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Bradlee Speice
2016-10-22 22:29:18 -04:00
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@ -134,7 +134,7 @@ Because these are all very similar, we decided to demonstrate all 3 products at
<div class=" highlight hl-julia"><pre><span class="n">S0</span> <span class="o">=</span> <span class="mf">102.2</span>
<span class="n">nominal</span> <span class="o">=</span> <span class="mi">100</span>
<span class="n">q</span> <span class="o">=</span> <span class="mf">2.84</span> <span class="o">/</span> <span class="mi">100</span>
<span class="err">σ</span> <span class="o">=</span> <span class="mf">15.37</span> <span class="o">/</span> <span class="mi">100</span>
<span class="n">σ</span> <span class="o">=</span> <span class="mf">15.37</span> <span class="o">/</span> <span class="mi">100</span>
<span class="n">term</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">.</span><span class="mi">49</span><span class="p">,</span> <span class="o">.</span><span class="mi">9</span><span class="p">,</span> <span class="mf">1.21</span><span class="p">,</span> <span class="mf">1.45</span><span class="p">,</span> <span class="mf">1.69</span><span class="p">]</span> <span class="o">/</span> <span class="mi">100</span> <span class="o">+</span> <span class="mi">1</span>
<span class="c">###</span>
@ -187,7 +187,7 @@ Because these are all very similar, we decided to demonstrate all 3 products at
<div class="prompt input_prompt">In&nbsp;[3]:</div>
<div class="inner_cell">
<div class="input_area">
<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="err">μ</span><span class="p">,</span> <span class="err">σ</span><span class="p">,</span> <span class="n">T</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
<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>
<span class="c"># Set the initial state</span>
<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>
<span class="n">t</span> <span class="o">=</span> <span class="n">T</span> <span class="o">/</span> <span class="n">n</span>
@ -196,7 +196,7 @@ Because these are all very similar, we decided to demonstrate all 3 products at
<span class="c"># Build out all states</span>
<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">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<span class="n">motion</span><span class="p">[:,</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">motion</span><span class="p">[:,</span><span class="n">i</span><span class="p">]</span> <span class="o">.*</span> <span class="n">exp</span><span class="p">((</span><span class="err">μ</span> <span class="o">-</span> <span class="err">σ</span><span class="o">^</span><span class="mi">2</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="n">t</span><span class="p">)</span> <span class="o">.*</span> <span class="n">exp</span><span class="p">(</span><span class="n">sqrt</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">*</span> <span class="err">σ</span> <span class="o">.*</span> <span class="n">randn</span><span class="p">(</span><span class="n">m</span><span class="p">))</span>
<span class="n">motion</span><span class="p">[:,</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">motion</span><span class="p">[:,</span><span class="n">i</span><span class="p">]</span> <span class="o">.*</span> <span class="n">exp</span><span class="p">((</span><span class="n">μ</span> <span class="o">-</span> <span class="n">σ</span><span class="o">^</span><span class="mi">2</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="n">t</span><span class="p">)</span> <span class="o">.*</span> <span class="n">exp</span><span class="p">(</span><span class="n">sqrt</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">*</span> <span class="n">σ</span> <span class="o">.*</span> <span class="n">randn</span><span class="p">(</span><span class="n">m</span><span class="p">))</span>
<span class="k">end</span>
<span class="k">return</span> <span class="n">motion</span>
@ -260,7 +260,7 @@ Because these are all very similar, we decided to demonstrate all 3 products at
<div class="input_area">
<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>
<span class="c"># Using μ=0, T=.25 for now, we&#39;ll use the proper values later</span>
<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="err">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>
<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>
<span class="n">display_motion</span><span class="p">(</span><span class="n">motion</span><span class="p">,</span> <span class="o">.</span><span class="mi">25</span><span class="p">)</span>
</pre></div>
@ -1943,8 +1943,8 @@ fig.select("#fig-3a6dd25ad25c4037a166889ee51bb151-element-20")
<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>
<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>
<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>
<span class="err">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>
<span class="n">year_motion</span> <span class="o">=</span> <span class="n">simulate_gbm</span><span class="p">(</span><span class="n">full_motion</span><span class="p">[:,</span><span class="k">end</span><span class="p">],</span> <span class="err">μ</span><span class="p">,</span> <span class="err">σ</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
