def simulateHestonModel( T, N, R, mu, kappa, vBar, sigmaV, rho, x0, v0 ) :
deltaT = T / (float)(N - 1)
x = [af.constant(x0, R, dtype=af.Dtype.f32), af.constant(0, R, dtype=af.Dtype.f32)]
v = [af.constant(v0, R, dtype=af.Dtype.f32), af.constant(0, R, dtype=af.Dtype.f32)]
sqrtDeltaT = math.sqrt(deltaT)
sqrtOneMinusRhoSquare = math.sqrt(1-rho**2)
m = af.constant(0, 2, dtype=af.Dtype.f32)
m[0] = rho
m[1] = sqrtOneMinusRhoSquare
zeroArray = af.constant(0, R, 1, dtype=af.Dtype.f32)
for t in range(1, N) :
tPrevious = (t + 1) % 2
tCurrent = t % 2
dBt = af.randn(R, 2, dtype=af.Dtype.f32) * sqrtDeltaT
vLag = af.maxof(v[tPrevious], zeroArray)
sqrtVLag = af.sqrt(vLag)
x[tCurrent] = x[tPrevious] + (mu - 0.5 * vLag) * deltaT + sqrtVLag * dBt[:, 0]
v[tCurrent] = vLag + kappa * (vBar - vLag) * deltaT + sigmaV * (sqrtVLag * af.matmul(dBt, m))
return (x[tCurrent], af.maxof(v[tCurrent], zeroArray))
def monte_carlo_options(N,
K,
t,
vol,
r,
strike,
steps,
use_barrier=True,
B=None,
ty=af.Dtype.f32):
payoff = af.constant(0, N, 1, dtype=ty)
dt = t / float(steps - 1)
s = af.constant(strike, N, 1, dtype=ty)
randmat = af.randn(N, steps - 1, dtype=ty)
randmat = af.exp((r - (vol * vol * 0.5)) * dt +
vol * math.sqrt(dt) * randmat)
S = af.product(af.join(1, s, randmat), 1)
if (use_barrier):
S = S * af.all_true(S < B, 1)
payoff = af.maxof(0, S - K)
return af.mean(payoff) * math.exp(-r * t)
def simple_random(verbose=False):
display_func = _util.display_func(verbose)
display_func(af.randu(3, 3, 1, 2))
display_func(af.randu(3, 3, 1, 2, af.Dtype.b8))
display_func(af.randu(3, 3, dtype=af.Dtype.c32))
display_func(af.randn(3, 3, 1, 2))
display_func(af.randn(3, 3, dtype=af.Dtype.c32))
af.set_seed(1024)
assert (af.get_seed() == 1024)
engine = af.Random_Engine(af.RANDOM_ENGINE.MERSENNE_GP11213, 100)
display_func(af.randu(3, 3, 1, 2, engine=engine))
display_func(af.randu(3, 3, 1, 2, af.Dtype.s32, engine=engine))
display_func(af.randu(3, 3, dtype=af.Dtype.c32, engine=engine))
display_func(af.randn(3, 3, engine=engine))
engine.set_seed(100)
assert (engine.get_seed() == 100)
def simple_random(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
display_func(af.randu(3, 3, 1, 2))
display_func(af.randu(3, 3, 1, 2, af.Dtype.b8))
display_func(af.randu(3, 3, dtype=af.Dtype.c32))
display_func(af.randn(3, 3, 1, 2))
display_func(af.randn(3, 3, dtype=af.Dtype.c32))
af.set_seed(1024)
assert(af.get_seed() == 1024)
engine = af.Random_Engine(af.RANDOM_ENGINE.MERSENNE_GP11213, 100)
display_func(af.randu(3, 3, 1, 2, engine=engine))
display_func(af.randu(3, 3, 1, 2, af.Dtype.s32, engine=engine))
display_func(af.randu(3, 3, dtype=af.Dtype.c32, engine=engine))
display_func(af.randn(3, 3, engine=engine))
engine.set_seed(100)
assert(engine.get_seed() == 100)
def gamma_rand_marsaglia_and_tsang_arrayfire(alpha: float,
lambda_: float,
n: int) \
-> af.array:
random_numbers = af.constant(0, n, dtype=Dtype.f32)
# Gamma(alpha, lambda) generator using Marsaglia and Tsang method
# Algorithm 4.33
if alpha >= 1.0:
