Module: OptionLab::BlackScholes

Defined in:
lib/option_lab/black_scholes.rb

Class Method Summary collapse

Class Method Details

.get_bs_info(s, x, r, vol, years_to_maturity, y = 0.0) ⇒ Models::BlackScholesInfo

Get all Black-Scholes info



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# File 'lib/option_lab/black_scholes.rb', line 226

def get_bs_info(s, x, r, vol, years_to_maturity, y = 0.0)
  d1 = get_d1(s, x, r, vol, years_to_maturity, y)
  d2 = get_d2(s, x, r, vol, years_to_maturity, y)

  call_price = get_option_price('call', s, x, r, years_to_maturity, d1, d2, y)
  put_price = get_option_price('put', s, x, r, years_to_maturity, d1, d2, y)
  call_delta = get_delta('call', d1, years_to_maturity, y)
  put_delta = get_delta('put', d1, years_to_maturity, y)
  call_theta = get_theta('call', s, x, r, vol, years_to_maturity, d1, d2, y)
  put_theta = get_theta('put', s, x, r, vol, years_to_maturity, d1, d2, y)
  gamma = get_gamma(s, vol, years_to_maturity, d1, y)
  vega = get_vega(s, years_to_maturity, d1, y)
  call_rho = get_rho('call', x, r, years_to_maturity, d2)
  put_rho = get_rho('put', x, r, years_to_maturity, d2)
  call_itm_prob = get_itm_probability('call', d2, years_to_maturity, y)
  put_itm_prob = get_itm_probability('put', d2, years_to_maturity, y)

  Models::BlackScholesInfo.new(
    call_price: call_price,
    put_price: put_price,
    call_delta: call_delta,
    put_delta: put_delta,
    call_theta: call_theta,
    put_theta: put_theta,
    gamma: gamma,
    vega: vega,
    call_rho: call_rho,
    put_rho: put_rho,
    call_itm_prob: call_itm_prob,
    put_itm_prob: put_itm_prob,
  )
end

.get_d1(s0, x, r, vol, years_to_maturity, y = 0.0) ⇒ Float, Numo::DFloat

Get d1 parameter for Black-Scholes formula



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# File 'lib/option_lab/black_scholes.rb', line 20

def get_d1(s0, x, r, vol, years_to_maturity, y = 0.0)
  # Handle edge cases
  return 0.0 if years_to_maturity <= 0.0 || vol <= 0.0

  numerator = Math.log(s0 / x) + (r - y + 0.5 * vol * vol) * years_to_maturity
  denominator = vol * Math.sqrt(years_to_maturity)
  numerator / denominator
end

.get_d2(s0, x, r, vol, years_to_maturity, y = 0.0) ⇒ Float, Numo::DFloat

Get d2 parameter for Black-Scholes formula



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# File 'lib/option_lab/black_scholes.rb', line 37

def get_d2(s0, x, r, vol, years_to_maturity, y = 0.0)
  # Handle edge cases
  return 0.0 if years_to_maturity <= 0.0 || vol <= 0.0

  d1 = get_d1(s0, x, r, vol, years_to_maturity, y)
  d1 - vol * Math.sqrt(years_to_maturity)
end

.get_delta(option_type, d1, years_to_maturity, y = 0.0) ⇒ Float, Numo::DFloat

Get option delta



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# File 'lib/option_lab/black_scholes.rb', line 81

def get_delta(option_type, d1, years_to_maturity, y = 0.0)
  yfac = Math.exp(-y * years_to_maturity)

  case option_type
  when 'call'
    yfac * Distribution::Normal.cdf(d1)
  when 'put'
    yfac * (Distribution::Normal.cdf(d1) - 1.0)
  else
    raise ArgumentError, "Option type must be either 'call' or 'put'!"
  end
end

.get_gamma(s0, vol, years_to_maturity, d1, y = 0.0) ⇒ Float, Numo::DFloat

Get option gamma



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# File 'lib/option_lab/black_scholes.rb', line 101

def get_gamma(s0, vol, years_to_maturity, d1, y = 0.0)
  yfac = Math.exp(-y * years_to_maturity)

  # PDF of d1
  cdf_d1_prime = Math.exp(-0.5 * d1 * d1) / Math.sqrt(2.0 * Math::PI)

  yfac * cdf_d1_prime / (s0 * vol * Math.sqrt(years_to_maturity))
end

.get_implied_vol(option_type, oprice, s0, x, r, years_to_maturity, y = 0.0) ⇒ Float

Get implied volatility



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# File 'lib/option_lab/black_scholes.rb', line 200

def get_implied_vol(option_type, oprice, s0, x, r, years_to_maturity, y = 0.0)
  # Start with volatilities from 0.001 to 1.0 in steps of 0.001
  volatilities = (1..1000).map { |i| i * 0.001 }

