Module: OptionLab::Support

Defined in:
lib/option_lab/support.rb

Class Method Summary collapse

Class Method Details

._get_array_price_from_BS(inputs, n) ⇒ Numo::DFloat (private)

Generate array of prices using Black-Scholes model

Parameters:

Returns:

  • (Numo::DFloat) —

    Array of prices



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# File 'lib/option_lab/support.rb', line 437

def _get_array_price_from_BS(inputs, n)
  # Calculate mean and std
  mean = Math.log(inputs.stock_price) + 
         (inputs.interest_rate - inputs.dividend_yield - 0.5 * inputs.volatility**2) * 
         inputs.years_to_target_date
  std = inputs.volatility * Math.sqrt(inputs.years_to_target_date)
  
  # Generate random values
  random_values = Numo::DFloat.new(n).rand_norm(0, 1)
  
  # Apply formula
  Numo::NMath.exp(mean + std * random_values)
end

._get_array_price_from_laplace(inputs, n) ⇒ Numo::DFloat (private)

Generate array of prices using Laplace distribution

Parameters:

Returns:

  • (Numo::DFloat) —

    Array of prices



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# File 'lib/option_lab/support.rb', line 455

def _get_array_price_from_laplace(inputs, n)
  # Calculate location and scale
  location = Math.log(inputs.stock_price) + inputs.mu * inputs.years_to_target_date
  scale = (inputs.volatility * Math.sqrt(inputs.years_to_target_date)) / Math.sqrt(2.0)
  
  # Generate random values from uniform distribution
  u = Numo::DFloat.new(n).rand - 0.5
  
  # Convert to Laplace distribution
  laplace_values = location - scale * u.abs.map { |v| v < 0 ? -1 : 1 } * Numo::NMath.log(1 - 2 * u.abs)
  
  # Apply formula
  Numo::NMath.exp(laplace_values)
end

._get_payoff(option_type, s, x) ⇒ Numo::DFloat (private)

Calculate option payoff at expiration

Parameters:

  • option_type (String) —

    'call' or 'put'

  • s (Numo::DFloat) —

    Array of stock prices

  • x (Float) —

    Strike price

Returns:

  • (Numo::DFloat) —

    Option payoff



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# File 'lib/option_lab/support.rb', line 225

def _get_payoff(option_type, s, x)
  if option_type == 'call'
    diff = s - x
    (diff + diff.abs) / 2.0
  elsif option_type == 'put'
    diff = x - s
    (diff + diff.abs) / 2.0
  else
    raise ArgumentError, "Option type must be either 'call' or 'put'!"
  end
end

._get_pl_option(option_type, opvalue, action, s, x) ⇒ Numo::DFloat (private)

Calculate P/L of an option at expiration

Parameters:

  • option_type (String) —

    'call' or 'put'

  • opvalue (Float) —

    Option price

  • action (String) —

    'buy' or 'sell'

  • s (Numo::DFloat) —

    Array of stock prices

  • x (Float) —

    Strike price

Returns:

  • (Numo::DFloat) —

    P/L profile



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# File 'lib/option_lab/support.rb', line 210

def _get_pl_option(option_type, opvalue, action, s, x)
  if action == 'sell'
    opvalue - _get_payoff(option_type, s, x)
  elsif action == 'buy'
    _get_payoff(option_type, s, x) - opvalue
  else
    raise ArgumentError, "Action must be either 'sell' or 'buy'!"
  end
end

._get_pl_stock(s0, action, s) ⇒ Numo::DFloat (private)

Calculate P/L of a stock position

Parameters:

  • s0 (Float) —

    Spot price

  • action (String) —

    'buy' or 'sell'

  • s (Numo::DFloat) —

    Array of stock prices

Returns:

  • (Numo::DFloat) —

    P/L profile



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# File 'lib/option_lab/support.rb', line 242

def _get_pl_stock(s0, action, s)
  if action == 'sell'
    s0 - s
  elsif action == 'buy'
    s - s0
  else
    raise ArgumentError, "Action must be either 'sell' or 'buy'!"
  end
end

._get_pop_array(inputs, target) ⇒ Array<Float, Float, Float, Float> (private)

Calculate PoP using array of terminal prices

Parameters:

Returns:

  • (Array<Float, Float, Float, Float>) —

    PoP calculation results



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# File 'lib/option_lab/support.rb', line 312

def _get_pop_array(inputs, target)
  if inputs.array.size == 0
    raise ArgumentError, "The array is empty!"
  end
  
  # Split array by target
  above_target = inputs.array[inputs.array >= target]
  below_target = inputs.array[inputs.array < target]
  
