add example with black-scholes call pricing

option/blackscholes/blackscholes.js

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+!function()
+{
+    var blackscholes = {};
+
+    blackscholes.normal = new normal(0.0 /*mean*/, 1.0 /*sigma*/);
+
+    blackscholes.d1 = function(strike, tau, spot, vol, r)
+    {
+	var moneyness = spot/strike;
+	return (Math.log(moneyness) + (r + 0.5*vol*vol)*tau)/(vol*Math.sqrt(tau));
+    } /*d1*/
+
+    blackscholes.d2 = function(d1, tau, vol)
+    {
+	return d1 - vol * Math.sqrt(tau);
+    } /*d2*/
+
+    blackscholes.call_px1 = function(strike, tau, spot, r, d1, d2)
+    {
+	return blackscholes.normal.cdf(d1)*spot
+	    - blackscholes.normal.cdf(d2)*strike*Math.exp(-r*tau)
+    } /*call_px1*/
+
+    blackscholes.call_px = function(strike, tau, spot, vol, r)
+    {
+	var d1 = blackscholes.d1(strike, tau, spot, vol, r);
+	var d2 = blackscholes.d2(d1, tau, vol);
+
+	return blackscholes.call_px1(strike, tau, spot, r, d1, d2);
+    } /*call_px*/
+
+    blackscholes.call_delta = function(strike, tau, spot, vol, r)
+    {
+	var d1 = blackscholes.d1(strike, tau, spot, vol, r);
+
+	return blackscholes.normal.cdf(d1);
+    } /*call_delta*/
+
+    blackscholes.gamma = function(strike, tau, spot, vol, r)
+    {
+	var d1 = blackscholes.d1(strike, tau, spot, vol, r);
+
+	return blackscholes.normal.pdf(d1) / (spot * vol * Math.sqrt(tau));
+    } /*gamma*/
+
+    /* providing call_gamma() for consistency with call_px(), call_delta() */
+    blackscholes.call_gamma = blackscholes.gamma;
+
+    this.blackscholes = blackscholes;
+}();

option/blackscholes/drag6.css

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+.axis path,
+.axis line {
+    fill: none;
+    stroke: black;
+}
+
+.axis text {
+    font-family: sans-serif;
+    font-size: 11px;
+}

option/blackscholes/fx.js

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+../../d3/drag7/fx.js

option/blackscholes/fx_view.js

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+../../d3/drag7/fx_view.js

option/blackscholes/index-src.org

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+#+title: option/blackscholes .org source
+# org-publish options
+# H:2   controls section numbering.  
+#       number top-level and second-level headings only
+# ^:{}  require a_{b} before assuming that b should be subscripted.  
+#       without this option a_b will automatically subscript b.
+#+options: ^:{}
+#
+# options used exclusively by emacs
+#+startup: showall
+#
+# options used exclusively by the html exporter
+#+language: en
+#+infojs_opt: view: showall
+#+html_head: <link rel="stylesheet" type="text/css" href="../../css/notebook.css" />
+#+html_link_home: ../../index.html
+#+html_link_up: index.html
+
+#+include: "index.org" example

option/blackscholes/index.org

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+#+title: black-scholes example
+#
+# org-publish options
+# H:2   controls section numbering.  
+#       number top-level and second-level headings only
+# ^:{}  require a_{b} before assuming that b should be subscripted.  
+#       without this option a_b will automatically subscript b.
+#+options: ^:{}
+#
+# options used exclusively by emacs
+#+startup: showall
+#
+# options used exclusively by the html exporter
+#+language: en
+#+infojs_opt: view:showall toc:nil ltoc:nil mouse:#ffc0c0 path:/ext/org/org-info.js
+#+html_mathjax: align:left indent:5em path:/ext/mathjax/MathJax.js
+#+html_head: <script type="text/javascript" src="/ext/d3/d3.js"></script>
+#+html_head: <script type="text/javascript" src="point.js"></script>
+#+html_head: <script type="text/javascript" src="fx.js"></script>
+#+html_head: <script type="text/javascript" src="xyscale.js"></script>
+#+html_head: <script type="text/javascript" src="fx_view.js"></script>
+#+html_head: <script type="text/javascript" src="normal.js"></script>
+#+html_head: <script type="text/javascript" src="blackscholes.js"></script>
+#+html_head: <script type="text/javascript" src="parametric-drag-example.js"></script>
+#+html_head: <link rel="stylesheet" type="text/css" href="../../css/notebook.css" />
+#+html_head: <link rel="stylesheet" type="text/css" href="drag6.css" />
+#+html_link_home: ../../index.html
+#+html_link_up: ../../index.html
+
+* Introduction
+  This is intended to be an interactive Black-Scholes option-pricing demonstration.
+  *Warning: Work in progress*
+
+  - ~.org~ source for this page is here: [[file:index-src.org][index.org]]
+
+** Option pricing
+   The Black-Scholes formula for European call options is:
+   $$ C(s,t) = N(d_{1})S = N(d_{2})Ke^{-r\tau} $$
+   where $N(x)$ is the cumulative normal distribution function:
+   $$ N(x) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{x}{e^{-\frac{x^2}{2}} dx} $$
+   We also have $N'(x)$ is the normal probability density function:
+   $$ N'(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}} $$
+   $$ d_{1} = \frac{1}{\sigma\sqrt{\tau}}
+        \left[\ln{\left(\frac{S}{K}\right)}+\left(r+\frac{\sigma^2}{2}\right)\tau\right] $$
+   and
+   $$ d_{2} = d_{1} - \sigma\sqrt{\tau} $$
+
+   We also have greeks:
+   $$ delta: \frac{\partial C}{\partial S} = N(d_{1}) $$
+   $$ gamma: \frac{N'(d1)}{S\sigma\sqrt{\tau}} $$
+* Prerequisites
+  As for [[file:~/proj/org-howto/d3/drag1/index.org#Prerequisites][d3 example /#1/]]
+
+* Procedure
+
+** Cumulative normal distribution
+   We use the ubiquitous polynomial approximation.
+   Write ~normal.js~
+
+#+include: normal.js example
+
+** Black-Scholes call
+   Write ~blackscholes.js~
+
+#+include: blackscholes.js example
+
+** Insert html fragment to invoke our interactive javascript code
+   This also follows the same model we used in examples [[file:~/proj/org-howto/d3/drag3/index.org][/#3/]], [[file:~/proj/org-howto/d3/drag4/index.org][/#4/]], [[file:~/proj/org-howto/d3/drag5/index.org][/#5/]].
+   #+begin_example
+    ,#+begin_html
+    <div id="frame"></div>
+    <script type="text/javascript">
+      window.onload = function() { ex.start(this); }
+    </script>
+    #+end_html
+   #+end_example
+   The div element ~#frame~ will appear below this line:
+   #+begin_html
+   <div id="frame"></div>
+   <script type="text/javascript">
+     window.onload = function() { ex.start(this); }
+   </script>
+   #+end_html
+
+   