  # Calculate option prices for each volatility
  prices = volatilities.map do |vol|
    d1 = get_d1(s0, x, r, vol, years_to_maturity, y)
    d2 = get_d2(s0, x, r, vol, years_to_maturity, y)
    get_option_price(option_type, s0, x, r, years_to_maturity, d1, d2, y)
  end

  # Calculate absolute differences from market price
  diffs = prices.map { |price| (price - oprice).abs }

  # Return volatility with minimal difference
  volatilities[diffs.index(diffs.min)]
end

.get_itm_probability(option_type, d2, years_to_maturity, y = 0.0) ⇒ Float, Numo::DFloat

Get in-the-money probability



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# File 'lib/option_lab/black_scholes.rb', line 178

def get_itm_probability(option_type, d2, years_to_maturity, y = 0.0)
  yfac = Math.exp(-y * years_to_maturity)

  case option_type
  when 'call'
    yfac * Distribution::Normal.cdf(d2)
  when 'put'
    yfac * Distribution::Normal.cdf(-d2)
  else
    raise ArgumentError, "Option type must be either 'call' or 'put'!"
  end
end

.get_option_price(option_type, s0, x, r, years_to_maturity, d1, d2, y = 0.0) ⇒ Float, Numo::DFloat

Get option price using Black-Scholes formula



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# File 'lib/option_lab/black_scholes.rb', line 55

def get_option_price(option_type, s0, x, r, years_to_maturity, d1, d2, y = 0.0)
  # First validate option type
  unless ['call', 'put'].include?(option_type)
    raise ArgumentError, "Option type must be either 'call' or 'put'!"
  end

  # Calculate normally
  s = s0 * Math.exp(-y * years_to_maturity)
  discount_factor = Math.exp(-r * years_to_maturity)

  case option_type
  when 'call'
    # Call option price: S * N(d1) - X * e^(-rT) * N(d2)
    (s * Distribution::Normal.cdf(d1)) - (x * discount_factor * Distribution::Normal.cdf(d2))
  when 'put'
    # Put option price: X * e^(-rT) * N(-d2) - S * N(-d1)
    (x * discount_factor * Distribution::Normal.cdf(-d2)) - (s * Distribution::Normal.cdf(-d1))
  end
end

.get_rho(option_type, x, r, years_to_maturity, d2) ⇒ Float, Numo::DFloat

Get option rho



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# File 'lib/option_lab/black_scholes.rb', line 161

def get_rho(option_type, x, r, years_to_maturity, d2)
  case option_type
  when 'call'
    x * years_to_maturity * Math.exp(-r * years_to_maturity) * Distribution::Normal.cdf(d2) / 100
  when 'put'
    -x * years_to_maturity * Math.exp(-r * years_to_maturity) * Distribution::Normal.cdf(-d2) / 100
  else
    raise ArgumentError, "Option type must be either 'call' or 'put'!"
  end
end

.get_theta(option_type, s0, x, r, vol, years_to_maturity, d1, d2, y = 0.0) ⇒ Float, Numo::DFloat

Get option theta



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# File 'lib/option_lab/black_scholes.rb', line 121

def get_theta(option_type, s0, x, r, vol, years_to_maturity, d1, d2, y = 0.0)
  s = s0 * Math.exp(-y * years_to_maturity)

  # PDF of d1
  cdf_d1_prime = Math.exp(-0.5 * d1 * d1) / Math.sqrt(2.0 * Math::PI)

  common_term = -(s * vol * cdf_d1_prime / (2.0 * Math.sqrt(years_to_maturity)))

  case option_type
  when 'call'
    common_term - (r * x * Math.exp(-r * years_to_maturity) * Distribution::Normal.cdf(d2)) + (y * s * Distribution::Normal.cdf(d1))
  when 'put'
    common_term + (r * x * Math.exp(-r * years_to_maturity) * Distribution::Normal.cdf(-d2)) - (y * s * Distribution::Normal.cdf(-d1))
  else
    raise ArgumentError, "Option type must be either 'call' or 'put'!"
  end
end

.get_vega(s0, years_to_maturity, d1, y = 0.0) ⇒ Float, Numo::DFloat

Get option vega



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# File 'lib/option_lab/black_scholes.rb', line 145

def get_vega(s0, years_to_maturity, d1, y = 0.0)
  s = s0 * Math.exp(-y * years_to_maturity)

  # PDF of d1
  cdf_d1_prime = Math.exp(-0.5 * d1 * d1) / Math.sqrt(2.0 * Math::PI)

  s * cdf_d1_prime * Math.sqrt(years_to_maturity) / 100
end