  # Calculate probabilities
  probability_of_reaching_target = above_target.size.to_f / inputs.array.size
  probability_of_missing_target = 1.0 - probability_of_reaching_target
  
  # Calculate expected returns
  expected_return_above_target = above_target.size > 0 ? above_target.mean.round(2) : nil
  expected_return_below_target = below_target.size > 0 ? below_target.mean.round(2) : nil
  
  [
    probability_of_reaching_target,
    expected_return_above_target,
    probability_of_missing_target,
    expected_return_below_target
  ]
end

._get_pop_bs(s, profit, inputs, profit_range) ⇒ Array<Float, Float, Float, Float> (private)

Calculate PoP using Black-Scholes model

Parameters:

  • s (Numo::DFloat) —

    Array of stock prices

  • profit (Numo::DFloat) —

    Array of profits

  • inputs (Models::BlackScholesModelInputs) —

    Model inputs

  • profit_range (Array<Array<Array<Float>>>) —

    Profit and loss ranges

Returns:

  • (Array<Float, Float, Float, Float>) —

    PoP calculation results



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# File 'lib/option_lab/support.rb', line 258

def _get_pop_bs(s, profit, inputs, profit_range)
  # Initialize variables
  expected_return_above_target = nil
  expected_return_below_target = nil
  probability_of_reaching_target = 0.0
  probability_of_missing_target = 0.0
  
  # Calculate sigma
  sigma = inputs.volatility > 0.0 ? 
    inputs.volatility * Math.sqrt(inputs.years_to_target_date) : 1e-10
  
  # Calculate PoP for each range
  profit_range.each_with_index do |t, i|
    prob = 0.0
    
    if t != [[0.0, 0.0]]
      t.each do |p_range|
        # Calculate log values
        lval = p_range[0] > 0.0 ? Math.log(p_range[0]) : -Float::INFINITY
        hval = Math.log(p_range[1])
        
        # Calculate drift and mean
        drift = (
          inputs.interest_rate - 
          inputs.dividend_yield - 
          0.5 * inputs.volatility * inputs.volatility
        ) * inputs.years_to_target_date
        
        m = Math.log(inputs.stock_price) + drift
        
        # Calculate probability
        prob += Distribution::Normal.cdf((hval - m) / sigma) - Distribution::Normal.cdf((lval - m) / sigma)
      end
    end
    
    if i == 0
      probability_of_reaching_target = prob
    else
      probability_of_missing_target = prob
    end
  end
  
  [
    probability_of_reaching_target,
    expected_return_above_target,
    probability_of_missing_target,
    expected_return_below_target
  ]
end

._get_profit_range(s, profit, target = 0.01) ⇒ Array<Array<Array<Float>>> (private)

Find profit/loss ranges

Parameters:

  • s (Numo::DFloat) —

    Array of stock prices

  • profit (Numo::DFloat) —

    Array of profits

  • target (Float) (defaults to: 0.01) —

    Profit target

Returns:

  • (Array<Array<Array<Float>>>) —

    Profit and loss ranges



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# File 'lib/option_lab/support.rb', line 342

def _get_profit_range(s, profit, target = 0.01)
  profit_range = []
  loss_range = []
  
  # Find where profit crosses target
  crossings = _get_sign_changes(profit, target)
  n_crossings = crossings.size
  
  # Handle case with no crossings
  if n_crossings == 0
    if profit[0] >= target
      return [[[0.0, Float::INFINITY]], [[0.0, 0.0]]]
    else
      return [[[0.0, 0.0]], [[0.0, Float::INFINITY]]]
    end
  end
  
  # Find profit and loss ranges
  lb_profit = hb_profit = nil
  lb_loss = hb_loss = nil
  
  crossings.each_with_index do |index, i|
    if i == 0
      if profit[index] < profit[index - 1]
        lb_profit = 0.0
        hb_profit = s[index - 1]
        lb_loss = s[index]
        
        hb_loss = Float::INFINITY if n_crossings == 1
      else
        lb_profit = s[index]
        lb_loss = 0.0
        hb_loss = s[index - 1]
        
        hb_profit = Float::INFINITY if n_crossings == 1
      end
    elsif i == n_crossings - 1
      if profit[index] > profit[index - 1]
        lb_profit = s[index]
        hb_profit = Float::INFINITY
        hb_loss = s[index - 1]
      else
        hb_profit = s[index - 1]
        lb_loss = s[index]
        hb_loss = Float::INFINITY
      end
    else
      if profit[index] > profit[index - 1]
        lb_profit = s[index]
        hb_loss = s[index - 1]
      else
        hb_profit = s[index - 1]
        lb_loss = s[index]
      end
    end
    
    if lb_profit && hb_profit
      profit_range << [lb_profit, hb_profit]
      lb_profit = hb_profit = nil
    end
    
    if lb_loss && hb_loss
      loss_range << [lb_loss, hb_loss]
      lb_loss = hb_loss = nil
    end
  end
  
