英文标题：
《Efficient European and American option pricing under a jump-diffusion
process》
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作者：
Marcellino Gaudenzi and Alice Spangaro and Patrizia Stucchi
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最新提交年份：
2017
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英文摘要：
When the underlying asset displays oscillations, spikes or heavy-tailed distributions, the lognormal diffusion process (for which Black and Scholes developed their momentous option pricing formula) is inadequate: in order to overcome these real world difficulties many models have been developed. Merton proposed a jump-diffusion model, where the dynamics of the price of the underlying are subject to variations due to a Brownian process and also to possible jumps, driven by a compound Poisson process. Merton\'s model admits a series solution for the European option price, and there have been a lot of attempts to obtain a discretisation of the Merton model with tree methods in order to price American or more complex options, e. g. Amin, the $O(n^3)$ procedure by Hilliard and Schwartz and the $O(n^{2.5})$ procedure by Dai et al. Here, starting from the implementation of the seven-nodes procedure by Hilliard and Schwartz, we prove theoretically that it is possible to reduce the complexity to $O(n \\ln n)$ in the European case and $O(n^2 \\ln n)$ in the American put case. These theoretical results can be obtained through suitable truncation of the lattice structure and the proofs provide closed formulas for the truncation limitations.
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中文摘要：
当标的资产显示出振荡、尖峰或重尾分布时，对数正态扩散过程（Black和Scholes为其开发了重要的期权定价公式）是不充分的：为了克服这些现实世界的困难，已经开发了许多模型。默顿提出了一个跳跃扩散模型，在该模型中，标的资产价格的动态会受到布朗过程的影响，也会受到复合泊松过程驱动的可能跳跃的影响。默顿模型为欧式期权价格提供了一个级数解，为了给美式或更复杂的期权定价，已经有很多人尝试用树方法对默顿模型进行离散化，例如Amin、Hilliard和Schwartz的$O（n^3）$程序和Dai等人的$O（n^2.5）$程序，从Hilliard和Schwartz的七节点程序的实现出发，我们从理论上证明了在欧洲情况下可以将复杂性降低到$O（n\\ln n）$，在美国put情况下可以将复杂性降低到$O（n^2\\ln n）$。通过对晶格结构进行适当的截断，可以得到这些理论结果，证明了截断限制的闭合公式。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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