the context of foreign exchange markets.

中文翻译：

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Heston 随机局部波动率模型的新校准及其在 GPU 上的并行实现

摘要 在本文中，我们提出了一种新的更一般的 Heston 随机局部波动率 (HSLV) 模型校准方法。更准确地说，主要贡献是同时执行整套参数的直接校准，而不是通常的两步程序。此外，所提出的方法允许使用奇异选项来校准 HSLV 模型，从而使其更加灵活和通用。然而，由于没有可用的分析公式来为校准模型的奇异期权定价，校准过程中涉及的成本函数（HSLV 定价器）必须使用蒙特卡罗方法计算，从而导致计算问题要求很高。因此，我们还为定价者提出了蒙特卡罗技术的高效并行 GPU 实现。此外，为了解决由此产生的全局优化问题，我们开发了两种最常见的随机元启发式全局优化算法的定制并行多 CPU 实现：差分进化和模拟退火。已经对两种算法进行了比较。第二级并行化是通过将成本函数实现为单个 GPU 内核并保持优化算法的 OpenMP 并行化来实现的，从而导致校准器的混合多 GPU 实现。所有这些实施都经过了外汇市场背景下欧洲和障碍期权的真实市场数据的测试。差分进化和模拟退火。已经对两种算法进行了比较。第二级并行化是通过将成本函数实现为单个 GPU 内核并保持优化算法的 OpenMP 并行化来实现的，从而导致校准器的混合多 GPU 实现。所有这些实施都经过了外汇市场背景下欧洲和障碍期权的真实市场数据的测试。差分进化和模拟退火。已经对两种算法进行了比较。第二级并行化是通过将成本函数实现为单个 GPU 内核并保持优化算法的 OpenMP 并行化来实现的，从而导致校准器的混合多 GPU 实现。所有这些实施都经过了外汇市场背景下欧洲和障碍期权的真实市场数据的测试。从而导致校准器的混合多 GPU 实现。所有这些实施都经过了外汇市场背景下欧洲和障碍期权的真实市场数据的测试。从而导致校准器的混合多 GPU 实现。所有这些实施都经过了外汇市场背景下欧洲和障碍期权的真实市场数据的测试。