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New blog post on Kaggle competition
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Bradlee Speice
@ -28,6 +28,17 @@
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<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
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<![endif]-->
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<!-- /Google Analytics -->
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</head>
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@ -84,7 +95,7 @@ Because these are all very similar, we decided to demonstrate all 3 products at
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<div class="prompt input_prompt">In [1]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-julia"><pre><span class="k">using</span> <span class="n">Gadfly</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="k">using</span> <span class="n">Gadfly</span>
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</pre></div>
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</div>
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@ -120,7 +131,7 @@ Because these are all very similar, we decided to demonstrate all 3 products at
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<div class="prompt input_prompt">In [2]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-julia"><pre><span class="n">S0</span> <span class="o">=</span> <span class="mf">102.2</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">S0</span> <span class="o">=</span> <span class="mf">102.2</span>
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<span class="n">nominal</span> <span class="o">=</span> <span class="mi">100</span>
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<span class="n">q</span> <span class="o">=</span> <span class="mf">2.84</span> <span class="o">/</span> <span class="mi">100</span>
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<span class="n">σ</span> <span class="o">=</span> <span class="mf">15.37</span> <span class="o">/</span> <span class="mi">100</span>
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@ -176,7 +187,7 @@ Because these are all very similar, we decided to demonstrate all 3 products at
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<div class="prompt input_prompt">In [3]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-julia"><pre><span class="n">simulate_gbm</span> <span class="o">=</span> <span class="n">function</span><span class="p">(</span><span class="n">S0</span><span class="p">,</span> <span class="n">μ</span><span class="p">,</span> <span class="n">σ</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">simulate_gbm</span> <span class="o">=</span> <span class="n">function</span><span class="p">(</span><span class="n">S0</span><span class="p">,</span> <span class="n">μ</span><span class="p">,</span> <span class="n">σ</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
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<span class="c"># Set the initial state</span>
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<span class="n">m</span> <span class="o">=</span> <span class="n">length</span><span class="p">(</span><span class="n">S0</span><span class="p">)</span>
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<span class="n">t</span> <span class="o">=</span> <span class="n">T</span> <span class="o">/</span> <span class="n">n</span>
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@ -247,7 +258,7 @@ Because these are all very similar, we decided to demonstrate all 3 products at
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<div class="prompt input_prompt">In [4]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-julia"><pre><span class="n">initial</span> <span class="o">=</span> <span class="n">ones</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span> <span class="o">*</span> <span class="n">S0</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">initial</span> <span class="o">=</span> <span class="n">ones</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span> <span class="o">*</span> <span class="n">S0</span>
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<span class="c"># Using μ=0, T=.25 for now, we'll use the proper values later</span>
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<span class="n">motion</span> <span class="o">=</span> <span class="n">simulate_gbm</span><span class="p">(</span><span class="n">initial</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">σ</span><span class="p">,</span> <span class="o">.</span><span class="mi">25</span><span class="p">,</span> <span class="mi">200</span><span class="p">)</span>
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@ -1855,7 +1866,7 @@ fig.select("#fig-3a6dd25ad25c4037a166889ee51bb151-element-20")
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<div class="prompt input_prompt">In [5]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-julia"><pre><span class="n">forward_term</span> <span class="o">=</span> <span class="n">function</span><span class="p">(</span><span class="n">yearly_term</span><span class="p">)</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">forward_term</span> <span class="o">=</span> <span class="n">function</span><span class="p">(</span><span class="n">yearly_term</span><span class="p">)</span>
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<span class="c"># It is assumed that we have a yearly term structure passed in, and starts at year 0</span>
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<span class="c"># This implies a nominal rate above 0 for the first year!</span>
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<span class="n">years</span> <span class="o">=</span> <span class="n">length</span><span class="p">(</span><span class="n">term</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span> <span class="c"># because we start at 0</span>
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@ -1885,14 +1896,14 @@ fig.select("#fig-3a6dd25ad25c4037a166889ee51bb151-element-20")
