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<li class="toctree-l1"><a class="reference internal" href="system%20settings.html">第0章 与定价相关的系统全局设置</a></li>
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<li class="toctree-l1"><a class="reference internal" href="european.html">第1章 欧式期权</a></li>
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<li class="toctree-l1"><a class="reference internal" href="american.html">第2章 美式期权</a></li>
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<li class="toctree-l1"><a class="reference internal" href="asian.html">第3章 亚式期权</a></li>
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<li class="toctree-l1"><a class="reference internal" href="binary.html">第4章 二元期权</a></li>
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<li class="toctree-l1"><a class="reference internal" href="barrier.html">第5章 障碍期权</a></li>
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<li class="toctree-l1"><a class="reference internal" href="snowball.html">第6章 雪球期权</a></li>
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<li class="toctree-l1"><a class="reference internal" href="phoenix.html">第7章 凤凰期权</a></li>
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<li class="toctree-l1"><a class="reference internal" href="airbag.html">第8章 气囊结构</a></li>
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<li class="toctree-l1"><a class="reference internal" href="shuangsha.html">第9章 双鲨期权</a></li>
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<li class="toctree-l1"><a class="reference internal" href="rangeaccrual.html">第10章 区间累积期权</a></li>
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<li class="toctree-l1 current"><a class="current reference internal" href="#">附录1:希腊值</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="#id2">1.定价页面希腊值的含义</a></li>
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<li class="toctree-l2"><a class="reference internal" href="#id3">2.定价系统中希腊字母的计算方法</a><ul>
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<li class="toctree-l3"><a class="reference internal" href="#id4">2.1 解析解</a></li>
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<li class="toctree-l3"><a class="reference internal" href="#id5">2.2 差分法</a></li>
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<li class="toctree-l1"><a class="reference internal" href="model.html">附录2:期权定价方法概述</a></li>
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<section id="my-reference-label3">
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<span id="id1"></span><h1>附录1:希腊值<a class="headerlink" href="#my-reference-label3" title="Permalink to this headline"></a></h1>
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<section id="id2">
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<h2>1.定价页面希腊值的含义<a class="headerlink" href="#id2" title="Permalink to this headline"></a></h2>
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<table class="docutils align-default">
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<col style="width: 83%" />
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<thead>
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<tr class="row-odd"><th class="head"><p>指标</p></th>
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<th class="head"><p>定价页面希腊值的含义</p></th>
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</tr>
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</thead>
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<tbody>
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<tr class="row-even"><td><p>Delta</p></td>
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<td><p><strong>每报价单位Delta*交易份额/每手数量</strong>(即每报价单位Delta*手数)</p></td>
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</tr>
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<tr class="row-odd"><td><p>Gamma</p></td>
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<td><p><strong>每报价单位Gamma*交易份额/每手数量</strong>(即每报价单位Gamma*手数)</p></td>
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</tr>
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<tr class="row-even"><td><p>Vega</p></td>
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<td><p>每报价单位Vega*交易份额</p></td>
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</tr>
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<tr class="row-odd"><td><p>Theta</p></td>
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<td><p>每报价单位Theta*交易份额</p></td>
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</tr>
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<tr class="row-even"><td><p>Rho</p></td>
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<td><p>每报价单位Rho*交易份额*100</p></td>
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</tr>
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</tbody>
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</table>
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<div class="admonition note">
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<p class="admonition-title">Note</p>
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<ul class="simple">
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<li><p>“交易份额”即为系统定价页面的“有效成交数量”;</p></li>
