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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"><a class="reference internal" href="greeks.html">附录1:希腊值</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 class="tex2jax_ignore mathjax_ignore" id="bs">
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<h1>BS模型下的雪球定价<a class="headerlink" href="#bs" title="Permalink to this headline"></a></h1>
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<p>标的资产价格遵循Black-Scholes随机微分方程</p>
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<div class="math notranslate nohighlight">
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\[
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dS = \mu Sdt+\sigma SdW
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\]</div>
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<p>其中 <span class="math notranslate nohighlight">\(\mu\)</span>, <span class="math notranslate nohighlight">\(\sigma\)</span> 是常数， <span class="math notranslate nohighlight">\(dW\)</span> 是一个维纳过程。</p>
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<section id="id1">
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<h2>标准雪球,挂钩中证500<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h2>
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<table class="colwidths-auto docutils align-default">
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<thead>
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<tr class="row-odd"><th class="head"><p>雪球合约</p></th>
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<th class="head"><p></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>起始日</p></td>
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<td><p>2022-08-03</p></td>
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</tr>
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<tr class="row-odd"><td><p>到期日</p></td>
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<td><p>2023-08-03</p></td>
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</tr>
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<tr class="row-even"><td><p>期初标的价格</p></td>
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<td><p>6472.52</p></td>
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||
</tr>
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||
<tr class="row-odd"><td><p>敲入观察日</p></td>
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<td><p>每日</p></td>
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</tr>
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<tr class="row-even"><td><p>敲入障碍价格</p></td>
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<td><p>5178.016(80%)</p></td>
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</tr>
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<tr class="row-odd"><td><p>敲入赔付</p></td>
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||
<td><p>-<span class="math notranslate nohighlight">\(\text{Max}(S_0 - S_T, 0)\)</span></p></td>
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||
</tr>
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||
<tr class="row-even"><td><p>敲出观察日</p></td>
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||
<td><p>每月</p></td>
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||
</tr>
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||
<tr class="row-odd"><td><p>敲出障碍价格</p></td>
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||
<td><p>6472.52 (100%)</p></td>
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||
</tr>
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||
<tr class="row-even"><td><p>利息率</p></td>
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||
<td><p>25.63% (按自然日/365天年化)</p></td>
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||
</tr>
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<tr class="row-odd"><td><p>类型</p></td>
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<td><p>向上敲出向下敲入</p></td>
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||
</tr>
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||
</tbody>
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||
</table>
|
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<hr class="docutils" />
|
||
<p>敲出观察日 :</p>
|
||
<p>2022-09-05, 2022-10-10, 2022-11-03, 2022-12-05, 2023-01-04, 2023-02-03</p>
|
||
<p>2023-03-03, 2023-04-06, 2023-05-04, 2023-06-05, 2023-07-03, 2023-08-03</p>
|
||
<hr class="docutils" />
|
||
<section id="id2">
|
||
