Class: DhanHQ::OptionAnalytics::BlackScholes

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

Overview

Black-Scholes option pricing model for calculating theoretical option prices and Greeks.

Examples:

Calculate option price

price = DhanHQ::OptionAnalytics::BlackScholes.price(
  spot: 24000,
  strike: 24200,
  time_to_expiry: 0.038, # ~10 days
  risk_free_rate: 0.065,
  volatility: 0.15,
  option_type: :call
)

Class Method Summary collapse

Class Method Details

.greeks(spot:, strike:, time_to_expiry:, risk_free_rate:, volatility:, option_type:) ⇒ Hash

Calculate option Greeks (Delta, Gamma, Theta, Vega, Rho).

Parameters:

  • spot (Float) —

    Current spot price

  • strike (Float) —

    Strike price

  • time_to_expiry (Float) —

    Time to expiry in years

  • risk_free_rate (Float) —

    Risk-free interest rate (annualized)

  • volatility (Float) —

    Implied volatility (annualized)

  • option_type (Symbol) —

    :call or :put

Returns:

  • (Hash) —

    Hash with :delta, :gamma, :theta, :vega, :rho



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# File 'lib/DhanHQ/option_analytics/black_scholes.rb', line 50

def self.greeks(spot:, strike:, time_to_expiry:, risk_free_rate:, volatility:, option_type:)
  return empty_greeks if time_to_expiry <= 0

  d1 = calculate_d1(spot, strike, time_to_expiry, risk_free_rate, volatility)
  d2 = calculate_d2(d1, time_to_expiry, volatility)

  gamma = normal_pdf(d1) / (spot * volatility * Math.sqrt(time_to_expiry))

  theta = if option_type == :call
            calculate_call_theta(spot, strike, time_to_expiry, risk_free_rate, volatility, d1, d2)
          else
            calculate_put_theta(spot, strike, time_to_expiry, risk_free_rate, volatility, d1, d2)
          end

  vega = spot * normal_pdf(d1) * Math.sqrt(time_to_expiry) / 100

  rho = if option_type == :call
          calculate_call_rho(spot, strike, time_to_expiry, risk_free_rate, d2)
        else
          calculate_put_rho(spot, strike, time_to_expiry, risk_free_rate, d2)
        end

  {
    delta: calculate_delta(spot, strike, time_to_expiry, risk_free_rate, volatility, option_type),
    gamma: gamma,
    theta: theta / 365.0, # Daily theta
    vega: vega,
    rho: rho / 100.0
  }
end

.implied_volatility(market_price:, spot:, strike:, time_to_expiry:, risk_free_rate:, option_type:, tolerance: 0.0001, max_iterations: 100) ⇒ Float

Calculate implied volatility using Newton-Raphson method.

rubocop:disable Metrics/ParameterLists

Parameters:

  • market_price (Float) —

    Observed market price of the option

  • spot (Float) —

    Current spot price

  • strike (Float) —

    Strike price

  • time_to_expiry (Float) —

    Time to expiry in years

  • risk_free_rate (Float) —

    Risk-free interest rate (annualized)

  • option_type (Symbol) —

    :call or :put

  • tolerance (Float) (defaults to: 0.0001) —

    Convergence tolerance (default: 0.0001)

  • max_iterations (Integer) (defaults to: 100) —

    Maximum iterations (default: 100)

Returns:

  • (Float) —

    Implied volatility



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# File 'lib/DhanHQ/option_analytics/black_scholes.rb', line 93

def self.implied_volatility(market_price:, spot:, strike:, time_to_expiry:, risk_free_rate:, option_type:,
                            tolerance: 0.0001, max_iterations: 100)
  # rubocop:enable Metrics/ParameterLists
  return 0.0 if time_to_expiry <= 0 || market_price <= 0

  # Initial guess
  iv = 0.2
  max_iterations.times do
    theoretical_price = price(
      spot: spot, strike: strike, time_to_expiry: time_to_expiry,
      risk_free_rate: risk_free_rate, volatility: iv, option_type: option_type
    )

    diff = theoretical_price - market_price
    return iv if diff.abs < tolerance

    # Vega for Newton-Raphson
    vega = spot * normal_pdf(calculate_d1(spot, strike, time_to_expiry, risk_free_rate, iv)) *
           Math.sqrt(time_to_expiry)

    return iv if vega < 1e-10

    iv -= diff / vega
    iv = [iv, 0.001].max # Prevent negative volatility
  end

  iv
end

.price(spot:, strike:, time_to_expiry:, risk_free_rate:, volatility:, option_type:) ⇒ Float

Calculate theoretical option price using Black-Scholes model.

Parameters:

  • spot (Float) —

    Current spot price

  • strike (Float) —

    Strike price

  • time_to_expiry (Float) —

    Time to expiry in years

  • risk_free_rate (Float) —

    Risk-free interest rate (annualized)

  • volatility (Float) —

    Implied volatility (annualized)

  • option_type (Symbol) —

    :call or :put

Returns:

  • (Float) —

    Theoretical option price



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# File 'lib/DhanHQ/option_analytics/black_scholes.rb', line 28

def self.price(spot:, strike:, time_to_expiry:, risk_free_rate:, volatility:, option_type:)
  return 0.0 if time_to_expiry <= 0

  d1 = calculate_d1(spot, strike, time_to_expiry, risk_free_rate, volatility)
  d2 = calculate_d2(d1, time_to_expiry, volatility)

  if option_type == :call
    (spot * normal_cdf(d1)) - (strike * Math.exp(-risk_free_rate * time_to_expiry) * normal_cdf(d2))
  else
    (strike * Math.exp(-risk_free_rate * time_to_expiry) * normal_cdf(-d2)) - (spot * normal_cdf(-d1))
  end
end