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<li><p>“每手数量”即为“合约乘数”,可在“数据管理-标的资产”页面查看;</p></li>
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<li><p>以欧式香草期权 <a class="reference internal" href="european.html#my-reference-label"><span class="std std-ref">1.2.3 系统定价结果及其说明</span></a> 为例,对系统定价页面所展示的Delta的计算逻辑进行展示,其中</p></li>
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</ul>
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<blockquote>
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<tr class="row-odd"><td><p>每报价单位delta</p></td>
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<td><p>0.28972</p></td>
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</tr>
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<tr class="row-even"><td><p>有效成交数量</p></td>
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<td><p>55035.7733</p></td>
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</tr>
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<tr class="row-odd"><td><p>合约乘数</p></td>
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<td><p>100</p></td>
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</tr>
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<tr class="row-even"><td><p><strong>展示的delta</strong></p></td>
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<td><p><strong>159.45=0.28972*55035.7733/100</strong></p></td>
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</tr>
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</tbody>
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</table>
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</div></blockquote>
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</div>
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</section>
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<section id="id3">
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<h2>2.定价系统中希腊字母的计算方法<a class="headerlink" href="#id3" title="Permalink to this headline"></a></h2>
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<div class="admonition note">
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<p class="admonition-title">Note</p>
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<p>香草期权默认使用解析求导方法计算。其它类型的期权都采用有限差分法。</p>
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</div>
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<section id="id4">
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<h3>2.1 解析解<a class="headerlink" href="#id4" title="Permalink to this headline"></a></h3>
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<table class="docutils align-default">
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<col style="width: 9%" />
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<tr class="row-odd"><th class="head"><p>指标</p></th>
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<th class="head"><p>解析解</p></th>
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</tr>
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</thead>
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<tbody>
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<tr class="row-even"><td><p>Delta</p></td>
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<td><p><span class="math notranslate nohighlight">\(\Delta_\mathrm{call}=\frac{\partial c}{\partial S}=e^{(b-r)T}N(d_\mathrm{1})\)</span></p></td>
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</tr>
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<tr class="row-odd"><td><p></p></td>
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<td><p><span class="math notranslate nohighlight">\(\Delta_\mathrm{put}=\frac{\partial p}{\partial S}=e^{(b-r)T}[N(d_\mathrm{1})-1]\)</span></p></td>
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</tr>
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<tr class="row-even"><td><p>Gamma</p></td>
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<td><p><span class="math notranslate nohighlight">\(\Gamma_\mathrm{call,put}=\frac{\partial^2c}{\partial S^2}=\frac{\partial^2p}{\partial S^2}=\frac{n(d_\mathrm{1})e^{(b-r)T}}{S\sigma\sqrt{T}}\)</span></p></td>
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</tr>
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<tr class="row-odd"><td><p>Vega</p></td>
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<td><p><span class="math notranslate nohighlight">\(Vega_\mathrm{call,put}=\frac{\partial c}{\partial \sigma}=\frac{\partial p}{\partial \sigma}=Se^{(b-r)T}n(d_\mathrm{1})\sqrt{T}\)</span></p></td>
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</tr>
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<tr class="row-even"><td><p>Theta</p></td>
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<td><p><span class="math notranslate nohighlight">\(\Theta_\mathrm{call}=-\frac{\partial c}{\partial T}=-\frac{Se^{(b-r)T}n(d_\mathrm{1})\sigma}{2\sqrt{T}}-(b-r)Se^{(b-r)T}N(d_\mathrm{1})-rXe^{-rT}N(d_\mathrm{2})\)</span></p></td>
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</tr>
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<tr class="row-odd"><td><p></p></td>
