def random_empty_book(maturity, dimension, rate, drift, volatility, seed=None):
tf.random.set_seed(seed)
rate = float(rate)
drift = _fit_to_dimension(dimension, drift)
volatility = _fit_to_dimension(dimension, volatility)
# scale diffusion to have row norms equal to volatility
diffusion = tf.random.uniform((dimension, dimension), minval=-1, maxval=1)
norm = tf.linalg.norm(diffusion, axis=1)
diffusion *= (volatility / norm)[:, tf.newaxis]
init_instruments = _fit_to_dimension(dimension, 100.0)
init_numeraire = tf.constant([1.0], FLOAT_DTYPE)
instrument_simulator = simulators.GBM(rate, drift, diffusion)
numeraire_simulator = simulators.ConstantBankAccount(rate)
book = books.DerivativeBook(
maturity, instrument_simulator, numeraire_simulator)
return init_instruments, init_numeraire, book
def random_basket_book(maturity, dimension, volatility, seed=None):
tf.random.set_seed(seed)
volatility = _fit_to_dimension(dimension, volatility)
spot = strike = 1.0
# scale diffusion to have row norms equal to volatility
diffusion = tf.random.uniform((dimension, dimension), minval=-1, maxval=1)
norm = tf.linalg.norm(diffusion, axis=1)
diffusion *= (volatility / norm)[:, tf.newaxis]
init_instruments = _fit_to_dimension(dimension, spot)
init_numeraire = tf.constant([1.0], FLOAT_DTYPE)
instrument_simulator = simulators.BrownianMotion(diffusion)
numeraire_simulator = simulators.ConstantBankAccount(0.0)
book = books.BasketBook(
maturity, instrument_simulator, numeraire_simulator)
weights = tf.random.uniform((dimension, ))
derivative = derivatives.BachelierBasketCall(
maturity, strike, diffusion, weights)
book.add_derivative(derivative, 0, 1.0)
return init_instruments, init_numeraire, book
cost = False
spot = 1
strike = 1
timesteps = 14
sigma = 0.2
maturity = timesteps / 250
if cost:
instrument_simulator = simulators.GBM(0.0, 0.0, [[sigma]])
derivative = derivatives.PutCall(maturity, strike, 0.0, sigma, 1)
else:
instrument_simulator = BrownianMotion(sigma)
derivative = BachelierBinary(maturity, strike, sigma)
numeraire_simulator = simulators.ConstantBankAccount(0.0)
book = books.DerivativeBook(maturity, instrument_simulator,
numeraire_simulator)
book.add_derivative(derivative, 0, 1.0)
init_instruments = tf.constant([spot], FLOAT_DTYPE)
init_numeraire = tf.constant([1.0], FLOAT_DTYPE)
driver = utils.HedgeDriver(
timesteps=timesteps,
frequency=0, # no need for frequency for non-path dependent derivatives.
init_instruments=init_instruments,
init_numeraire=init_numeraire,
book=book,