https://yy-tech.online/zh/categories/quant/ Recent content in Quant on H&W Hugo zh-Hant Thu, 28 May 2026 17:25:00 +0800 https://yy-tech.online/zh/post/var-backtesting-and-ewma-volatility-forecast-for-var-backtesting/ Thu, 28 May 2026 17:25:00 +0800 https://yy-tech.online/zh/post/var-backtesting-and-ewma-volatility-forecast-for-var-backtesting/ <h2 id="task-3var-回测与基于-ewma-波动率预测的-var-回测">Task 3：VaR 回测与基于 EWMA 波动率预测的 VaR 回测</h2> <h1 id="var-回测">VaR 回测</h1> <ul> <li>在大多数情况下，我们假设日收益率服从正态分布，并且按照题目要求，VaR 取 99% 置信水平。</li> </ul> <p><strong>导入库</strong></p> <div class="highlight"><div class="chroma"> <table class="lntable"><tr><td class="lntd"> <pre tabindex="0" class="chroma"><code><span class="lnt">1 </span></code></pre></td> <td class="lntd"> <pre tabindex="0" class="chroma"><code class="language-python" data-lang="python"><span class="line"><span class="cl"><span class="k">await</span> <span class="nb">__import__</span><span class="p">(</span><span class="s2">&#34;piplite&#34;</span><span class="p">)</span><span class="o">.</span><span class="n">install</span><span class="p">(</span><span class="s1">&#39;numpy&#39;</span><span class="p">,</span> <span class="s1">&#39;scipy&#39;</span><span class="p">,</span> <span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;pandas&#39;</span><span class="p">,</span> <span class="s1">&#39;tabulate&#39;</span><span class="p">)</span> </span></span></code></pre></td></tr></table> </div> </div><div class="highlight"><div class="chroma"> <table class="lntable"><tr><td class="lntd"> <pre tabindex="0" class="chroma"><code><span class="lnt">1 </span><span class="lnt">2 </span></code></pre></td> <td class="lntd"> <pre tabindex="0" class="chroma"><code class="language-python" data-lang="python"><span class="line"><span class="cl"><span class="c1"># hyy:fix the import failed issue</span> </span></span><span class="line"><span class="cl"><span class="k">await</span> <span class="nb">__import__</span><span class="p">(</span><span class="s2">&#34;piplite&#34;</span><span class="p">)</span><span class="o">.</span><span class="n">install</span><span class="p">(</span><span class="s1">&#39;tabulate&#39;</span><span class="p">)</span> </span></span></code></pre></td></tr></table> </div> </div><div class="highlight"><div class="chroma"> <table class="lntable"><tr><td class="lntd"> <pre tabindex="0" class="chroma"><code><span class="lnt">1 </span><span class="lnt">2 </span></code></pre></td> <td class="lntd"> <pre tabindex="0" class="chroma"><code class="language-python" data-lang="python"><span class="line"><span class="cl"><span class="c1"># hyy:fix excel issue, miss the excel read library, install here.</span> </span></span><span class="line"><span class="cl"><span class="k">await</span> <span class="nb">__import__</span><span class="p">(</span><span class="s2">&#34;piplite&#34;</span><span class="p">)</span><span class="o">.</span><span class="n">install</span><span class="p">(</span><span class="s1">&#39;openpyxl&#39;</span><span class="p">)</span> </span></span></code></pre></td></tr></table> </div> </div><div class="highlight"><div class="chroma"> <table class="lntable"><tr><td class="lntd"> <pre tabindex="0" class="chroma"><code><span class="lnt">1 </span><span class="lnt">2 </span><span class="lnt">3 </span><span class="lnt">4 </span><span class="lnt">5 </span></code></pre></td> <td class="lntd"> <pre tabindex="0" class="chroma"><code class="language-python" data-lang="python"><span class="line"><span class="cl"><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> </span></span><span class="line"><span class="cl"><span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span> </span></span><span class="line"><span class="cl"><span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">stats</span> </span></span><span class="line"><span class="cl"><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span> </span></span><span class="line"><span class="cl"><span class="kn">from</span> <span class="nn">tabulate</span> <span class="kn">import</span> <span class="n">tabulate</span> </span></span></code></pre></td></tr></table> </div> </div><div class="highlight"><div class="chroma"> <table class="lntable"><tr><td class="lntd"> <pre tabindex="0" class="chroma"><code><span class="lnt">1 </span><span class="lnt">2 </span></code></pre></td> <td class="lntd"> <pre tabindex="0" class="chroma"><code class="language-python" data-lang="python"><span class="line"><span class="cl"><span class="c1"># set precision</span> </span></span><span class="line"><span class="cl"><span class="n">pd</span><span class="o">.</span><span class="n">set_option</span><span class="p">(</span><span class="s1">&#39;display.precision&#39;</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span> </span></span></code></pre></td></tr></table> </div> </div><p><strong>加载数据</strong></p> https://yy-tech.online/zh/post/pricing-european-and-binary-options-using-monte-carlo-simulation/ Thu, 28 May 2026 16:01:00 +0800 https://yy-tech.online/zh/post/pricing-european-and-binary-options-using-monte-carlo-simulation/ <h1 id="使用蒙特卡洛模拟对欧式与二元期权定价">使用蒙特卡洛模拟对欧式与二元期权定价</h1> <h2 id="1-引言">1. 引言</h2> <p>本文在风险中性框架下，使用蒙特卡洛模拟研究欧式看涨期权与二元看涨期权的定价问题。根据资产定价基本定理，期权价值 $V(S,t)$ 等于风险中性测度 $\mathbb{Q}$ 下贴现支付的期望：</p>