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rageSpin committed Jun 23, 2024
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4 changes: 2 additions & 2 deletions content/posts/finance/monte_carlo/Black-Scholes/index.md
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Expand Up @@ -154,11 +154,11 @@ plt.ylabel("Frequency")
plt.show()
```

{{< img src="/posts/finance/monte_carlo/Black-Scholes/images/simulation_path.png" align="center" title="Paths">}}
{{< img src="/posts/finance/monte_carlo/black-scholes/images/simulation_path.png" align="center" title="Paths">}}

These visualizations show the range of possible stock price paths and the distribution of final stock prices, providing insight into the option's potential outcomes.

{{< img src="/posts/finance/monte_carlo/Black-Scholes/images/simulation_histogram.png" align="center" title="Histogram">}}
{{< img src="/posts/finance/monte_carlo/black-scholes/images/simulation_histogram.png" align="center" title="Histogram">}}

## 6. Comparison with Analytical Solutions

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11 changes: 6 additions & 5 deletions public/posts/finance/monte_carlo/black-scholes/index.html
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Expand Up @@ -519,7 +519,9 @@ <h2 id="5-visualization-and-analysis">5. Visualization and Analysis</h2>
</span></span><span style="display:flex;"><span>plt<span style="color:#f92672">.</span>xlabel(<span style="color:#e6db74">&#34;Stock Price&#34;</span>)
</span></span><span style="display:flex;"><span>plt<span style="color:#f92672">.</span>ylabel(<span style="color:#e6db74">&#34;Frequency&#34;</span>)
</span></span><span style="display:flex;"><span>plt<span style="color:#f92672">.</span>show()
</span></span></code></pre></div><img src="/posts/finance/monte_carlo/Black-Scholes/images/simulation_path.png"
</span></span></code></pre></div><img src="/posts/finance/monte_carlo/black-scholes/images/simulation_path.png"

alt="Paths"



Expand All @@ -529,8 +531,8 @@ <h2 id="5-visualization-and-analysis">5. Visualization and Analysis</h2>

>

<hr>
<img src="/posts/finance/monte_carlo/Black-Scholes/images/simulation_histogram.png"
<p>These visualizations show the range of possible stock price paths and the distribution of final stock prices, providing insight into the option&rsquo;s potential outcomes.</p>
<img src="/posts/finance/monte_carlo/black-scholes/images/simulation_histogram.png"

alt="Histogram"

Expand All @@ -542,7 +544,6 @@ <h2 id="5-visualization-and-analysis">5. Visualization and Analysis</h2>

>

<p>These visualizations show the range of possible stock price paths and the distribution of final stock prices, providing insight into the option&rsquo;s potential outcomes.</p>
<h2 id="6-comparison-with-analytical-solutions">6. Comparison with Analytical Solutions</h2>
<p>To validate our Monte Carlo results, we can compare them with the Black-Scholes analytical solution:</p>
<div class="highlight"><pre tabindex="0" style="color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;"><code class="language-python" data-lang="python"><span style="display:flex;"><span><span style="color:#f92672">from</span> scipy.stats <span style="color:#f92672">import</span> norm
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