Module: Iro::OptionBlackScholes

Included in:
Option
Defined in:
app/models/iro/option_black_scholes.rb

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

.rate_annual ⇒ Object 



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# File 'app/models/iro/option_black_scholes.rb', line 128

def self.rate_annual
  0.05
end

.rate_daily ⇒ Object

# test

inn = 100 n.times { inn = inn*(1.0+out) } inn



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# File 'app/models/iro/option_black_scholes.rb', line 140

def self.rate_daily
  n = 250.0 # days
  # n = 12 # months

  out = (1.0+self.rate_annual)**(1.0/n) - 1.0
  puts! out, 'rate_daily'
  return out
end

Instance Method Details

#call_price ⇒ Object 



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# File 'app/models/iro/option_black_scholes.rb', line 111

def call_price
  last   = stock.last
  r      = self.class.rate_annual

  out = N.cdf( d1 ) * last - N.cdf( d2 ) * strike * Math::E**( -1 * r * t )
  return out
end

#d1 ⇒ Object

##

##
##
annual to daily:

AR = ((DR + 1)^365 – 1) x 100

##
##
##
From: https://www.investopedia.com/articles/optioninvestor/07/options_beat_market.asp

K :: strike price
S_t :: last
r :: risk-free rate
t :: time to maturity

C = S_t N( d1 ) - K e^-rt N( d2 )

d1 = ln( St / K ) + (r + theta**2 /  2 )t
  /{ theta_s * sqrt( t ) }

d2 = d1 - theta_s sqrt( t )

##
## From: https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model
##

D  ::  e^(rt)    # discount factor
F  ::  e^(rt) S  # forward price of underlying

C(F,t) = D[ N(d1)F - N(d2)K ]

d1 = ln(F/K) + stdev**2 t / 2
  /{ stdev sqrt(t) }
d2 = d1 - stdev sqrt(t)

##
## From: https://www.daytrading.com/options-pricing-models
##
C0 = S0N(d1) – Xe-rtN(d2)

C0 = current call premium
S0 = current stock price
N(d1) = the probability that a value in a normal distribution will be less than d
N(d2) = the probability that the option will be in the money by expiration
X = strike price of the option
T = time until expiration (expressed in years)
r = risk-free interest rate
e = 2.71828, the base of the natural logarithm
ln = natural logarithm function
σ = standard deviation of the stock’s annualized rate of return (compounded continuously)
d1 = ln(S0/X) + (r + σ2/2)Tσ√T

d2 = d1 – σ√T

Note that:

Xe-rt = X/ert = the present value of the strike price using a continuously compounded interest rate

##
## From: https://www.wallstreetmojo.com/black-scholes-model/
##

## init
require 'distribution'
N = Distribution::Normal
stock = Iro::Stock.find_by ticker: 'NVDA'
strike = 910.0
r = Iro::Option.rate_daily
stdev = 91.0
t = 7.0
expires_on = '2024-03-22'



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# File 'app/models/iro/option_black_scholes.rb', line 88

def d1
  last   = stock.last
  r      = self.class.rate_annual

  out = Math.log( last / strike ) + ( r + stdev**2 / 2 ) * t
  out = out /( stdev * Math.sqrt(t) )
  return out
end

#d2 ⇒ Object 



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# File 'app/models/iro/option_black_scholes.rb', line 96

def d2
  last   = stock.last
  r      = self.class.rate_annual

  out = d1 - stdev * Math.sqrt( t )
  return out
end

#put_price ⇒ Object 



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# File 'app/models/iro/option_black_scholes.rb', line 119

def put_price
  last   = stock.last
  r      = self.class.rate_annual

  out = N.cdf(-d2) * strike * exp(-r*t) - N.cdf(-d1) * last
  return out
end

#stdev ⇒ Object 



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# File 'app/models/iro/option_black_scholes.rb', line 107

def stdev
  recompute = nil
  stock.stdev( recompute: recompute )
end

#t ⇒ Object 



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# File 'app/models/iro/option_black_scholes.rb', line 103

def t
  # t      = 1.0 / 365 * Date.today.business_days_until( expires_on )
  t      = 1.0 / 365 * (expires_on - Date.today).to_i
end