<p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">&nbsp;&nbsp;&nbsp; 首先，从方法论上我有一些看法，做一篇论文最终的目的是要让自己的结论被别人接受，为了达到这个目的，我们从理论和实证两个方面去说明和论证，二者是缺一不可的。如果缺少理论基础，仅仅通过回归等实证手段分析出了某个结论，这样的结论自然会受到大家的质疑：（</span><span lang="EN-US"><font face="Times New Roman">1</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">）通过回归得出的结论依赖于文章的数据，如果没有理论推导出该结论，那么怎么能肯定该结论不是由该特定数据得出的结论，结论的普遍性受到质疑；（</span><span lang="EN-US"><font face="Times New Roman">2</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">）得出某个结论，怎样证明它不是一个局部的最优答案，而是一个在综合考虑所有情况后的全局最优结果；所以，要想做好一篇令人信服的论文，不仅要有坚实的理论基础，构建合理的模型，可以做出适当的简化，但是仍然要考虑足够的现实情况，以免做出的结论与实际情况出入太大。但是，在目前我们硕士生这个阶段，估计做出十分创新的模型和理论是比较困难的，我觉得把重点放在对模型的发展和扩展上是最好的选择，也应该会得到一些成果吧。</span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US"><span style="mso-spacerun: yes;"><font face="Times New Roman">&nbsp;&nbsp;&nbsp; </font></span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">最近，通过读文献和听</span><span lang="EN-US"><font face="Times New Roman">forum</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">，自己也思考了一些可能性的方向，还需要继续深入下去，观察和体会每个想法的可操作性。对于每个选题的可操作性是非常重要的，虽然有时候我们的想法很好，但是到了最后却无法继续下去，关键在于，我们目前的知识和水平无法达到解决它的程度，这就需要我们自己能够判断这个题目的“深浅”，需要在近期就培养这种能力。基础的</span><span lang="EN-US"><font face="Times New Roman">BS</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">公式可以由无套利原则得到，而且是在</span><span lang="EN-US"><span style="POSITION: relative; TOP: 3pt; mso-text-raise: -3.0pt;"><shapetype id="_x0000_t75" stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" opreferrelative="t" ospt="75" coordsize="21600,21600"><font face="Times New Roman">
<stroke joinstyle="miter"></stroke><formulas><f eqn="if lineDrawn pixelLineWidth 0"></f><f eqn="sum @0 1 0"></f><f eqn="sum 0 0 @1"></f><f eqn="prod @2 1 2"></f><f eqn="prod @3 21600 pixelWidth"></f><f eqn="prod @3 21600 pixelHeight"></f><f eqn="sum @0 0 1"></f><f eqn="prod @6 1 2"></f><f eqn="prod @7 21600 pixelWidth"></f><f eqn="sum @8 21600 0"></f><f eqn="prod @7 21600 pixelHeight"></f><f eqn="sum @10 21600 0"></f></formulas><path oconnecttype="rect" gradientshapeok="t" oextrusionok="f"></path><lock aspectratio="t" vext="edit"></lock></font></shapetype><shape id="_x0000_i1025" oole="" type="#_x0000_t75" style="WIDTH: 38.25pt; HEIGHT: 14.25pt;"><imagedata otitle="" src="file:///F:\DOCUME~1\ADMINI~1\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz"></imagedata></shape></span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的情况下得出来的，但是实际情况中，如果考虑了交易成本和交易的现实，则连续的套利交易是不可能的，那么，在这种情况下，连续模型是否还成立？如果使用了离散的时间，那么离散的模型又应该如何应用？</span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US"><span style="mso-tab-count: 1;"><font face="Times New Roman">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </font></span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">本文主要是研究：每一种推广是否或者在多大程度上改进了期权定价和套期保值。通过使用</span><span lang="EN-US"><font face="Times New Roman">S&amp;P500</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">期权，从三个方面检验这些推广模型：（</span><span lang="EN-US"><font face="Times New Roman">1</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">）隐含波动率与相关的时间序列数据的内在一致性；（</span><span lang="EN-US"><font face="Times New Roman">2</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">）样本外期权；（</span><span lang="EN-US"><font face="Times New Roman">3</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">）套期保值。</span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US"><span style="mso-tab-count: 1;"><font face="Times New Roman">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </font></span></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">文章主要对基础的</span><span lang="EN-US"><font face="Times New Roman">BS</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">模型、加入随机波动率的</span><span lang="EN-US"><font face="Times New Roman">SV</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">模型、在</span><span lang="EN-US"><font face="Times New Roman">SV</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">模型中加入跳跃过程的</span><span lang="EN-US"><font face="Times New Roman">SVJ</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">模型，以及在</span><span lang="EN-US"><font face="Times New Roman">SV</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">模型中加入随机利率的</span><span lang="EN-US"><font face="Times New Roman">SVSI</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">模型这四个模型的结果进行了比较，从数据实证的角度得出他们的定价结果和</span><span lang="EN-US"><font face="Times New Roman">hedge</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的效果的优劣，并且解释之所以出现这样的结果的原因是什么。下面，我们要先从理论上说明一下每个模型的优劣，对他们可能出现的结果进行一下预测，再通过实证检验，如果得出与我们的理论预测一样的结果的话，就说明我们的理论基础是坚实的，也说明实证检验是合理的。