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<div class="prompt input_prompt">In [6]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-julia"><pre><span class="c"># Example term structure taken from:</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="c"># Example term structure taken from:</span>
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<span class="c"># http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield</span>
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<span class="c"># Linear interpolation used years in-between periods, assuming real-dollar</span>
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<span class="c"># interest rates</span>
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<span class="n">forward_yield</span> <span class="o">=</span> <span class="n">forward_term</span><span class="p">(</span><span class="n">term</span><span class="p">)</span>
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<span class="n">calculated_term2</span> <span class="o">=</span> <span class="n">term</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">forward_yield</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
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<span class="n">println</span><span class="p">(</span><span class="s">"Actual term[2]: </span><span class="si">$</span><span class="s">(term[2]); Calculated term[2]: </span><span class="si">$(calculated_term2)</span><span class="s">"</span><span class="p">)</span>
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<span class="n">println</span><span class="p">(</span><span class="s">"Actual term[2]: </span><span class="si">$(term[2])</span><span class="s">; Calculated term[2]: </span><span class="si">$(calculated_term2)</span><span class="s">"</span><span class="p">)</span>
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</pre></div>
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</div>
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@ -1929,7 +1940,7 @@ fig.select("#fig-3a6dd25ad25c4037a166889ee51bb151-element-20")
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<div class="prompt input_prompt">In [7]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-julia"><pre><span class="n">full_motion</span> <span class="o">=</span> <span class="n">ones</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span> <span class="o">*</span> <span class="n">S0</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">full_motion</span> <span class="o">=</span> <span class="n">ones</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span> <span class="o">*</span> <span class="n">S0</span>
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<span class="n">full_term</span> <span class="o">=</span> <span class="n">vcat</span><span class="p">(</span><span class="n">term</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">forward_yield</span><span class="p">)</span>
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<span class="k">for</span> <span class="n">i</span><span class="o">=</span><span class="mi">1</span><span class="p">:</span><span class="n">T</span>
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<span class="n">μ</span> <span class="o">=</span> <span class="p">(</span><span class="n">full_term</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">q</span><span class="p">)</span>
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@ -3490,7 +3501,7 @@ fig.select("#fig-0378e04b897742b597befd2e8e1c169e-element-20")
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<div class="prompt input_prompt">In [8]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-julia"><pre><span class="n">full_simulation</span> <span class="o">=</span> <span class="n">function</span><span class="p">(</span><span class="n">S0</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">term</span><span class="p">)</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">full_simulation</span> <span class="o">=</span> <span class="n">function</span><span class="p">(</span><span class="n">S0</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">term</span><span class="p">)</span>
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<span class="n">forward</span> <span class="o">=</span> <span class="n">vcat</span><span class="p">(</span><span class="n">term</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">forward_term</span><span class="p">(</span><span class="n">term</span><span class="p">))</span>
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<span class="c"># And an S0 to kick things off.</span>
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@ -3506,7 +3517,7 @@ fig.select("#fig-0378e04b897742b597befd2e8e1c169e-element-20")
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<span class="n">tic</span><span class="p">()</span>
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<span class="n">full_simulation</span><span class="p">(</span><span class="n">S0</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">term</span><span class="p">)</span>
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<span class="n">time</span> <span class="o">=</span> <span class="n">toq</span><span class="p">()</span>
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<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Time to run simulation: %.2fs"</span><span class="p">,</span> <span class="n">time</span><span class="p">)</span>
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<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Time to run simulation: </span><span class="si">%.2f</span><span class="s">s"</span><span class="p">,</span> <span class="n">time</span><span class="p">)</span>
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</pre></div>
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</div>
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@ -3551,7 +3562,7 @@ fig.select("#fig-0378e04b897742b597befd2e8e1c169e-element-20")
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<div class="prompt input_prompt">In [9]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-julia"><pre><span class="n">call_barrier</span> <span class="o">=</span> <span class="n">S0</span>
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<div class=" highlight hl-julia"><pre><span></span><span class="n">call_barrier</span> <span class="o">=</span> <span class="n">S0</span>