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<td><p><span class="math notranslate nohighlight">\(\Theta_\mathrm{put}=-\frac{\partial p}{\partial T}=-\frac{Se^{(b-r)T}n(d_\mathrm{1})\sigma}{2\sqrt{T}}+(b-r)Se^{(b-r)T}N(-d_\mathrm{1})+rXe^{-rT}N(-d_\mathrm{2})\)</span></p></td>
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</tr>
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<tr class="row-even"><td><p>Rho</p></td>
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<td><p><span class="math notranslate nohighlight">\(\rho_\mathrm{call}=\frac{\partial c}{\partial r}=TXe^{-rT}N(d_\mathrm{2})\)</span></p></td>
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</tr>
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<tr class="row-odd"><td><p></p></td>
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<td><p><span class="math notranslate nohighlight">\(\rho_\mathrm{put}=\frac{\partial p}{\partial r}=-TXe^{-rT}N(-d_\mathrm{2})\)</span></p></td>
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</tr>
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<tr class="row-even"><td><p>期货期权Rho值计算</p></td>
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<td><p><span class="math notranslate nohighlight">\(\rho_\mathrm{call}=\frac{\partial c}{\partial r}=-Tc\)</span></p></td>
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</tr>
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<tr class="row-odd"><td><p></p></td>
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<td><p><span class="math notranslate nohighlight">\(\rho_\mathrm{put}=\frac{\partial p}{\partial r}=-Tp\)</span></p></td>
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</tr>
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</tbody>
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</table>
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</section>
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<section id="id5">
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<h3>2.2 差分法<a class="headerlink" href="#id5" title="Permalink to this headline"></a></h3>
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<table class="docutils align-default">
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<colgroup>
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<col style="width: 10%" />
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<col style="width: 90%" />
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<thead>
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<tr class="row-odd"><th class="head"><p>指标</p></th>
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<th class="head"><p>差分法</p></th>
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</tr>
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</thead>
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<tbody>
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<tr class="row-even"><td><p>Delta</p></td>
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<td><p>设当前标的价格为 <span class="math notranslate nohighlight">\(S\)</span>,设 <span class="math notranslate nohighlight">\(S_\mathrm{u}=S+S_\mathrm{\bigtriangleup},S_\mathrm{d}=S-S_\mathrm{\bigtriangleup}\)</span></p>
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<p>将 <span class="math notranslate nohighlight">\(S_\mathrm{u}和S_\mathrm{d}\)</span> 代入定价公式, 得到期权价值 <span class="math notranslate nohighlight">\(V_\mathrm{u}和V_\mathrm{d}\)</span>; 则</p>
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<p><span class="math notranslate nohighlight">\(Delta=(V_\mathrm{u}-V_\mathrm{d})/(S*0.01)\)</span></p>
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<p>系统中 <span class="math notranslate nohighlight">\(S_\mathrm{\bigtriangleup}\)</span> 为 <span class="math notranslate nohighlight">\(0.005*S\)</span></p>
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</td>
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</tr>
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<tr class="row-odd"><td><p>DeltaCash</p></td>
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<td><p><span class="math notranslate nohighlight">\(DeltaCash = Delta*S\)</span></p></td>
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</tr>
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<tr class="row-even"><td><p>Gamma</p></td>
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<td><p>设当前标的价格为 <span class="math notranslate nohighlight">\(S\)</span>, 期权理论价值为 <span class="math notranslate nohighlight">\(V\)</span>; 设 <span class="math notranslate nohighlight">\(S_\mathrm{u}=S+S_\mathrm{\bigtriangleup},S_\mathrm{d}=S-S_\mathrm{\bigtriangleup}\)</span></p>
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<p>将 <span class="math notranslate nohighlight">\(S_\mathrm{u}和S_\mathrm{d}\)</span> 代入定价公式,得到期权价值 <span class="math notranslate nohighlight">\(V_\mathrm{u}和V_\mathrm{d}\)</span>; 则</p>
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<p><span class="math notranslate nohighlight">\(Gamma=(V_\mathrm{u}+V_\mathrm{d}-2V)/S_\mathrm{\bigtriangleup}^2\)</span></p>
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<p>系统中 <span class="math notranslate nohighlight">\(S_\mathrm{\bigtriangleup}\)</span> 为 <span class="math notranslate nohighlight">\(0.01*S\)</span></p>
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</td>