<h3>定价测试<a class="headerlink" href="#id2" title="Permalink to this headline"></a></h3>
|
||
<p><strong>测试案例A1 - 未敲入</strong></p>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>定价参数</p></th>
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||
<th class="head"><p></p></th>
|
||
<th class="head"><p></p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>valuation date</p></td>
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||
<td><p>2022-08-03</p></td>
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<td><p>End of day valuation</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>risk free rate</p></td>
|
||
<td><p>2.00%</p></td>
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||
<td><p></p></td>
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||
</tr>
|
||
<tr class="row-even"><td><p>b</p></td>
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||
<td><p>-4.00%</p></td>
|
||
<td><p><span class="math notranslate nohighlight">\(b = r - q, F = e^{-qT}S\)</span></p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p><span class="math notranslate nohighlight">\(\sigma\)</span></p></td>
|
||
<td><p>22%</p></td>
|
||
<td><p></p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><strong>定价结果</strong></p>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>标的价格</p></th>
|
||
<th class="head"><p>pv (积分法)</p></th>
|
||
<th class="head"><p>pv (10M蒙卡)</p></th>
|
||
<th class="head"><p>误差</p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>6148.894</p></td>
|
||
<td><p>-196.0527043</p></td>
|
||
<td><p>-196.00972802 <span class="math notranslate nohighlight">\(\pm\)</span> 1.05E+00</p></td>
|
||
<td><p>4.30E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6213.619</p></td>
|
||
<td><p>-148.0428289</p></td>
|
||
<td><p>-148.24677039 <span class="math notranslate nohighlight">\(\pm\)</span> 1.67E+00</p></td>
|
||
<td><p>2.04E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6278.344</p></td>
|
||
<td><p>-104.4854665</p></td>
|
||
<td><p>-104.57889976 <span class="math notranslate nohighlight">\(\pm\)</span> 1.39E+00</p></td>
|
||
<td><p>9.34E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6343.070</p></td>
|
||
<td><p>-65.3566709</p></td>
|
||
<td><p>-65.29542971 <span class="math notranslate nohighlight">\(\pm\)</span> 6.90E-01</p></td>
|
||
<td><p>6.12E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6407.795</p></td>
|
||
<td><p>-30.5691389</p></td>
|
||
<td><p>-30.08973053 <span class="math notranslate nohighlight">\(\pm\)</span> 7.90E-01</p></td>
|
||
<td><p>4.79E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6472.520</p></td>
|
||
<td><p>0.0323706</p></td>
|
||
<td><p>-0.17733488 <span class="math notranslate nohighlight">\(\pm\)</span> 1.00E+00</p></td>
|
||
<td><p>2.10E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6537.245</p></td>
|
||
<td><p>26.6515177</p></td>
|
||
<td><p>27.01615853 <span class="math notranslate nohighlight">\(\pm\)</span> 1.02E+00</p></td>
|
||
<td><p>3.65E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6601.970</p></td>
|
||
<td><p>49.5457148</p></td>
|
||
<td><p>49.84049483 <span class="math notranslate nohighlight">\(\pm\)</span> 8.23E-01</p></td>
|
||
<td><p>2.95E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6666.696</p></td>
|
||
<td><p>69.0093770</p></td>
|
||
<td><p>69.07223885 <span class="math notranslate nohighlight">\(\pm\)</span> 7.81E-01</p></td>
|
||
<td><p>6.29E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6731.421</p></td>
|
||
<td><p>85.3611400</p></td>
|
||
<td><p>85.3839709 <span class="math notranslate nohighlight">\(\pm\)</span> 5.43E-01</p></td>
|
||
<td><p>2.28E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6796.146</p></td>
|
||
<td><p>98.9340196</p></td>
|
||
<td><p>99.11063364 <span class="math notranslate nohighlight">\(\pm\)</span> 5.88E-01</p></td>
|
||
<td><p>1.77E-01</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><img alt="image info" src="_images/SnowballTestCaseA.png" /></p>
|
||
<p><strong>测试案例B</strong></p>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>定价参数</p></th>
|
||
<th class="head"><p></p></th>
|
||
<th class="head"><p></p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>valuation date</p></td>
|
||
<td><p>2023-01-05</p></td>
|
||
<td><p>End of day valuation</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>risk free rate</p></td>
|
||
<td><p>2.00%</p></td>
|
||
<td><p></p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>b</p></td>
|
||
<td><p>-4.00%</p></td>
|
||
