Module: PureGreeks::Engines::CrrBinomialAmerican

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

Constant Summary collapse

DEFAULT_STEPS = 
200

Class Method Summary collapse

Class Method Details

.backward_induct(type, strike, spot, steps, params) ⇒ Object 



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# File 'lib/pure_greeks/engines/crr_binomial_american.rb', line 83

def backward_induct(type, strike, spot, steps, params)
  backward_induct_with_intermediates(type, strike, spot, steps, params)[:price]
end

.backward_induct_with_intermediates(type, strike, spot, steps, params) ⇒ Object 



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# File 'lib/pure_greeks/engines/crr_binomial_american.rb', line 87

def backward_induct_with_intermediates(type, strike, spot, steps, params)
  u = params[:u]
  d = params[:d]
  p = params[:p]
  disc = params[:disc]
  sign = type == :call ? 1.0 : -1.0

  values = Array.new(steps + 1)
  (0..steps).each do |j|
    spot_at_leaf = spot * (u**(steps - j)) * (d**j)
    values[j] = [0.0, sign * (spot_at_leaf - strike)].max
  end

  step2 = nil
  step1 = nil

  (steps - 1).downto(0) do |i|
    (0..i).each do |j|
      continuation = disc * (p * values[j] + (1 - p) * values[j + 1])
      spot_at_node = spot * (u**(i - j)) * (d**j)
      intrinsic = [0.0, sign * (spot_at_node - strike)].max
      values[j] = [continuation, intrinsic].max
    end
    step2 = values[0..2].dup if i == 2
    step1 = values[0..1].dup if i == 1
  end

  { price: values[0], step1: step1, step2: step2 }
end

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



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# File 'lib/pure_greeks/engines/crr_binomial_american.rb', line 21

def calculate(type:, strike:, underlying_price:, time_to_expiry:, implied_volatility:,
              risk_free_rate:, dividend_yield:, steps: DEFAULT_STEPS)
  params = tree_parameters(
    time_to_expiry: time_to_expiry,
    steps: steps,
    implied_volatility: implied_volatility,
    risk_free_rate: risk_free_rate,
    dividend_yield: dividend_yield
  )
  result = backward_induct_with_intermediates(type, strike, underlying_price, steps, params)
  price = result[:price]
  v_step1 = result[:step1]
  v_step2 = result[:step2]
  u = params[:u]
  d = params[:d]

  delta = (v_step1[0] - v_step1[1]) / (underlying_price * u - underlying_price * d)

  s_uu = underlying_price * u * u
  s_ud = underlying_price * u * d
  s_dd = underlying_price * d * d
  delta_upper = (v_step2[0] - v_step2[1]) / (s_uu - s_ud)
  delta_lower = (v_step2[1] - v_step2[2]) / (s_ud - s_dd)
  gamma = (delta_upper - delta_lower) / (0.5 * (s_uu - s_dd))

  theta = (v_step2[1] - price) / (2.0 * params[:dt]) / 365.0

  bumped_vol_params = tree_parameters(
    time_to_expiry: time_to_expiry,
    steps: steps,
    implied_volatility: implied_volatility + 0.01,
    risk_free_rate: risk_free_rate,
    dividend_yield: dividend_yield
  )
  price_vol_up = backward_induct_with_intermediates(type, strike, underlying_price, steps, bumped_vol_params)[:price]
  vega = (price_vol_up - price) / (0.01 * 100.0)

  bumped_rate_params = tree_parameters(
    time_to_expiry: time_to_expiry,
    steps: steps,
    implied_volatility: implied_volatility,
    risk_free_rate: risk_free_rate + 0.01,
    dividend_yield: dividend_yield
  )
  price_rate_up = backward_induct_with_intermediates(type, strike, underlying_price, steps, bumped_rate_params)[:price]
  rho = (price_rate_up - price) / (0.01 * 100.0)

  Greeks.new(
    delta: delta,
    gamma: gamma,
    theta: theta,
    vega: vega,
    rho: rho,
    price: price,
    model: :crr_binomial_american
  )
end

.price(**args) ⇒ Object 



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# File 'lib/pure_greeks/engines/crr_binomial_american.rb', line 79

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

.tree_parameters(time_to_expiry:, steps:, implied_volatility:, risk_free_rate:, dividend_yield:) ⇒ Object 



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# File 'lib/pure_greeks/engines/crr_binomial_american.rb', line 12

def tree_parameters(time_to_expiry:, steps:, implied_volatility:, risk_free_rate:, dividend_yield:)
  dt = time_to_expiry / steps.to_f
  u = ::Math.exp(implied_volatility * ::Math.sqrt(dt))
  d = 1.0 / u
  p = (::Math.exp((risk_free_rate - dividend_yield) * dt) - d) / (u - d)
  disc = ::Math.exp(-risk_free_rate * dt)
  { dt: dt, u: u, d: d, p: p, disc: disc }
end