  [profit_range, loss_range]
end

._get_sign_changes(profit, target) ⇒ Array<Integer> (private)

Find indices where profit crosses target

Parameters:

  • profit (Numo::DFloat) —

    Array of profits

  • target (Float) —

    Profit target

Returns:

  • (Array<Integer>) —

    Array of indices



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# File 'lib/option_lab/support.rb', line 416

def _get_sign_changes(profit, target)
  # Subtract target and add small epsilon
  p_temp = profit - target + 1e-10
  
  # Get signs (convert to array first since Numo::DFloat doesn't have collect)
  signs_1 = p_temp[0...-1].to_a.map { |v| v > 0 ? 1 : -1 }
  signs_2 = p_temp[1..-1].to_a.map { |v| v > 0 ? 1 : -1 }
  
  # Find sign changes
  changes = []
  signs_1.each_with_index do |s1, i|
    changes << i + 1 if s1 * signs_2[i] < 0
  end
  
  changes
end

.create_price_array(inputs_data, n: 100_000, seed: nil) ⇒ Numo::DFloat

Create price array for simulations

Parameters:

Returns:

  • (Numo::DFloat) —

    Array of prices



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# File 'lib/option_lab/support.rb', line 169

def create_price_array(inputs_data, n: 100_000, seed: nil)
  # Set random seed if provided
  Kernel.srand(seed) if seed
  
  # Convert hash to appropriate model if needed
  inputs = if inputs_data.is_a?(Hash)
            if %w[black-scholes normal].include?(inputs_data[:model] || inputs_data['model'])
              Models::BlackScholesModelInputs.new(inputs_data)
            elsif (inputs_data[:model] || inputs_data['model']) == 'laplace'
              Models::LaplaceInputs.new(inputs_data)
            else
              raise ArgumentError, "Invalid model type!"
            end
          else
            inputs_data
          end
  
  # Generate array based on model
  arr = if inputs.is_a?(Models::BlackScholesModelInputs)
          _get_array_price_from_BS(inputs, n)
        elsif inputs.is_a?(Models::LaplaceInputs)
          _get_array_price_from_laplace(inputs, n)
        else
          raise ArgumentError, "Invalid inputs type!"
        end
  
  # Reset random seed
  Kernel.srand if seed
  
  arr
end

.create_price_seq(min_price, max_price) ⇒ Numo::DFloat

Generate a sequence of stock prices from min to max with $0.01 increment

Parameters:

  • min_price (Float) —

    Minimum stock price

  • max_price (Float) —

    Maximum stock price

Returns:

  • (Numo::DFloat) —

    Array of sequential stock prices



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# File 'lib/option_lab/support.rb', line 100

def create_price_seq(min_price, max_price)
  cache_key = "#{min_price}-#{max_price}"
  
  # Return cached result if available
  return @price_seq_cache[cache_key] if @price_seq_cache.key?(cache_key)
  
  if max_price > min_price
    # Create array with increment 0.01
    steps = ((max_price - min_price) * 100 + 1).to_i
    arr = Numo::DFloat.new(steps).seq(min_price, 0.01)
    
    # Round to 2 decimal places (Numo::DFloat doesn't support arguments to round)
    arr = arr.round
    
    # Cache the result
    @price_seq_cache[cache_key] = arr
    
    arr
  else
    raise ArgumentError, "Maximum price cannot be less than minimum price!"
  end
end

.get_pl_profile(option_type, action, x, val, n, s, commission = 0.0) ⇒ Array<Numo::DFloat, Float>

Get profit/loss profile and cost of an options trade at expiration

Parameters:

  • option_type (String) —

    'call' or 'put'

  • action (String) —

    'buy' or 'sell'

  • x (Float) —

    Strike price

  • val (Float) —

    Option price

  • n (Integer) —

    Number of options

  • s (Numo::DFloat) —

    Array of stock prices

  • commission (Float) (defaults to: 0.0) —

    Brokerage commission

Returns:

  • (Array<Numo::DFloat, Float>) —

    P/L profile and cost



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# File 'lib/option_lab/support.rb', line 21

def get_pl_profile(option_type, action, x, val, n, s, commission = 0.0)
  if action == 'buy'
    cost = -val
  elsif action == 'sell'
    cost = val
  else
    raise ArgumentError, "Action must be either 'buy' or 'sell'!"
  end
  
  if Models::OPTION_TYPES.include?(option_type)
    [
      n * _get_pl_option(option_type, val, action, s, x) - commission,
      n * cost - commission
    ]
  else
    raise ArgumentError, "Option type must be either 'call' or 'put'!"
  end
end

