期货套期保值决策理论研究及其应用

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3.0 赵德峰 2024-11-19 4 4 2MB 144 页 15积分

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摘要

如何利用期货套期保值规避现货市场的风险不仅是一个重要的实际问题，也

是一个重要的学术问题。考虑到对这一问题的深入研究应兼顾套期保值者不同的

投资理念、不同的投资目标以及对风险不同的厌恶水平等因素，本文围绕套期保

值优化策略如何确定这个中心问题，从不同侧面分别构建了若干符合不同套期保

值者心理感受的套期保值优化策略理论模型，求出了每种情形下的最优套期保值

比，取得了一系列具有创新性的成果。本文从不同侧面所构建的模型弥补了以往

在套期保值问题研究中缺少考虑套期保值者目的多样性等因素方面存在的不足，

解决了原有模型计算结果的单一与笼统等问题，在一定程度上实现了为不同套期

保值者提供多元化、具体化的最优套期保值策略的目的。特别是我们将 VaR、CVaR

以及 LPMs 应用到套期保值问题中，由此求出的确定最优套期保值比的公式更为

灵活也更贴近实际。本文的主要研究成果如下：

1、在以往对套期保值问题的研究中仅将组合期望收益率大于零作为目标函数

的约束条件，这并不符合一些套期保值者的真实心理，为了克服这一缺陷，本文

引入目标收益率作为判别套期保值行为盈亏的界线(目标收益率是一个任意实

数)，构建了基于改进的收益率与风险比率相对数最大化的期货套期保值优化决策

模型，以单位风险下组合期望收益率大于目标收益率的概率尽可能大为目的，从

理论上推导和分析了空头和多头最优套期保值比率，解决了原有收益率与风险比

率套期保值模型计算结果的单一与笼统等问题，在一定程度上实现了为不同套期

保值者提供“多元化”、“具体化”的最优套期保值策略的目的，同时为利用期货

市场转移现货市场价格波动风险的套期保值者或企业提供一定的理论依据，帮助

从事期货套期保值的现货生产者和加工企业等做出更符合实际的决策。

2、基于 VaR 和CVaR 最小的期货套期保值比的优化原理，构建了以 VaR 和

CVaR 为目标函数的期货套期保值优化决策模型，综合考虑套期保值者的期望收益

率和风险偏好，解决了现有研究忽略套期保值者期望收益率和风险偏好参数人为

设定的不足，使期货合约的选择直接反映套期保值者的风险承受能力；不管利用

VaR 还是利用 CVaR 来控制风险限额，都能找到符合条件的任一给定置信水平下的

空头和多头最优套期保值比。特别地，利用 CVaR 来控制下方风险，可以实现“双

限”监管，不易遭受不法操作与篡改，在期货最优套期保值比确定问题上具有一

定的可靠性和稳定性。

3、从理论上分析研究了基于下偏矩(LPMs)的套期保值优化模型，给出了计算

空头和多头最优套期保值比的理论原则以及最优套期保值比对目标收益率以及阶

数敏感度的分析。在假设套期保值资产组合收益率服从正态分布的前提下，得到

了不同目标收益率以及风险厌恶下计算最优套期保值比的表达式。利用衡量套期

保值行为绩效的公式，结合具体实例对套期保值行为进行了评价。这部分的研究

成果为下偏矩在套期保值问题中更好的应用提供了理论依据。

4、为改进 CARA 均值-方差模型不能体现风险易变性方面的不足，提出了

CRRA 均值-风险效用函数最大化模型。该类模型将收益与风险进行权衡，使得收

益较大的同时风险达到最小，解决了风险最小化模型中忽略收益的不足，符合一

些经济主体的心理感受，并且此类模型由常数相对风险厌恶系数



体现风险的易

变性，为套期保值的优化决策提供了科学的方法，同时提高了模型的精确性，使

得套期保值决策分析更为适用更为灵活方便。

5、在提出 CARA 均值-方差

( , )V

 

模型存在不足的基础上，提出了改进的

CRRA 均值-方差

( , )V

 

模型以及 CRRA 均值-标准差

( , )V

 