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</tr>
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<tr class="row-odd"><td><p>GammaCash</p></td>
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<td><p><span class="math notranslate nohighlight">\(GammaCash = 0.01*Gamma*S^2\)</span></p></td>
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</tr>
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<tr class="row-even"><td><p>Vega</p></td>
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<td><p>设当前波动率为𝜎, 设 <span class="math notranslate nohighlight">\(𝜎_\mathrm{u}=𝜎+𝜎_\mathrm{\bigtriangleup},𝜎_\mathrm{d}=𝜎-𝜎_\mathrm{\bigtriangleup}\)</span></p>
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<p>将 <span class="math notranslate nohighlight">\(𝜎_\mathrm{u}和𝜎_\mathrm{d}\)</span> 代入定价公式,得到期权价值 <span class="math notranslate nohighlight">\(V_\mathrm{u}和V_\mathrm{d}\)</span>; 则</p>
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<p><span class="math notranslate nohighlight">\(Vega=V_\mathrm{u}-V_\mathrm{d}\)</span></p>
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<p>系统中 <span class="math notranslate nohighlight">\(𝜎_\mathrm{\bigtriangleup}\)</span> 为 0.5%</p>
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</td>
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</tr>
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<tr class="row-odd"><td><p>Vega(1bp)</p></td>
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<td><p><span class="math notranslate nohighlight">\(Vega(1bp) = Vega \times 0.0001\)</span>（标的波动率 σ 上升 1 个基点对应的价值变动）</p></td>
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</tr>
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<tr class="row-odd"><td><p>Theta</p></td>
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<td><p>设当前期权到期时间为 <span class="math notranslate nohighlight">\(T\)</span>, 期权理论价值为 <span class="math notranslate nohighlight">\(V,T'=T-frac(1),\)</span></p>
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<p>其中 <span class="math notranslate nohighlight">\(𝑓𝑟𝑎𝑐(1)\)</span> 是根据设定的日期规则计算一天的年化时间长度。例如：</p>
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<p>如果日期规则是 <strong>Bus244</strong>，则： <strong>frac(1) = 1.0/244</strong></p>
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<p>如果日期规则是 <strong>Act365</strong>，则： <strong>frac(1) = 1.0/365</strong></p>
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<p>将 <span class="math notranslate nohighlight">\(T'\)</span> 代入定价公式，得到期权价值 <span class="math notranslate nohighlight">\(V'\)</span>; 则</p>
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<p><span class="math notranslate nohighlight">\(Theta = 𝑉'-V\)</span></p>
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</td>
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</tr>
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<tr class="row-even"><td><p>Rho</p></td>
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<td><p>设无风险利率为 <span class="math notranslate nohighlight">\(r\)</span>,期权理论价值为 <span class="math notranslate nohighlight">\(V\)</span>; 设 <span class="math notranslate nohighlight">\(r_\mathrm{u}=r+10bp\)</span>;</p>
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<p>将 <span class="math notranslate nohighlight">\(r_\mathrm{u}\)</span> 代入定价公式，得到期权价值 <span class="math notranslate nohighlight">\(V_\mathrm{u}\)</span>；则</p>
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<p><span class="math notranslate nohighlight">\(Rho=(V_\mathrm{u}-V)/10bp\)</span></p>
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</td>
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</tr>
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<tr class="row-odd"><td><p>亚式期权Delta</p></td>
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<td><p>设当前已观察到的标的平均价格为 <span class="math notranslate nohighlight">\(S_\mathrm{A}\)</span>, 设 <span class="math notranslate nohighlight">\(S_\mathrm{A_\mathrm{u}}=S_\mathrm{A}+S_\mathrm{A_\mathrm{\bigtriangleup}}\)</span></p>
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<p>将 <span class="math notranslate nohighlight">\(S_\mathrm{A_\mathrm{u}}\)</span> 代入定价公式，得到期权价值 <span class="math notranslate nohighlight">\(V_\mathrm{u}\)</span>; 则</p>
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<p><span class="math notranslate nohighlight">\(Delta=(V_\mathrm{u}-V)/S_\mathrm{A_\mathrm{\bigtriangleup}}\)</span></p>
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<p>系统中 <span class="math notranslate nohighlight">\(S_\mathrm{A_\mathrm{\bigtriangleup}}\)</span> 为 <span class="math notranslate nohighlight">\(0.01*S_\mathrm{A}\)</span></p>
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</td>
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</tr>
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</tbody>
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</table>
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</section>
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</section>
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</section>
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</div>
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</div>
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