﻿ SHIBOR时序数据分析：基于Levy过程模型 Analyzing of SHIBOR Time Series: Based on Levy Process Models

Finance
Vol. 08  No. 06 ( 2018 ), Article ID: 27494 , 10 pages
10.12677/FIN.2018.86030

Analyzing of SHIBOR Time Series: Based on Levy Process Models

Huijun Wen

School of Economics and Mathematics, Southwestern University of Finance and Economics, Chengdu Sichuan

Received: Oct. 17th, 2018; accepted: Nov. 6th, 2018; published: Nov. 13th, 2018

ABSTRACT

SHIBOR time series play an increasingly important role in the financial markets and related areas as the marketization of the RMB interest rate is more and more frequently advocated. Many scholars have made a number of studies on SHIBOR and the related fields. But most of them focus on the correlation between their own research fields and SHIBOR based upon regression model instead of on Levy process model and the characters of SHIBOR. This paper, from angles of real time and business time, by introducing Levy process, building multiple Levy process models and analyzing the results from the models, aims to reflect the changing trend and relevant characters of SHIBOR time series so as to enrich the research of SHIBOR time series and lay a sound foundation for the pricing of SHIBOR.

Keywords:SHIBOR, Business Time, Levy Process, Pricing of SHIBOR

SHIBOR时序数据分析：基于Levy过程模型

1. 引言

2. SHIBOR时间序列统计特征

SHIBOR时间序列有八个指标，分别为隔夜、一周、两周、一个月、三个月、六个月、九个月与年数据。为了对SHIBOR进行较好的研究，在统计分析上，我们采用了2013以来的数据，其时间序列路径如图1

Figure 1. Path of SHIBOR time series

Table 1. SHIBOR time series six major statistical indicators

Figure 2. Density function of SHIBOR

Figure 3. The distribution function of SHIBOR

3. Levy过程模型

(一) Levy过程与Levy测度介绍

Table 2. Measure and characteristic function of five kinds of Levy processes

(二) 具体模型介绍

${X}_{t}=\mu t+\sigma {W}_{t}+\underset{i=1}{\overset{{N}_{t}}{\sum }}{Y}_{i}$

$\text{E}\left[{\text{e}}^{iu{X}_{t}}\right]=\mathrm{exp}\left\{t\left(i\mu u-\frac{1}{2}{\sigma }^{2}{u}^{2}+\lambda \left({\text{e}}^{i\alpha u-\frac{1}{2}{\delta }^{2}{u}^{2}}-1\right)\right)\right\}$

$\text{E}\left[{\text{e}}^{iu{X}_{t}}\right]=\mathrm{exp}\left\{t\left[i\mu u-\frac{1}{2}{\sigma }^{2}{u}^{2}+iu\lambda \left(\frac{p}{{\eta }_{1}-iu}-\frac{1-p}{{\eta }_{2}+iu}\right)\right]\right\}$

$\text{E}\left[{\text{e}}^{iu{X}_{t}}\right]=\left\{\begin{array}{l}\mathrm{exp}\left\{t\left[i\mu u-\frac{1}{2}{\sigma }^{2}{u}^{2}-{\sigma }_{1}^{\alpha }{|u|}^{\alpha }\left(1-i\beta sign\left(u\right)\mathrm{tan}\frac{\text{π}\alpha }{2}\right)\right]\right\},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}\alpha \ne 1\\ \mathrm{exp}\left\{t\left[i\mu u-\frac{1}{2}{\sigma }^{2}{u}^{2}-{\sigma }_{1}|u|\left(1+i\beta sign\left(u\right)\frac{2}{\text{π}}\mathrm{log}|\theta |\right)\right]\right\},\text{ }\text{ }\text{if}\text{\hspace{0.17em}}\alpha =1\end{array}$

4. 实证与检验

(一) 实证参数估计

Table 3. Parameter estimation based on Merton jump process model

Table 4. Parameter estimation based on double exponential jump process model

Table 5. Parameter estimation based on normal inverse Gauss process model

Table 6. Parameter estimation based on variance gamma process model

Table 7. Parameter estimation based on α stable process

(二) 随机模拟

Figure 4. Simulation path versus real path comparison

(三) 实证检验分析

Figure 5. Analysis chart of Density function simulated sample and real SHIBOR sample

Figure 6. Analysis chart of distribution function of simulated sample and real SHIBOR sample

5. 结论

Analyzing of SHIBOR Time Series: Based on Levy Process Models[J]. 金融, 2018, 08(06): 255-264. https://doi.org/10.12677/FIN.2018.86030

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