这样的研究思路是正确的，就像物理学中牛顿首先得到一个关于万有引力的猜想，猜想引力与重力成正比，而与距离成反比，然后得出自己的公式，最后在天体运行中预测其他的行星，这样就最终证明了自己结论的正确性。</span></p><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';"><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21.75pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">首先，我们得出了基本的</span><span lang="EN-US"><font face="Times New Roman">BS</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型，但是</span><span lang="EN-US"><font face="Times New Roman">BS</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型是有它的假设条件的：（</span><span lang="EN-US"><font face="Times New Roman">1</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">）没有红利支付；（</span><span lang="EN-US"><font face="Times New Roman">2</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">）交易成本；（</span><span lang="EN-US"><font face="Times New Roman">3</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">）利率保持不变；（</span><span lang="EN-US"><font face="Times New Roman">4</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">）标的资产服从对数正态分布；（</span><span lang="EN-US"><font face="Times New Roman">5</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">）波动率保持不变。而这些假设条件在现实中往往不合理，那么要放松这些假设就带来了模型的改进，而改进效果如何就是本文的研究重点。</span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21.75pt;"><span lang="EN-US"><font face="Times New Roman">SV</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型是在</span><span lang="EN-US"><font face="Times New Roman">BS</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型的基础上推翻假设（</span><span lang="EN-US"><font face="Times New Roman">5</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">），其实也是与假设（</span><span lang="EN-US"><font face="Times New Roman">4</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">）有关，从实证中存在</span><span lang="EN-US"><font face="Times New Roman">volatility smile</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">，说明实际中波动率并不是常数，加入随机波动率肯定能改善模型的定价准确程度，从表现上来说肯定有:SV&gt;BS</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">；</span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21.75pt;"><span lang="EN-US"><font face="Times New Roman">SVJ</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型是在</span><span lang="EN-US"><font face="Times New Roman">SV</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型的基础上又加入了</span><span lang="EN-US"><font face="Times New Roman">Jump Process</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">，这其实也是对假设（</span><span lang="EN-US"><font face="Times New Roman">4</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">）的一种放松，因为一旦加入跳跃过程，对数正态分布肯定会被打破。但是，又比</span><span lang="EN-US"><font face="Times New Roman">SV</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型更进一步地改善定价结果，因为毕竟考虑了标的资产的价格跳跃。而且，如果把期权分为长期期权和短期期权，那么我们几乎可以肯定地说，跳跃过程对长期期权的影响一定大于对短期期权的影响。这个道理不言自明，因为跳跃的概率在长期中会越来越大，而在短时期中发生的概率要相对低得多。所以，对长期期权的影响一定大于对短期期权的影响。从模型表现上来说肯定有:SVJ&gt;SV&gt;BS</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">；</span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21.75pt;"><span lang="EN-US"><font face="Times New Roman">SVSI</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型是在</span><span lang="EN-US"><font face="Times New Roman">SV</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型的基础上加入了</span><span lang="EN-US"><font face="Times New Roman">stochastic interest rate</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">，这是对假设（</span><span lang="EN-US"><font face="Times New Roman">3</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">）的一种放松，可以预测到，这会对定价模型有一定的改善，因为毕竟放松了一条假设。但是，我们这里研究的主要是股票期权，标的资产是股票，而股票对利率的变动并不是很敏感，债券等</span><span lang="EN-US"><font face="Times New Roman">Fixed-Income</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">的证券对利率才是非常敏感的。所以，如果股票对利率变动不是很敏感的话，那么股票期权也可能不敏感，从股票的特性上来说，我们推测</span><span lang="EN-US"><font face="Times New Roman">SVSI</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型的改善效果应该不会太大，在下面的实证部分就是要检验</span><span lang="EN-US"><font face="Times New Roman">SVSI</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型与</span><span lang="EN-US"><font face="Times New Roman">SVJ</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">和</span><span lang="EN-US"><font face="Times New Roman">SV</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">模型的表现，这里因为暂时预测他们的表现效果为:SVSI???SVJ&gt;SV&gt;BS</span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: &quot;Times New Roman&quot;; mso-hansi-font-family: &quot;Times New Roman&quot;;">。</span></p><p style="MARGIN: 0cm 0cm 0pt;"></p></span><p style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';"></span></p><p style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';"></span></p><br/>