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<span class="n">strike</span> <span class="o">=</span> <span class="n">S0</span>
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<span class="n">protection_barrier</span> <span class="o">=</span> <span class="n">S0</span> <span class="o">*</span> <span class="o">.</span><span class="mi">6</span>
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<span class="n">coupon</span> <span class="o">=</span> <span class="n">nominal</span> <span class="o">*</span> <span class="o">.</span><span class="mi">07</span>
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@ -3595,13 +3606,13 @@ fig.select("#fig-0378e04b897742b597befd2e8e1c169e-element-20")
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<span class="n">tic</span><span class="p">()</span>
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<span class="n">mean_payoffs</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">athena</span><span class="p">()</span>
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<span class="n">time</span> <span class="o">=</span> <span class="n">toq</span><span class="p">()</span>
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<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Mean of simulation %i: \</span><span class="si">$</span><span class="s">%.4f; Simulation time: %.2fs</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">mean_payoffs</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">time</span><span class="p">)</span>
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<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Mean of simulation </span><span class="si">%i</span><span class="s">: \$</span><span class="si">%.4f</span><span class="s">; Simulation time: </span><span class="si">%.2f</span><span class="s">s</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">mean_payoffs</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">time</span><span class="p">)</span>
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<span class="k">end</span>
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<span class="n">final_mean</span> <span class="o">=</span> <span class="n">mean</span><span class="p">(</span><span class="n">mean_payoffs</span><span class="p">)</span>
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<span class="n">println</span><span class="p">(</span><span class="s">"Mean over </span><span class="si">$</span><span class="s">num_simulations simulations: </span><span class="si">$</span><span class="s">(mean(mean_payoffs))"</span><span class="p">)</span>
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<span class="n">println</span><span class="p">(</span><span class="s">"Mean over </span><span class="si">$num_simulations</span><span class="s"> simulations: </span><span class="si">$(mean(mean_payoffs))</span><span class="s">"</span><span class="p">)</span>
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<span class="n">pv</span> <span class="o">=</span> <span class="n">final_mean</span> <span class="o">*</span> <span class="p">(</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">prod</span><span class="p">(</span><span class="n">forward_structure</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="n">T</span><span class="p">))</span>
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<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Present value of Athena note: \</span><span class="si">$</span><span class="s">%.2f, notional: \</span><span class="si">$</span><span class="s">%.2f"</span><span class="p">,</span> <span class="n">pv</span><span class="p">,</span> <span class="n">nominal</span><span class="p">)</span>
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<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Present value of Athena note: \$</span><span class="si">%.2f</span><span class="s">, notional: \$</span><span class="si">%.2f</span><span class="s">"</span><span class="p">,</span> <span class="n">pv</span><span class="p">,</span> <span class="n">nominal</span><span class="p">)</span>
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</pre></div>
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</div>
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@ -3662,7 +3673,7 @@ Present value of Athena note: $95.00, notional: $100.00</pre>
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<div class="prompt input_prompt">In [10]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-julia"><pre><span class="n">call_barrier</span> <span class="o">=</span> <span class="n">S0</span>
|
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<div class=" highlight hl-julia"><pre><span></span><span class="n">call_barrier</span> <span class="o">=</span> <span class="n">S0</span>
|
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<span class="n">coupon_barrier</span> <span class="o">=</span> <span class="n">S0</span> <span class="o">*</span> <span class="o">.</span><span class="mi">8</span>
|
||||
<span class="n">protection_barrier</span> <span class="o">=</span> <span class="n">S0</span> <span class="o">*</span> <span class="o">.</span><span class="mi">6</span>
|
||||
<span class="n">coupon</span> <span class="o">=</span> <span class="n">nominal</span> <span class="o">*</span> <span class="o">.</span><span class="mi">06</span>
|
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@ -3709,13 +3720,13 @@ Present value of Athena note: $95.00, notional: $100.00</pre>
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<span class="n">tic</span><span class="p">()</span>
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<span class="n">mean_payoffs</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">phoenix_no_memory</span><span class="p">()</span>
|
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<span class="n">time</span> <span class="o">=</span> <span class="n">toq</span><span class="p">()</span>
|
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<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Mean of simulation %i: \</span><span class="si">$</span><span class="s">%.4f; Simulation time: %.2fs</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">mean_payoffs</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">time</span><span class="p">)</span>