模型，以效用函数

最大化为策略计算出了空头和多头最优套期保值比。CRRA 均值-标准差效用函数

可以针对不同的风险厌恶系数求出不同策略下的最优套期保值比，计算公式简单

可靠，具有一定的可行性。

6、构建了 CRRA 均值-LPMs

( , )V LPMs



效用最大化模型，将期望收益率考

虑到模型中，弥补了最小 LPMs 模型忽略收益率的缺陷，同时利用 LPMs 在计量风

险上的优势，可以灵活的计算出具有不同目标收益率的空头和多头最优套期保值

比，具有很强的经济适用性，使得最优套期保值比的确定更加精确更加灵活了。

关键词：期货套期保值最优套期保值比下方风险 VaR CVaR

下偏矩 PLMs 风险厌恶效用最大化

ABSTRACT

It is not only an important realistic problem but also a significant academic issue

how to use hedging with futures contracts to evade risk of the spot markets. Considering

that the thorough study for this problem should take account of hedgers’ different

investment ideas, different aims and different risk aversion and so on, in this paper we

focus on the problem how to confirm hedge optimization strategy, and from different

respects we set up a number of hedge optimization strategy models which accord with

the sense of various hedgers, and the optimal hedge ratios are obtained in the every case,

then some creative works are achieved. These models make up the deficiencies of

overlooking hedgers’ varied aims and others respects in the previous literatures, solve

some problems of computing results on singleness and generality in previous models

and achieve the goal of providing diversified and concrete hedge strategy programs for

various hedgers partially. Specifically, we apply VaR, CVaR and LPMs to hedging

problems, and some formulae obtained from these models which used to calculate the

optimal hedge ratios are more flexible and more practical. The key achievements of this

work are listed as follows:

1. In the previous hedge research, the authors only use the hedge portfolio returns

exceeding zero as restrict condition of target function, which does not accord with

hedgers’ true thought. In order to overcome the shortcoming, the target return is

introduced as the boarder which is used to judge whether profit or loss for hedging (the

target return is an arbitrary real number), then the futures hedging optimization strategy

models based on the improved ratio profit and risk are made up, which make the ratio

between portfolio returns exceeding the target return and risks maximize in every unit

risk, and the optimal short and long hedge ratios are calculated and analyzed

theoretically, which solve some problems of computing results on singleness and

generality in previous models only based upon the ratio of profit and risk, achieve the

goal of providing diversified and concrete hedging optimization strategies for various

hedgers partially, provide concrete reference project for each individual, and help spot

producers and machining corporations in the futures trading to work out practical

strategies.

2. Based upon the hedge optimization theory of minimizing VaR and CVaR, we set

up the futures hedge optimization strategy models by using VaR and CVaR as target

function, which comprehensively consider expected returns and risk aversion. The

models make up the deficiencies of overlooking hedgers’ expected returns and risk

aversion parameter enacted artificially in the previous literatures, and the choice for

futures contracts direct reflect hedgers’ capability of enduring risk; No matter using VaR

or CVaR as risk measuring index, we can obtain the satisfactory and optimal short and

long hedge ratios in any given trust region. Specifically, using CVaR to measure hedge

portfolio downside risk, we can realize double supervisions and it is not easy to be

subjected to lawless operation and misrepresentation. So the method is dependable and

stable in calculating the optimal future hedge ratio.

3. We analyze the future hedge optimization strategy models based on the lower

partial moments (LPMs) theoretically, and the general theory formulae which can be

used to calculate the short and long optimal ratios are obtained. And the optimal hedge

ratios how to behave with respect to target returns and orders of moment chosen is

presented. Then the specific hidden expressions are derived when the joint distribution

of the spot and future returns is normal distribution when target returns and risk

aversion are different. Using the formulae used to measure hedging performance, we

evaluate hedging performance by combining the concrete example. The section of

research achievement provides theory foundation for the better application of LPMs in

hedging strategy problems.

4. In order to improve the shortcoming of CARA mean-variance model which can

not exhibit risk vulnerability, we present CRRA mean-risk utility function maximization

models. The models make return great and risk small simultaneously by combining

mean with downside risk and accords with the sense of economy actors, which makes

up the deficiency of risk minimization model that neglects return. And the CRRA utility

functions exhibit risk vulnerability by the constant relative risk aversion coefficient



The models provide scientific method for hedging strategy, increases the accuracy and

makes hedging strategy analysis more useful, more flexible and more convenient.