<td><p><span class="math notranslate nohighlight">\(b = r - q, F = e^{-qT}S\)</span></p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p><span class="math notranslate nohighlight">\(\sigma\)</span></p></td>
|
||
<td><p>22%</p></td>
|
||
<td><p></p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><strong>定价结果 B1: 未敲入</strong></p>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>标的价格</p></th>
|
||
<th class="head"><p>pv (积分法)</p></th>
|
||
<th class="head"><p>pv (10M蒙卡)</p></th>
|
||
<th class="head"><p>误差</p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>6148.894</p></td>
|
||
<td><p>427.325062</p></td>
|
||
<td><p>427.9228192 <span class="math notranslate nohighlight">\(\pm\)</span> 1.38E+00</p></td>
|
||
<td><p>5.98E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6213.619</p></td>
|
||
<td><p>492.7445585</p></td>
|
||
<td><p>493.1424038 <span class="math notranslate nohighlight">\(\pm\)</span> 1.47E+00</p></td>
|
||
<td><p>3.98E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6278.344</p></td>
|
||
<td><p>550.9069733</p></td>
|
||
<td><p>551.2859545 <span class="math notranslate nohighlight">\(\pm\)</span> 1.07E+00</p></td>
|
||
<td><p>3.79E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6343.070</p></td>
|
||
<td><p>601.9983288</p></td>
|
||
<td><p>602.2868404 <span class="math notranslate nohighlight">\(\pm\)</span> 7.99E-01</p></td>
|
||
<td><p>2.89E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6407.795</p></td>
|
||
<td><p>646.2981965</p></td>
|
||
<td><p>646.5486041 <span class="math notranslate nohighlight">\(\pm\)</span> 6.78E-01</p></td>
|
||
<td><p>2.50E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6472.520</p></td>
|
||
<td><p>684.1838004</p></td>
|
||
<td><p>684.4620590 <span class="math notranslate nohighlight">\(\pm\)</span> 8.51E-01</p></td>
|
||
<td><p>2.78E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6537.245</p></td>
|
||
<td><p>716.1099193</p></td>
|
||
<td><p>716.2424969 <span class="math notranslate nohighlight">\(\pm\)</span> 7.60E-01</p></td>
|
||
<td><p>1.33E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6601.970</p></td>
|
||
<td><p>742.6105229</p></td>
|
||
<td><p>742.6392973 <span class="math notranslate nohighlight">\(\pm\)</span> 8.23E-01</p></td>
|
||
<td><p>2.88E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6666.696</p></td>
|
||
<td><p>764.2603656</p></td>
|
||
<td><p>764.1403718 <span class="math notranslate nohighlight">\(\pm\)</span> 8.55E-01</p></td>
|
||
<td><p>1.20E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6731.421</p></td>
|
||
<td><p>781.6548032</p></td>
|
||
<td><p>781.7166434 <span class="math notranslate nohighlight">\(\pm\)</span> 5.46E-01</p></td>
|
||
<td><p>6.18E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6796.146</p></td>
|
||
<td><p>795.3989672</p></td>
|
||
<td><p>795.5211704 <span class="math notranslate nohighlight">\(\pm\)</span> 6.30E-01</p></td>
|
||
<td><p>1.22E-01</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><img alt="image info" src="_images/SnowballTestCaseB1.png" /></p>
|
||
<p><strong>定价结果 B2: 已敲入</strong></p>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>标的价格</p></th>
|
||
<th class="head"><p>pv (积分法)</p></th>
|
||
<th class="head"><p>pv (10M蒙卡)</p></th>
|
||
<th class="head"><p>误差</p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>6148.894</p></td>
|
||
<td><p>38.7057021</p></td>
|
||
<td><p>38.3458455 <span class="math notranslate nohighlight">\(\pm\)</span> 7.10E-01</p></td>
|
||
<td><p>3.60E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6213.619</p></td>
|
||
<td><p>128.6549666</p></td>
|
||
<td><p>128.3170770 <span class="math notranslate nohighlight">\(\pm\)</span> 9.48E-01</p></td>
|
||
<td><p>3.38E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6278.344</p></td>
|
||
<td><p>215.6031344</p></td>
|
||
<td><p>215.5695826 <span class="math notranslate nohighlight">\(\pm\)</span> 6.06E-01</p></td>
|
||
<td><p>3.36E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6343.070</p></td>
|
||
<td><p>298.5808561</p></td>
|
||
<td><p>298.6465002 <span class="math notranslate nohighlight">\(\pm\)</span> 7.57E-01</p></td>
|
||
<td><p>6.56E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6407.795</p></td>
|
||
<td><p>376.6242609</p></td>
|
||
<td><p>376.4077947 <span class="math notranslate nohighlight">\(\pm\)</span> 5.65E-01</p></td>
|
||
<td><p>2.16E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6472.520</p></td>
|
||
<td><p>448.8585180</p></td>
|
||