.get_pl_profile_bs(option_type, action, x, val, r, target_to_maturity_years, volatility, n, s, y = 0.0, commission = 0.0) ⇒ Array<Numo::DFloat, Float>

Get profit/loss profile and cost of an options trade before expiration using Black-Scholes

Parameters:

  • option_type (String) —

    'call' or 'put'

  • action (String) —

    'buy' or 'sell'

  • x (Float) —

    Strike price

  • val (Float) —

    Option price

  • r (Float) —

    Risk-free interest rate

  • target_to_maturity_years (Float) —

    Time remaining to maturity from target date

  • volatility (Float) —

    Volatility

  • n (Integer) —

    Number of options

  • s (Numo::DFloat) —

    Array of stock prices

  • y (Float) (defaults to: 0.0) —

    Dividend yield

  • commission (Float) (defaults to: 0.0) —

    Brokerage commission

Returns:

  • (Array<Numo::DFloat, Float>) —

    P/L profile and cost



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# File 'lib/option_lab/support.rb', line 75

def get_pl_profile_bs(option_type, action, x, val, r, target_to_maturity_years, volatility, n, s, y = 0.0, commission = 0.0)
  if action == 'buy'
    cost = -val
    factor = 1
  elsif action == 'sell'
    cost = val
    factor = -1
  else
    raise ArgumentError, "Action must be either 'buy' or 'sell'!"
  end
  
  # Calculate prices using Black-Scholes
  d1 = BlackScholes.get_d1(s, x, r, volatility, target_to_maturity_years, y)
  d2 = BlackScholes.get_d2(s, x, r, volatility, target_to_maturity_years, y)
  calc_price = BlackScholes.get_option_price(option_type, s, x, r, target_to_maturity_years, d1, d2, y)
  
  profile = factor * n * (calc_price - val) - commission
  
  [profile, n * cost - commission]
end

.get_pl_profile_stock(s0, action, n, s, commission = 0.0) ⇒ Array<Numo::DFloat, Float>

Get profit/loss profile and cost of a stock position

Parameters:

  • s0 (Float) —

    Initial stock price

  • action (String) —

    'buy' or 'sell'

  • n (Integer) —

    Number of shares

  • s (Numo::DFloat) —

    Array of stock prices

  • commission (Float) (defaults to: 0.0) —

    Brokerage commission

Returns:

  • (Array<Numo::DFloat, Float>) —

    P/L profile and cost



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# File 'lib/option_lab/support.rb', line 47

def get_pl_profile_stock(s0, action, n, s, commission = 0.0)
  if action == 'buy'
    cost = -s0
  elsif action == 'sell'
    cost = s0
  else
    raise ArgumentError, "Action must be either 'buy' or 'sell'!"
  end
  
  [
    n * _get_pl_stock(s0, action, s) - commission,
    n * cost - commission
  ]
end

.get_pop(s, profit, inputs_data, target = 0.01) ⇒ Models::PoPOutputs

Estimate probability of profit

Parameters:

Returns:



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# File 'lib/option_lab/support.rb', line 129

def get_pop(s, profit, inputs_data, target = 0.01)
  # Initialize variables
  probability_of_reaching_target = 0.0
  probability_of_missing_target = 0.0
  expected_return_above_target = nil
  expected_return_below_target = nil
  
  # Get profit ranges
  t_ranges = _get_profit_range(s, profit, target)
  
  reaching_target_range = t_ranges[0] == [[0.0, 0.0]] ? [] : t_ranges[0]
  missing_target_range = t_ranges[1] == [[0.0, 0.0]] ? [] : t_ranges[1]
  
  # Calculate PoP based on inputs model
  if inputs_data.is_a?(Models::BlackScholesModelInputs)
    probability_of_reaching_target, expected_return_above_target,
    probability_of_missing_target, expected_return_below_target = 
      _get_pop_bs(s, profit, inputs_data, t_ranges)
  elsif inputs_data.is_a?(Models::ArrayInputs)
    probability_of_reaching_target, expected_return_above_target,
    probability_of_missing_target, expected_return_below_target = 
      _get_pop_array(inputs_data, target)
  end
  
  # Return outputs
  Models::PoPOutputs.new(
    probability_of_reaching_target: probability_of_reaching_target,
    probability_of_missing_target: probability_of_missing_target,
    reaching_target_range: reaching_target_range,
    missing_target_range: missing_target_range,
    expected_return_above_target: expected_return_above_target,
    expected_return_below_target: expected_return_below_target
  )
end