option/blackscholes/normal.js

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+!function()
+{
+    /* e.g. N = normal(0,1)
+     *      N.cdf(0.0) -> 0.5
+     */
+    function normal(mean, sigma)
+    {
+	this.mean = mean;
+	this.sigma = sigma;
+	this.sigma_2 = sigma*sigma;
+	this.cdf = function(x) {
+	    var z = (x-mean)/Math.sqrt(2*this.sigma_2);
+	    var t = 1/(1+0.3275911*Math.abs(z));
+	    var a1 =  0.254829592;
+	    var a2 = -0.284496736;
+	    var a3 =  1.421413741;
+	    var a4 = -1.453152027;
+	    var a5 =  1.061405429;
+	    var erf = 1-(((((a5*t + a4)*t) + a3)*t + a2)*t + a1)*t*Math.exp(-z*z);
+	    var sign = 1;
+	    if(z < 0)
+	    {
+		sign = -1;
+	    }
+	    return (1/2)*(1+sign*erf);
+	} /*cdf*/
+	this.pdf = function(x) {
+	    var z = (x-mean)/Math.sqrt(2*this.sigma_2);
+	    
+	    return (1.0/Math.sqrt(2*Math.PI)) * Math.exp(-0.5*z*z);
+	} /*pdf*/
+    } /*normal*/
+    
+    this.normal = normal;
+}();

option/blackscholes/parametric-drag-example.js

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+!function() {
+    var ex = {};
+    
+    /* Requires: 
+     * - point.js
+     * - fx.js
+     * - fx_view.js
+     */
+
+    ex.box_pt = {x: 700, y: 450};
+
+    ex.strike = 1.0;
+    ex.tau = 1.0;
+    ex.vol = 0.55;
+    ex.r = 0.02;
+
+    /* target function f(x)
+     * x :: number
+     * returns :: number
+     */
+    ex.target_fn = function(x) {
+	return blackscholes.call_px(ex.strike, ex.tau, x, ex.vol, ex.r);
+    } /*target_fn*/
+
+    /* derivative f'(x) of fx.target_fn
+     * x :: number
+     * returns :: number
+     */
+    ex.target_deriv_fn = function(x) {
+	return blackscholes.call_delta(ex.strike, ex.tau, x, ex.vol, ex.r);
+    } /*target_deriv_fn*/
+
+    /* 2nd derivative f''(x) of fx.target_fn
+     * x :: number
+     * returns :: number
+     */
+    ex.target_deriv2_fn = function(x) {
+	return blackscholes.call_gamma(ex.strike, ex.tau, x, ex.vol, ex.r);
+    } /*target_deriv2_fn*/
+
+    /* w :: Window */
+    ex.start = function(w)
+    {
+	fx_view.init_sequence(ex.target_fn,
+			      ex.target_deriv_fn,
+			      ex.target_deriv2_fn,
+			      ex.box_pt, 200.0 /*scale_factor*/,
+			      +0.01 /*lo_x*/, +2.0 /*hi_x*/,
+			      0.0 /*lo_y*/, 1.0 /*hi_y*/,
+			      200 /*n_pt*/);
+	fx_view.draw("#frame");
+    }
+    
+    this.ex = ex;
+}();

option/blackscholes/point.js

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+../../d3/drag7/point.js

option/blackscholes/xyscale.js

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+../../d3/drag7/xyscale.js