<td><p>448.6964908 <span class="math notranslate nohighlight">\(\pm\)</span> 5.25E-01</p></td>
|
||
<td><p>1.62E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6537.245</p></td>
|
||
<td><p>514.5598903</p></td>
|
||
<td><p>514.0085162 <span class="math notranslate nohighlight">\(\pm\)</span> 6.46E-01</p></td>
|
||
<td><p>5.51E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6601.970</p></td>
|
||
<td><p>573.2317933</p></td>
|
||
<td><p>572.9944114 <span class="math notranslate nohighlight">\(\pm\)</span> 8.47E-01</p></td>
|
||
<td><p>2.37E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6666.696</p></td>
|
||
<td><p>624.6220783</p></td>
|
||
<td><p>624.5185256 <span class="math notranslate nohighlight">\(\pm\)</span> 8.50E-01</p></td>
|
||
<td><p>1.04E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6731.421</p></td>
|
||
<td><p>668.7400067</p></td>
|
||
<td><p>669.0810299 <span class="math notranslate nohighlight">\(\pm\)</span> 4.65E-01</p></td>
|
||
<td><p>3.41E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6796.146</p></td>
|
||
<td><p>705.8501155</p></td>
|
||
<td><p>706.0451325 <span class="math notranslate nohighlight">\(\pm\)</span> 4.84E-01</p></td>
|
||
<td><p>1.95E-01</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><img alt="image info" src="_images/SnowballTestCaseB2.png" /></p>
|
||
</section>
|
||
</section>
|
||
<section id="id3">
|
||
<h2>反向雪球<a class="headerlink" href="#id3" title="Permalink to this headline"></a></h2>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>雪球合约</p></th>
|
||
<th class="head"><p></p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>起始日</p></td>
|
||
<td><p>2022-08-03</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>到期日</p></td>
|
||
<td><p>2023-08-03</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>期初标的价格</p></td>
|
||
<td><p>6472.52</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>敲入观察日</p></td>
|
||
<td><p>daily</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>敲入障碍价格</p></td>
|
||
<td><p>7767.024 （120%）</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>敲入赔付</p></td>
|
||
<td><p>-<span class="math notranslate nohighlight">\(\text{Max}(S_T - S_0, 0)\)</span></p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>敲出观察日</p></td>
|
||
<td><p>monthly</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>敲出障碍价格</p></td>
|
||
<td><p>6472.52 （100%）</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>票息率</p></td>
|
||
<td><p>15.72%（按自然日/365天年化）</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>类型</p></td>
|
||
<td><p>向下敲出向上敲入</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<hr class="docutils" />
|
||
<p>敲出观察日 :</p>
|
||
<p>2022-09-05, 2022-10-10, 2022-11-03, 2022-12-05, 2023-01-04, 2023-02-03</p>
|
||
<p>2023-03-03, 2023-04-06, 2023-05-04, 2023-06-05, 2023-07-03, 2023-08-03</p>
|
||
<hr class="docutils" />
|
||
<section id="id4">
|
||
<h3>定价测试<a class="headerlink" href="#id4" title="Permalink to this headline"></a></h3>
|
||
<p><strong>测试案例 C</strong></p>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>定价参数</p></th>
|
||
<th class="head"><p></p></th>
|
||
<th class="head"><p></p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>valuation date</p></td>
|
||
<td><p>2022-08-03</p></td>
|
||
<td><p>End of day valuation</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>risk free rate</p></td>
|
||
<td><p>2.00%</p></td>
|
||
<td><p></p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>b</p></td>
|
||
<td><p>-4.00%</p></td>
|
||
<td><p><span class="math notranslate nohighlight">\(b = r - q, F = e^{-qT}S\)</span></p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p><span class="math notranslate nohighlight">\(\sigma\)</span></p></td>
|
||
<td><p>22%</p></td>
|
||
<td><p></p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><strong>定价结果</strong></p>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>标的价格</p></th>
|
||
<th class="head"><p>pv (积分法)</p></th>
|
||
<th class="head"><p>pv (10M蒙卡)</p></th>
|
||
<th class="head"><p>误差</p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>6148.894</p></td>
|
||
<td><p>65.3448933</p></td>
|
||
<td><p>65.3452647 <span class="math notranslate nohighlight">\(\pm\)</span> 2.98E-01</p></td>
|
||
<td><p>3.71E-04</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6213.619</p></td>
|
||
<td><p>56.6940233</p></td>
|
||
<td><p>56.7330567 <span class="math notranslate nohighlight">\(\pm\)</span> 4.18E-01</p></td>
|
||
