The QUAD method is a fast, flexible numerical pricing technique, widely applicable to many option types in its QUAD I and QUAD II versions where the underlying process has a closed-form density function or characteristic function. In its most advanced version, QUAD III, sacrificing only a little speed, it retains all the flexibility and applicability of earlier versions while covering an even greater range of underlying processes through use of approximations of the density functions. Here, we show how cases without suitable approximations can be handled by using finite difference methods for (only) that part of the calculation. We illustrate with the no arbitrage SABR model for the underlying. TOPICS:Derivatives, options Key Findings • Option pricing techniques under the umbrella term QUAD are the fastest generally applicable and flexible numerical methods we have for derivatives pricing. • Cases where there is no transition density function or characteristic function can be solved by using an approximation of the particular density function. However, in this article, an alternative approach is demonstrated, substituting finite difference calculations for the approximation. • The no-arbitrage SABR model is used as an example, since it is of special interest to practitioners.

中文翻译：

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通过使用有限差分计算过渡密度来扩大QUAD衍生产品定价的基础范围（针对无套利SABR模型演示）

QUAD方法是一种快速，灵活的数字定价技术，可广泛应用于其QUAD I和QUAD II版本中的许多期权类型，其中基础过程具有封闭形式的密度函数或特征函数。在其最先进的版本QUAD III中，仅牺牲了一点速度，它保留了早期版本的所有灵活性和适用性，同时通过使用密度函数的近似涵盖了更大范围的基础过程。在这里，我们展示了如何通过使用有限差分方法（仅）用于那部分计算来处理没有合适近似值的情况。我们用底层的无套利SABR模型进行说明。主题：衍生物，期权的主要发现•QUAD术语下的期权定价技术是衍生工具定价中最快的普遍适用且灵活的数值方法。•没有过渡密度函数或特征函数的情况可以通过使用特定密度函数的近似值来解决。但是，在本文中，展示了一种替代方法，用有限差分计算替代近似值。•以无套利SABR模型为例，因为它对从业人员特别感兴趣。用有限差分计算代替近似值。•以无套利SABR模型为例，因为它对从业人员特别感兴趣。用有限差分计算代替近似值。•以无套利SABR模型为例，因为它对从业人员特别感兴趣。