Utilizing frame duality and a FFT-based implementation of density projection we develop a novel and efficient transform method to price Asian options for very general asset dynamics, including regime switching Lévy processes and other jump diffusions as well as stochastic volatility models with jumps. The method combines continuous-time Markov chain approximation, with Fourier pricing techniques. In particular, our method encompasses Heston, Hull-White, Stein-Stein, 3/2 model as well as recently proposed Jacobi, $$\alpha $$ α -Hypergeometric, and 4/2 models, for virtually any type of jump amplitude distribution in the return process. This framework thus provides a ‘ unified ’ approach to pricing Asian options in stochastic jump diffusion models and is readily extended to alternative exotic contracts. We also derive a characteristic function recursion by generalizing the Carverhill-Clewlow factorization which enables the application of transform methods in general. Numerical results are provided to illustrate the effectiveness of the method. Various extensions of this method have since been developed, including the pricing of barrier, American, and realized variance derivatives.

中文翻译：

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在制度转换跳跃扩散和随机波动率模型下的有效亚洲期权定价

利用帧对偶和基于FFT的密度投影实现方法，我们开发了一种新颖而有效的变换方法，可以为非常一般的资产动力学定价亚洲期权，包括政权转换Lévy过程和其他跳跃扩散以及具有跳跃的随机波动率模型。该方法将连续时间马尔可夫链逼近与傅立叶定价技术结合在一起。特别地，我们的方法包括Heston，Hull-White，Stein-Stein，3/2模型以及最近提出的Jacobi模型，$ \ alpha $$α-超几何和4/2模型，几乎适用于任何类型的跳跃幅度退货过程中的分配。因此，该框架为随机跳动扩散模型中的亚洲期权定价提供了一种“统一”的方法，并且很容易扩展到另类的异国合约。我们还通过推广Carverhill-Clewlow因式分解来推导特征函数递归，这通常可以应用变换方法。数值结果表明了该方法的有效性。此后，已经开发了此方法的各种扩展，包括障碍，美国和已实现方差衍生工具的定价。