<td><p>3.90E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6278.344</p></td>
|
||
<td><p>46.0518268</p></td>
|
||
<td><p>46.0270761 <span class="math notranslate nohighlight">\(\pm\)</span> 4.22E-01</p></td>
|
||
<td><p>2.48E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6343.070</p></td>
|
||
<td><p>33.1932399</p></td>
|
||
<td><p>33.1540734 <span class="math notranslate nohighlight">\(\pm\)</span> 4.53E-01</p></td>
|
||
<td><p>3.92E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6407.795</p></td>
|
||
<td><p>17.9173506</p></td>
|
||
<td><p>17.6653259 <span class="math notranslate nohighlight">\(\pm\)</span> 4.85E-01</p></td>
|
||
<td><p>2.52E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6472.520</p></td>
|
||
<td><p>0.0507756</p></td>
|
||
<td><p>-0.0731201 <span class="math notranslate nohighlight">\(\pm\)</span> 6.13E-01</p></td>
|
||
<td><p>1.24E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6537.245</p></td>
|
||
<td><p>-20.5433362</p></td>
|
||
<td><p>-20.5894126 <span class="math notranslate nohighlight">\(\pm\)</span> 9.12E-01</p></td>
|
||
<td><p>4.61E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6601.970</p></td>
|
||
<td><p>-43.9599523</p></td>
|
||
<td><p>-44.1733741 <span class="math notranslate nohighlight">\(\pm\)</span> 7.55E-01</p></td>
|
||
<td><p>2.13E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6666.696</p></td>
|
||
<td><p>-70.2579891</p></td>
|
||
<td><p>-70.3019983 <span class="math notranslate nohighlight">\(\pm\)</span> 4.40E-01</p></td>
|
||
<td><p>4.40E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6731.421</p></td>
|
||
<td><p>-99.4516585</p></td>
|
||
<td><p>-99.8852855 <span class="math notranslate nohighlight">\(\pm\)</span> 8.58E-01</p></td>
|
||
<td><p>4.34E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6796.146</p></td>
|
||
<td><p>-131.5212902</p></td>
|
||
<td><p>-131.7481609 <span class="math notranslate nohighlight">\(\pm\)</span> 8.76E-01</p></td>
|
||
<td><p>2.27E-01</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><img alt="image info" src="_images/SnowballTestCaseC.png" /></p>
|
||
<p><strong>测试案例 D</strong></p>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>定价参数</p></th>
|
||
<th class="head"><p></p></th>
|
||
<th class="head"><p></p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>valuation date</p></td>
|
||
<td><p>2023-01-05</p></td>
|
||
<td><p>End of day valuation</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>risk free rate</p></td>
|
||
<td><p>2.00%</p></td>
|
||
<td><p></p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>b</p></td>
|
||
<td><p>-4.00%</p></td>
|
||
<td><p><span class="math notranslate nohighlight">\(b = r - q, F = e^{-qT}S\)</span></p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p><span class="math notranslate nohighlight">\(\sigma\)</span></p></td>
|
||
<td><p>22%</p></td>
|
||
<td><p></p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><strong>定价结果 D1: 未敲入</strong></p>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>标的价格</p></th>
|
||
<th class="head"><p>pv (积分法)</p></th>
|
||
<th class="head"><p>pv (10M蒙卡)</p></th>
|
||
<th class="head"><p>误差</p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>6148.894</p></td>
|
||
<td><p>480.6164666</p></td>
|
||
<td><p>480.5418820 <span class="math notranslate nohighlight">\(\pm\)</span> 3.08E-01</p></td>
|
||
<td><p>7.46E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6213.619</p></td>
|
||
<td><p>468.2669310</p></td>
|
||
<td><p>468.1959089 <span class="math notranslate nohighlight">\(\pm\)</span> 3.39E-01</p></td>
|
||
<td><p>7.10E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6278.344</p></td>
|
||
<td><p>452.6208759</p></td>
|
||
<td><p>452.9667710 <span class="math notranslate nohighlight">\(\pm\)</span> 6.03E-01</p></td>
|
||
<td><p>3.46E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6343.070</p></td>
|
||
<td><p>433.2865243</p></td>
|
||
<td><p>433.6995642 <span class="math notranslate nohighlight">\(\pm\)</span> 5.45E-01</p></td>
|
||
<td><p>4.13E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6407.795</p></td>
|
||
<td><p>409.9354642</p></td>
|
||
<td><p>410.2911129 <span class="math notranslate nohighlight">\(\pm\)</span> 4.63E-01</p></td>
|
||
<td><p>3.56E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6472.520</p></td>
|
||
<td><p>382.3143624</p></td>
|
||
<td><p>382.4486253 <span class="math notranslate nohighlight">\(\pm\)</span> 4.55E-01</p></td>
|
||
<td><p>1.34E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6537.245</p></td>
