PSEUDODIFFUSIONS AND QUADRATIC TERM STRUCTURE MODELS
PSEUDODIFFUSIONS AND QUADRATIC TERM STRUCTURE MODELS
复制标题
伪扩散和二次项结构模型
DOI：
10.1111/j.1467-9965.2005.00226.x
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发表时间：
2005
影响因子：
1.6
通讯作者：
S. Levendorskii
中科院分区：
文献类型：
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作者：
S. Levendorskii
金融市场中观察到的过程的非高斯性和高斯模型相对良好的性能可以通过用 Lévy 过程代替布朗运动来协调，Lévy 密度衰减为 exp(−λ|x|) 或更快，其中 λ > 0 很大。这导致了渐近定价模型。首项 P0 是具有相同瞬时漂移和方差的高斯模型中的价格。第一个修正项取决于 3 阶以下的瞬时矩，即考虑了偏度，下一项也取决于 4 阶矩（峰度），等等。在实证研究中，可以应用渐近公式，而无需明确指定基础过程：只要假设大于 2 阶的瞬时矩相对较小就足够了。 1 阶和 2 阶矩，并使用高达 3 或 4 阶矩的经验数据。作为一种应用，解决了非高斯二次期限结构模型中的债券定价问题。对于接近到期日的期权定价，开发了一组不同的渐近公式；他们需要更详细的流程规范，尤其是其跳转部分。这些公式的主项仅取决于过程的跳跃部分，因此可以在实证研究中用于识别过程的跳跃特征。
The non‐Gaussianity of processes observed in financial markets and the relatively good performance of Gaussian models can be reconciled by replacing the Brownian motion with Lévy processes whose Lévy densities decay as exp(−λ|x|) or faster, where λ > 0 is large. This leads to asymptotic pricing models. The leading term, P0, is the price in the Gaussian model with the same instantaneous drift and variance. The first correction term depends on the instantaneous moments of order up to 3, that is, the skewness is taken into account, the next term depends on moments of order 4 (kurtosis) as well, etc. In empirical studies, the asymptotic formula can be applied without explicit specification of the underlying process: it suffices to assume that the instantaneous moments of order greater than 2 are small w.r.t. moments of order 1 and 2, and use empirical data on moments of order up to 3 or 4. As an application, the bond‐pricing problem in the non‐Gaussian quadratic term structure model is solved. For pricing of options near expiry, a different set of asymptotic formulas is developed; they require more detailed specification of the process, especially of its jump part. The leading terms of these formulas depend on the jump part of the process only, so that they can be used in empirical studies to identify the jump characteristics of the process.