We develop a local correlation model that uses a given correlation matrix and a generic function g.t ; mi ; mj / to compute the local correlation between any asset–asset pair .i; j / of a basket of underlyings. The arguments mi , mj are spot moneynesses. The generic function is calibrated to fit the implied volatilities of an equity index such as the DAX or EURO STOXX 50. The advantage of this approach is that we do not need to simulate the complete index basket when pricing options on a (usually small) subset of this index. The approach does not suffer from the so-called chewing gum effect of correlation models, where the local correlation depends on just the index value. We first show how to calibrate the generic function for each time step with constraints on the positive definiteness of the resulting correlation matrixes and the smoothness of g to allow for stable evaluation. We then present numerical experiments that show the impact on prices and deltas for synthetic autocallable instruments.

中文翻译：

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成对局部相关模型

我们开发了一个使用给定相关矩阵和通用函数 gt 的局部相关模型；米；mj / 计算任何资产-资产对 .i 之间的局部相关性；j / 一篮子底层证券。参数 mi , mj 是现货货币。通用函数经过校准以适应股票指数（例如 DAX 或 EURO STOXX 50）的隐含波动率。 这种方法的优点是，当对（通常很小）子集的期权定价时，我们不需要模拟完整的指数篮子该指数的。该方法不受相关模型所谓的口香糖效应的影响，其中局部相关性仅取决于指数值。我们首先展示了如何为每个时间步校准通用函数，并限制结果相关矩阵的正定性和 g 的平滑度，以实现稳定的评估。然后，我们展示了数值实验，展示了合成可自动调用工具对价格和增量的影响。