|
||
<td><p>350.2504395</p></td>
|
||
<td><p>350.5597632 <span class="math notranslate nohighlight">\(\pm\)</span> 4.22E-01</p></td>
|
||
<td><p>3.09E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6601.970</p></td>
|
||
<td><p>313.6566351</p></td>
|
||
<td><p>313.8583732 <span class="math notranslate nohighlight">\(\pm\)</span> 3.93E-01</p></td>
|
||
<td><p>2.02E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6666.696</p></td>
|
||
<td><p>272.5210791</p></td>
|
||
<td><p>272.4193765 <span class="math notranslate nohighlight">\(\pm\)</span> 4.14E-01</p></td>
|
||
<td><p>1.02E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6731.421</p></td>
|
||
<td><p>226.8982120</p></td>
|
||
<td><p>226.8036417 <span class="math notranslate nohighlight">\(\pm\)</span> 5.31E-01</p></td>
|
||
<td><p>9.46E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6796.146</p></td>
|
||
<td><p>176.8869928</p></td>
|
||
<td><p>176.6121000 <span class="math notranslate nohighlight">\(\pm\)</span> 9.45E-01</p></td>
|
||
<td><p>2.75E-01</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><img alt="image info" src="_images/SnowballTestCaseD1.png" /></p>
|
||
<p><strong>定价结果 D2: 已敲入</strong></p>
|
||
<table class="colwidths-auto docutils align-default">
|
||
<thead>
|
||
<tr class="row-odd"><th class="head"><p>标的价格</p></th>
|
||
<th class="head"><p>pv (积分法)</p></th>
|
||
<th class="head"><p>pv (10M蒙卡)</p></th>
|
||
<th class="head"><p>误差</p></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="row-even"><td><p>6148.894</p></td>
|
||
<td><p>457.9406897</p></td>
|
||
<td><p>457.9956641 <span class="math notranslate nohighlight">\(\pm\)</span> 2.88E-01</p></td>
|
||
<td><p>5.50E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6213.619</p></td>
|
||
<td><p>438.2313091</p></td>
|
||
<td><p>438.1506878 <span class="math notranslate nohighlight">\(\pm\)</span> 2.11E-01</p></td>
|
||
<td><p>8.06E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6278.344</p></td>
|
||
<td><p>413.9737716</p></td>
|
||
<td><p>413.9394246 <span class="math notranslate nohighlight">\(\pm\)</span> 3.48E-01</p></td>
|
||
<td><p>3.43E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6343.070</p></td>
|
||
<td><p>384.9055300</p></td>
|
||
<td><p>384.8481964 <span class="math notranslate nohighlight">\(\pm\)</span> 3.57E-01</p></td>
|
||
<td><p>5.73E-02</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6407.795</p></td>
|
||
<td><p>350.9203744</p></td>
|
||
<td><p>350.8858678 <span class="math notranslate nohighlight">\(\pm\)</span> 4.53E-01</p></td>
|
||
<td><p>3.45E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6472.520</p></td>
|
||
<td><p>312.0694606</p></td>
|
||
<td><p>312.0674783 <span class="math notranslate nohighlight">\(\pm\)</span> 7.53E-01</p></td>
|
||
<td><p>1.98E-03</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6537.245</p></td>
|
||
<td><p>268.5470142</p></td>
|
||
<td><p>268.5783158 <span class="math notranslate nohighlight">\(\pm\)</span> 8.07E-01</p></td>
|
||
<td><p>3.13E-02</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6601.970</p></td>
|
||
<td><p>220.6706281</p></td>
|
||
<td><p>220.9279611 <span class="math notranslate nohighlight">\(\pm\)</span> 8.80E-01</p></td>
|
||
<td><p>2.57E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6666.696</p></td>
|
||
<td><p>168.8425323</p></td>
|
||
<td><p>169.2444951 <span class="math notranslate nohighlight">\(\pm\)</span> 6.48E-01</p></td>
|
||
<td><p>4.02E-01</p></td>
|
||
</tr>
|
||
<tr class="row-odd"><td><p>6731.421</p></td>
|
||
<td><p>113.5154808</p></td>
|
||
<td><p>113.7365403 <span class="math notranslate nohighlight">\(\pm\)</span> 8.22E-01</p></td>
|
||
<td><p>2.21E-01</p></td>
|
||
</tr>
|
||
<tr class="row-even"><td><p>6796.146</p></td>
|
||
<td><p>55.1471061</p></td>
|
||
<td><p>55.0962627 <span class="math notranslate nohighlight">\(\pm\)</span> 8.87E-01</p></td>
|
||
<td><p>5.08E-02</p></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
<p><img alt="image info" src="_images/SnowballTestCaseD2.png" /></p>
|
||
<p><strong><em>NOTE</em></strong></p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>1. 误差 = |pv (积分法) - pv (10M蒙卡)| ;
|
||
2. 根据中心极限定理，蒙特卡洛计算的pv是正态分布的。pv是通过10次一万次蒙特卡洛计算出来的， 取10次计算的平均值作为最终pv(相当于10M蒙特卡洛)，标准差作为误差项;
|
||
</pre></div>
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</div>
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</section>
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