5. Based on the shortcoming of constant absolute risk aversion mean-variance

utility function, the improved constant relative risk aversion mean-variance utility

function, the constant relative risk aversion mean- standard deviation utility function

and the constant relative risk aversion mean-LPMs utility function are presented and

relative utility function maximization models are set up to obtain the short and long

optimal hedge ratios. The CRRA mean- standard deviation utility function model can

obtain the optimal hedge ratios from different strategies according to different risk

aversion coefficients, and the computing formulae are simple, trustworthy and feasible.

6. The CRRA mean-LPMs utility function maximization models are presented. We

add expected return to the minimum LPMs models in order to make up the deficiency of

overlooking expected returns. Using advantage of LPMs in measuring downside risk,

the short and long optimal hedge ratios with different target returns are calculated

flexibly, which has the property of strong economic application that makes the solving

of the optimal hedge ratios more exact and more flexible.

Key Word: hedging with futures contracts, the optimal hedging ratio,

Downside-Risk, Value-at-Risk, Condition Value-at-Risk,

the lower partial moments, risk aversion,

utility maximization

中文摘要

ABSTRACT

第一章绪论——课题的来源及研究内容...................................................................1

§1.1 期货套期保值问题研究的意义.....................................................................1

§1.2 国内外研究现状.............................................................................................2

§1.3 问题的提出……………………………………………………………….....6

§1.4 本文的研究目的、内容及结构安排……………………………..…………7

§1.4.1 研究目的和研究思路…...……………………………………………...7

§1.4.2 研究内容……………………...………………………………………...8

§1.4.3 结构安排……..…………………...…………………………………...10

第二章期货套期保值理论与风险度量方法.............................................................13

§2.1 期货套期保值理论.......................................................................................13

§2.1.1 期货市场发展回顾………………...………………………………….13

§2.1.2 套期保值基本概念……………………...…………………………….14

§2.1.3 套期保值的经济学原理………………...…………………………….15

§2.1.4 对期货市场套期保值理论的评价………...………………………….16

§2.2 风险度量方法…………………………………………………….………..16

§2.2.1 风险度量概述………………...……………...……………………….17

§2.2.2 传统风险度量工具…………...……………...……………………….18

§2.2.3 下方风险(Downside-Risk)的风险度量方法...……………………….20

§2.2.4 各种风险度量方法的比较………………...………………………….23

§2.2.5 各种风险度量方法的有效性评价……………………………………25

§2.3 本章小结…………….……………………………………………………..29

第三章基于收益率与风险比率的期货套期保值问题.............................................31

§3.1 空头和多头期货套期保值的定义…….…………………………………..32

§3.2 传统的最小方差法…………………….…………………………………..33

§3.3 改进模型的建立……………………….…………………………………..34

§3.4 实例分析..….………………………….…………………………………...39

§3.5 本章小结……………………………….…………………………………..40

第四章基于 VaR 和CVaR 的期货套期保值问题....................................................41

§4.1 基于 VaR 和CVaR 期货套期保值比的确定原理........................................42

§4.1.1 VaR 作为风险计量工具寻求最优套期保值比的可行性.....................42

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摘要：

摘要如何利用期货套期保值规避现货市场的风险不仅是一个重要的实际问题，也是一个重要的学术问题。考虑到对这一问题的深入研究应兼顾套期保值者不同的投资理念、不同的投资目标以及对风险不同的厌恶水平等因素，本文围绕套期保值优化策略如何确定这个中心问题，从不同侧面分别构建了若干符合不同套期保值者心理感受的套期保值优化策略理论模型，求出了每种情形下的最优套期保值比，取得了一系列具有创新性的成果。本文从不同侧面所构建的模型弥补了以往在套期保值问题研究中缺少考虑套期保值者目的多样性等因素方面存在的不足，解决了原有模型计算结果的单一与笼统等问题，在一定程度上实现了为不同套期保值者提供多元化、具体化的最优套期保值策...

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