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Created November 30, 2016 06:55
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Black and Scholes formula in JS
function bns() {
// Sample input
spot = 8400;
strike = 8600;
expiry = "2016-12-01 23:59:00";
volt = 18;
int_rate = 7;
div_yld = 0;
//Validation
var error=null;
if(isNaN(spot) || isNaN(strike) || isNaN(volt) || isNaN(int_rate)) {
error = "Invalid Values";
alert(error);
}
else if(spot < 0 || strike < 0) {
error = "Spot and Strike should be positive values";
alert(error);
}
else if(volt <0 || volt >100) {
error = "Voltality should be between 0 - 100";
alert(error);
}
else if(int_rate <0 || int_rate >100) {
error = "Interest rate should be between 0 - 100";
alert(error);
}
else {
expiry = expiry.replace(" ", "T");
var date_expiry = new Date(expiry),
date_now = new Date();
var seconds = Math.floor((date_expiry - (date_now))/1000),
minutes = Math.floor(seconds/60),
hours = Math.floor(minutes/60),
delta_t = (Math.floor(hours/24))/365.0;
volt = volt/100;
int_rate = int_rate/100;
if(hours < 24) {
error = "Please select a later date and time <br> Expiry should be minimum 24 hours from now";
alert(error);
}
else {
var d1 = (Math.log(spot/strike) + (int_rate + Math.pow(volt,2)/2) * delta_t) / (volt*Math.sqrt(delta_t)),
d2 = (Math.log(spot/strike) + (int_rate - Math.pow(volt,2)/2) * delta_t) / (volt*Math.sqrt(delta_t));
var fv_strike = (strike)*Math.exp(-1*int_rate*delta_t);
//For calculating CDF and PDF using gaussian library. You need gaussian.js library for this.
var distribution = gaussian(0, 1);
//Premium Price
var call_premium = spot * distribution.cdf(d1) - fv_strike * distribution.cdf(d2),
put_premium = fv_strike * distribution.cdf(-1*d2) - spot * distribution.cdf(-1*d1);
//Option greeks
var call_delta = distribution.cdf(d1),
put_delta = call_delta-1;
var call_gamma = distribution.pdf(d1)/(spot*volt*Math.sqrt(delta_t)),
put_gamma = call_gamma;
var call_vega = spot*distribution.pdf(d1)*Math.sqrt(delta_t)/100,
put_vega = call_vega;
var call_theta = (-1*spot*distribution.pdf(d1)*volt/(2*Math.sqrt(delta_t)) - int_rate*fv_strike*distribution.cdf(d2))/365,
put_theta = (-1*spot*distribution.pdf(d1)*volt/(2*Math.sqrt(delta_t)) + int_rate*fv_strike*distribution.cdf(-1*d2))/365;
var call_rho = fv_strike*delta_t*distribution.cdf(d2)/100,
put_rho = -1*fv_strike*delta_t*distribution.cdf(-1*d2)/100;
bns_results = {
"call_option_prem_value": call_premium.toFixed(2),
"put_option_prem_value": put_premium.toFixed(2),
"call_option_delta_value": call_delta.toFixed(3),
"put_option_delta_value": put_delta.toFixed(3),
"option_gamma_value": call_gamma.toFixed(4),
"call_option_theta_value": call_theta.toFixed(3),
"put_option_theta_value": put_theta.toFixed(3),
"call_option_rho_value": call_rho.toFixed(3),
"put_option_rho_value": put_rho.toFixed(3),
"option_vega_value": call_vega.toFixed(3)
}
}
}
console.log(bns_results);
return false;
}
bns();
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