<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>
<span class="n">year_motion</span> <span class="o">=</span> <span class="n">simulate_gbm</span><span class="p">(</span><span class="n">full_motion</span><span class="p">[:,</span><span class="k">end</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="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
<span class="n">full_motion</span> <span class="o">=</span> <span class="n">hcat</span><span class="p">(</span><span class="n">full_motion</span><span class="p">,</span> <span class="n">year_motion</span><span class="p">)</span>
<span class="k">end</span>
@ -3507,8 +3507,8 @@ fig.select("#fig-0378e04b897742b597befd2e8e1c169e-element-20")
<span class="c"># And an S0 to kick things off.</span>
<span class="n">final_motion</span> <span class="o">=</span> <span class="n">ones</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">*</span> <span class="n">S0</span>
<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>
<span class="err">μ</span> <span class="o">=</span> <span class="p">(</span><span class="n">forward</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>
<span class="n">year_motion</span> <span class="o">=</span> <span class="n">simulate_gbm</span><span class="p">(</span><span class="n">final_motion</span><span class="p">[:,</span><span class="k">end</span><span class="p">],</span> <span class="err">μ</span><span class="p">,</span> <span class="err">σ</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
<span class="n">μ</span> <span class="o">=</span> <span class="p">(</span><span class="n">forward</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>
<span class="n">year_motion</span> <span class="o">=</span> <span class="n">simulate_gbm</span><span class="p">(</span><span class="n">final_motion</span><span class="p">[:,</span><span class="k">end</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="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
<span class="n">final_motion</span> <span class="o">=</span> <span class="n">hcat</span><span class="p">(</span><span class="n">final_motion</span><span class="p">,</span> <span class="n">year_motion</span><span class="p">)</span>
<span class="k">end</span>
<span class="k">return</span> <span class="n">final_motion</span>
@ -3576,7 +3576,7 @@ fig.select("#fig-0378e04b897742b597befd2e8e1c169e-element-20")
<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>
<span class="n">price</span> <span class="o">=</span> <span class="n">year_prices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="k">if</span> <span class="n">price</span> <span class="err">≥</span> <span class="n">call_barrier</span>
<span class="k">if</span> <span class="n">price</span> <span class="n">≥</span> <span class="n">call_barrier</span>
<span class="k">return</span> <span class="p">(</span><span class="n">nominal</span> <span class="o">+</span> <span class="n">coupon</span><span class="o">*</span><span class="n">i</span><span class="p">)</span> <span class="o">*</span> <span class="n">exp</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="n">i</span><span class="p">:</span><span class="k">end</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="o">-</span><span class="n">i</span><span class="p">))</span>
<span class="k">end</span>
<span class="k">end</span>
@ -3686,9 +3686,9 @@ Present value of Athena note: $95.00, notional: $100.00</pre>
<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>
<span class="n">price</span> <span class="o">=</span> <span class="n">year_prices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="k">if</span> <span class="n">price</span> <span class="err">≥</span> <span class="n">call_barrier</span>
<span class="k">if</span> <span class="n">price</span> <span class="n">≥</span> <span class="n">call_barrier</span>
<span class="k">return</span> <span class="p">(</span><span class="n">nominal</span> <span class="o">+</span> <span class="n">coupon</span> <span class="o">+</span> <span class="n">total_coupons</span><span class="p">)</span><span class="o">*</span><span class="n">exp</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="n">i</span><span class="p">:</span><span class="k">end</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="o">-</span><span class="n">i</span><span class="p">))</span>
<span class="k">elseif</span> <span class="n">price</span> <span class="err">≥</span> <span class="n">coupon_barrier</span>
<span class="k">elseif</span> <span class="n">price</span> <span class="n">≥</span> <span class="n">coupon_barrier</span>
<span class="n">total_coupons</span> <span class="o">=</span> <span class="n">total_coupons</span> <span class="o">*</span> <span class="n">exp</span><span class="p">(</span><span class="n">forward_structure</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="p">)</span> <span class="o">+</span> <span class="n">coupon</span>
<span class="k">else</span>
<span class="n">total_coupons</span> <span class="o">*=</span> <span class="n">exp</span><span class="p">(</span><span class="n">forward_structure</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="p">)</span>