Module: PureGreeks::Engines::BlackScholesEuropean

Defined in:
lib/pure_greeks/engines/black_scholes_european.rb

Class Method Summary collapse

Class Method Details

.calculate(type:, strike:, underlying_price:, time_to_expiry:, implied_volatility:, risk_free_rate:, dividend_yield:) ⇒ Object 



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# File 'lib/pure_greeks/engines/black_scholes_european.rb', line 11

def calculate(type:, strike:, underlying_price:, time_to_expiry:, implied_volatility:, risk_free_rate:, dividend_yield:)
  d1, d2 = d1_d2(strike, underlying_price, time_to_expiry, implied_volatility, risk_free_rate, dividend_yield)
  sqrt_t = ::Math.sqrt(time_to_expiry)
  s_disc = underlying_price * ::Math.exp(-dividend_yield * time_to_expiry)
  k_disc = strike * ::Math.exp(-risk_free_rate * time_to_expiry)
  nd1 = Math::Normal.cdf(d1)
  nd2 = Math::Normal.cdf(d2)
  n_neg_d1 = Math::Normal.cdf(-d1)
  n_neg_d2 = Math::Normal.cdf(-d2)
  pdf_d1 = Math::Normal.pdf(d1)

  price = type == :call ? s_disc * nd1 - k_disc * nd2 : k_disc * n_neg_d2 - s_disc * n_neg_d1
  delta = if type == :call
            ::Math.exp(-dividend_yield * time_to_expiry) * nd1
          else
            -::Math.exp(-dividend_yield * time_to_expiry) * n_neg_d1
          end
  gamma = ::Math.exp(-dividend_yield * time_to_expiry) * pdf_d1 / (underlying_price * implied_volatility * sqrt_t)

  theta_year =
    if type == :call
      -s_disc * pdf_d1 * implied_volatility / (2 * sqrt_t) -
        risk_free_rate * k_disc * nd2 +
        dividend_yield * s_disc * nd1
    else
      -s_disc * pdf_d1 * implied_volatility / (2 * sqrt_t) +
        risk_free_rate * k_disc * n_neg_d2 -
        dividend_yield * s_disc * n_neg_d1
    end

  vega_unit = s_disc * pdf_d1 * sqrt_t
  rho_unit = type == :call ? k_disc * time_to_expiry * nd2 : -k_disc * time_to_expiry * n_neg_d2

  Greeks.new(
    delta: delta,
    gamma: gamma,
    theta: theta_year / 365.0,
    vega: vega_unit / 100.0,
    rho: rho_unit / 100.0,
    price: price,
    model: :black_scholes_european
  )
end

.d1_d2(strike, spot, t, sigma, r, q) ⇒ Object 



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# File 'lib/pure_greeks/engines/black_scholes_european.rb', line 59

def d1_d2(strike, spot, t, sigma, r, q)
  sqrt_t = ::Math.sqrt(t)
  d1 = (::Math.log(spot / strike) + (r - q + 0.5 * sigma**2) * t) / (sigma * sqrt_t)
  d2 = d1 - sigma * sqrt_t
  [d1, d2]
end

.price(**args) ⇒ Object 



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# File 'lib/pure_greeks/engines/black_scholes_european.rb', line 55

def price(**args)
  calculate(**args).price
end