Class: BlackScholes

Inherits:
Object
  • Object
show all
Defined in:
lib/black_scholes.rb

Overview

JavaScript adopted from Bernt Arne Odegaard’s Financial Numerical Recipes

http://finance.bi.no/~bernt/gcc_prog/algoritms/algoritms/algoritms.html
by Steve Derezinski, CXWeb, Inc.  http://www.cxweb.com
Copyright (C) 1998  Steve Derezinski, Bernt Arne Odegaard

This program is free software; you can redistribute it and/or
modify it under the terms of the GNU General Public License
as published by the Free Software Foundation.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.
http://www.fsf.org/copyleft/gpl.html

Class Method Summary collapse

Class Method Details

.black_scholes(call, s, x, r, v, t) ⇒ Object 



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# File 'lib/black_scholes.rb', line 45

def black_scholes(call,s,x,r,v,t)
  # call = Boolean (to calc call, call=True, put: call=false)
  # s = stock prics, x = strike price, r = no-risk interest rate
  # v = volitility (1 std dev of s for (1 yr? 1 month?, you pick)
  # t = time to maturity

  sqt = Math.sqrt(t)

  d1 = (Math.log(s/x) + r*t)/(v*sqt) + 0.5*(v*sqt)
  d2 = d1 - (v*sqt)

  if call
    delta = n(d1)
    nd2 = n(d2)
  else # put
    delta = -n(-d1)
    nd2 = -n(-d2)
  end

  ert = Math.exp(-r*t)
  nd1 = ndist(d1)

  gamma = nd1/(s*v*sqt)
  vega = s*sqt*nd1
  theta = -(s*v*nd1)/(2*sqt) - r*x*ert*nd2
  rho = x*t*ert*nd2

  s*delta-x*ert*nd2
end

.call_iv(s, x, r, t, o) ⇒ Object 



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# File 'lib/black_scholes.rb', line 100

def call_iv(s,x,r,t,o)
  option_implied_volatility(true,s,x,r/100.0,t/365.0,o)
end

.n(z) ⇒ Object 



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# File 'lib/black_scholes.rb', line 22

def n(z)
  b1 =  0.31938153
  b2 = -0.356563782
  b3 =  1.781477937
  b4 = -1.821255978
  b5 =  1.330274429
  p  =  0.2316419
  c2 =  0.3989423

  a = z.abs

  return 1.0 if a > 6.0

  t = 1.0/(1.0+a*p)
  b = c2*Math.exp((-z)*(z/2.0))
  n = ((((b5*t+b4)*t+b3)*t+b2)*t+b1)*t
  n = 1.0-b*n

  n = 1.0 - n if z < 0.0

  n
end

.ndist(z) ⇒ Object 



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# File 'lib/black_scholes.rb', line 18

def ndist(z)
  (1.0/(Math.sqrt(2*Math::PI)))*Math.exp(-0.5*z)
end

.option_implied_volatility(call, s, x, r, t, o) ⇒ Object 



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# File 'lib/black_scholes.rb', line 75

def option_implied_volatility(call,s,x,r,t,o)
  # call = Boolean (to calc call, call=True, put: call=false)
  # s = stock prics, x = strike price, r = no-risk interest rate
  # t = time to maturity
  # o = option price

  sqt = Math.sqrt(t)
  accuracy = 0.0001

  sigma = (o/s)/(0.398*sqt)

  100.times do
    price = black_scholes(call,s,x,r,sigma,t)
    diff = o-price

    return sigma if diff.abs < accuracy

    d1 = (Math.log(s/x) + r*t)/(sigma*sqt) + 0.5*sigma*sqt
    vega = s*sqt*ndist(d1)
    sigma = sigma+diff/vega
  end

  raise "Failed to converge"
end

.probability(price, target, days, volatility) ⇒ Object

Returns probability of occuring below and above target price.



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# File 'lib/black_scholes.rb', line 105

def probability(price, target, days, volatility)
  p = price.to_f
  q = target.to_f
  t = days / 365.0
  v = volatility.to_f

  vt = v*Math.sqrt(t)
  lnpq = Math.log(q/p)

  d1 = lnpq / vt

  y = (1/(1+0.2316419*d1.abs)*100000).floor / 100000.0
  z = (0.3989423*Math.exp(-((d1*d1)/2))*100000).floor / 100000.0

  y5 = 1.330274*(y**5)
  y4 = 1.821256*(y**4)
  y3 = 1.781478*(y**3)
  y2 = 0.356538*(y**2)
  y1 = 0.3193815*y

  x = 1-z*(y5-y4+y3-y2+y1)

  x = (x*100000).floor / 100000.0

  x = 1-x if d1 < 0

  pbelow = (x*1000).floor / 10.0
  pabove = ((1-x)*1000).floor / 10.0;

  [pbelow/100,pabove/100];
end

.probability_above(price, target, days, volatility) ⇒ Object 



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# File 'lib/black_scholes.rb', line 137

def probability_above(price, target, days, volatility)
  probability(price, target, days, volatility)[1]
end

.probability_below(price, target, days, volatility) ⇒ Object 



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# File 'lib/black_scholes.rb', line 141

def probability_below(price, target, days, volatility)
  probability(price, target, days, volatility)[0]
end