|
||||
<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Mean of simulation </span><span class="si">%i</span><span class="s">: \$</span><span class="si">%.4f</span><span class="s">; Simulation time: </span><span class="si">%.2f</span><span class="s">s</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">mean_payoffs</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">time</span><span class="p">)</span>
|
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<span class="k">end</span>
|
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|
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<span class="n">final_mean</span> <span class="o">=</span> <span class="n">mean</span><span class="p">(</span><span class="n">mean_payoffs</span><span class="p">)</span>
|
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<span class="n">println</span><span class="p">(</span><span class="s">"Mean over </span><span class="si">$</span><span class="s">num_simulations simulations: </span><span class="si">$</span><span class="s">(mean(mean_payoffs))"</span><span class="p">)</span>
|
||||
<span class="n">println</span><span class="p">(</span><span class="s">"Mean over </span><span class="si">$num_simulations</span><span class="s"> simulations: </span><span class="si">$(mean(mean_payoffs))</span><span class="s">"</span><span class="p">)</span>
|
||||
<span class="n">pv</span> <span class="o">=</span> <span class="n">final_mean</span> <span class="o">*</span> <span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">prod</span><span class="p">(</span><span class="n">forward_structure</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">T</span><span class="p">))</span>
|
||||
<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Present value of Phoenix without memory note: \</span><span class="si">$</span><span class="s">%.2f"</span><span class="p">,</span> <span class="n">pv</span><span class="p">)</span>
|
||||
<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Present value of Phoenix without memory note: \$</span><span class="si">%.2f</span><span class="s">"</span><span class="p">,</span> <span class="n">pv</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
@ -3762,7 +3773,7 @@ Present value of Phoenix without memory note: $97.44</pre>
|
||||
<div class="prompt input_prompt">In [11]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-julia"><pre><span class="n">call_barrier</span> <span class="o">=</span> <span class="n">S0</span>
|
||||
<div class=" highlight hl-julia"><pre><span></span><span class="n">call_barrier</span> <span class="o">=</span> <span class="n">S0</span>
|
||||
<span class="n">coupon_barrier</span> <span class="o">=</span> <span class="n">S0</span> <span class="o">*</span> <span class="o">.</span><span class="mi">8</span>
|
||||
<span class="n">protection_barrier</span> <span class="o">=</span> <span class="n">S0</span> <span class="o">*</span> <span class="o">.</span><span class="mi">6</span>
|
||||
<span class="n">coupon</span> <span class="o">=</span> <span class="n">nominal</span> <span class="o">*</span> <span class="o">.</span><span class="mi">07</span>
|
||||
@ -3816,14 +3827,14 @@ Present value of Phoenix without memory note: $97.44</pre>
|
||||
<span class="n">tic</span><span class="p">()</span>
|
||||
<span class="n">mean_payoffs</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">phoenix_with_memory</span><span class="p">()</span>
|
||||
<span class="n">time</span> <span class="o">=</span> <span class="n">toq</span><span class="p">()</span>
|
||||
<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Mean of simulation %i: \</span><span class="si">$</span><span class="s">%.4f; Simulation time: %.2fs</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span>
|
||||
<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Mean of simulation </span><span class="si">%i</span><span class="s">: \$</span><span class="si">%.4f</span><span class="s">; Simulation time: </span><span class="si">%.2f</span><span class="s">s</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span>
|
||||
<span class="n">i</span><span class="p">,</span> <span class="n">mean_payoffs</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">time</span><span class="p">)</span>
|
||||
<span class="k">end</span>
|
||||
|
||||
<span class="n">final_mean</span> <span class="o">=</span> <span class="n">mean</span><span class="p">(</span><span class="n">mean_payoffs</span><span class="p">)</span>
|
||||
<span class="n">println</span><span class="p">(</span><span class="s">"Mean over </span><span class="si">$</span><span class="s">num_simulations simulations: </span><span class="si">$</span><span class="s">(mean(mean_payoffs))"</span><span class="p">)</span>
|
||||
<span class="n">println</span><span class="p">(</span><span class="s">"Mean over </span><span class="si">$num_simulations</span><span class="s"> simulations: </span><span class="si">$(mean(mean_payoffs))</span><span class="s">"</span><span class="p">)</span>
|
||||
<span class="n">pv</span> <span class="o">=</span> <span class="n">final_mean</span> <span class="o">*</span> <span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="n">prod</span><span class="p">(</span><span class="n">forward_structure</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="n">T</span><span class="p">))</span>
|
||||
<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Present value of Phoenix with memory note: \</span><span class="si">$</span><span class="s">%.2f"</span><span class="p">,</span> <span class="n">pv</span><span class="p">)</span>
|
||||
<span class="p">@</span><span class="n">printf</span><span class="p">(</span><span class="s">"Present value of Phoenix with memory note: \$</span><span class="si">%.2f</span><span class="s">"</span><span class="p">,</span> <span class="n">pv</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
@ -3857,6 +3868,20 @@ MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\(','\)']]}});
|
||||
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|
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|
||||
Reference in New Issue
Block a user