Pseudo-Diffusions and Quadratic Term Structure Models
Pseudo-Diffusions and Quadratic Term Structure Models
复制标题
伪扩散和二次项结构模型
DOI：
10.2139/ssrn.520044
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发表时间：
2002
期刊：
影响因子：
--
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的相对良好的性能可以通过用Levy过程代替布朗运动来协调，Levy过程的Levy密度随着exp（-λ）衰减|X|）或更快，其中lambda>0很大。这导致了渐近定价模型。首项P0是高斯模型中具有相同瞬时漂移和方差的价格。第一个校正项取决于瞬时的时刻，以便三，也就是说，考虑到偏度，下一项取决于时刻的顺序四（峰度），以及等在实证研究中，渐近公式可以应用没有明确的规范的基本过程：它足以假设，瞬时时刻的顺序大于两个小w.r.t.矩的顺序一和二，并使用经验数据的时刻顺序高达三或四。作为应用，解决了非高斯二次期限结构模型下的债券定价问题。对于临近到期的期权定价，我们给出了一组不同的渐近公式;它们需要更详细的过程说明，特别是其跳跃部分。这些公式的首项仅依赖于过程的跳跃部分，因此可以用于实证研究，以确定过程的跳跃特征。
The non-gaussianity of processes observed in financial markets and relatively good performance of gaussian models can be reconciled by replacing the Brownian motion with Levy processes whose Levy densities decay as exp(-lambda|x|) or faster, where lambda>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 three, that is, the skewness is taken into account, the next term depends on moments of order four (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 two are small w.r.t. moments of order one and two, and use empirical data on moments of order up to three or four. 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 depends 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.