d = alpha - 1 / 3
c = 1.0 / np.sqrt(9.0 * d)
number_generated = 0
number_generated_total = 0
while number_generated < n:
number_left = n - number_generated
z = af.randn(number_left, dtype=Dtype.f32)
y = (1.0 + c * z)
v = y * y * y
accept_index_1 = ((z >= -1.0 / c) & (v > 0.0))
z_accept_1 = z[accept_index_1]
# del z
v_accept_1 = v[accept_index_1]
# del v
u_accept_1 = af.randu(v_accept_1.elements(), dtype=Dtype.f32)
# del U
accept_index_2 = \
u_accept_1 < af.exp((0.5 * z_accept_1 * z_accept_1 + d - d * v_accept_1 + d * af.log(v_accept_1)))
x_accept = d * v_accept_1[accept_index_2] / lambda_
number_accept = x_accept.elements()
random_numbers[number_generated:np.minimum(n, number_generated + number_accept)] = \
x_accept[0:np.minimum(number_left, number_accept)]
number_generated += number_accept
number_generated_total += number_left
if GPUOptions.verbose:
print(f"Acceptance ratio = {n/number_generated_total}")
else:
random_numbers = gamma_rand_marsaglia_and_tsang_arrayfire(
alpha + 1, lambda_, n)
random_numbers *= af.randu(n, dtype=Dtype.f32)**(1.0 / alpha)
return random_numbers
def monte_carlo_options(N, K, t, vol, r, strike, steps, use_barrier = True, B = None, ty = af.Dtype.f32):
payoff = af.constant(0, N, 1, dtype = ty)
dt = t / float(steps - 1)
s = af.constant(strike, N, 1, dtype = ty)
randmat = af.randn(N, steps - 1, dtype = ty)
randmat = af.exp((r - (vol * vol * 0.5)) * dt + vol * math.sqrt(dt) * randmat);
S = af.product(af.join(1, s, randmat), 1)
if (use_barrier):
S = S * af.all_true(S < B, 1)
payoff = af.maxof(0, S - K)
return af.mean(payoff) * math.exp(-r * t)
def simulateHestonModel(T, N, R, mu, kappa, vBar, sigmaV, rho, x0, v0):
deltaT = T / (float)(N - 1)
x = [
af.constant(x0, R, dtype=af.Dtype.f32),
af.constant(0, R, dtype=af.Dtype.f32)
]
v = [
af.constant(v0, R, dtype=af.Dtype.f32),
af.constant(0, R, dtype=af.Dtype.f32)
]
sqrtDeltaT = math.sqrt(deltaT)
sqrtOneMinusRhoSquare = math.sqrt(1 - rho**2)
m = af.constant(0, 2, dtype=af.Dtype.f32)
m[0] = rho
m[1] = sqrtOneMinusRhoSquare
zeroArray = af.constant(0, R, 1, dtype=af.Dtype.f32)
for t in range(1, N):
tPrevious = (t + 1) % 2
tCurrent = t % 2
dBt = af.randn(R, 2, dtype=af.Dtype.f32) * sqrtDeltaT
vLag = af.maxof(v[tPrevious], zeroArray)
sqrtVLag = af.sqrt(vLag)
x[tCurrent] = x[tPrevious] + (
mu - 0.5 * vLag) * deltaT + sqrtVLag * dBt[:, 0]
v[tCurrent] = vLag + kappa * (vBar - vLag) * deltaT + sigmaV * (
sqrtVLag * af.matmul(dBt, m))
return (x[tCurrent], af.maxof(v[tCurrent], zeroArray))
import arrayfire as af af.display(af.constant(100, 3,3, dtype=af.f32)) af.display(af.constant(25, 3,3, dtype=af.c32)) af.display(af.constant(2**50, 3,3, dtype=af.s64)) af.display(af.constant(2+3j, 3,3)) af.display(af.constant(3+5j, 3,3, dtype=af.c32)) af.display(af.range(3, 3)) af.display(af.iota(3, 3, tile_dims=(2,2))) af.display(af.randu(3, 3, 1, 2)) af.display(af.randu(3, 3, 1, 2, af.b8)) af.display(af.randu(3, 3, dtype=af.c32)) af.display(af.randn(3, 3, 1, 2)) af.display(af.randn(3, 3, dtype=af.c32)) af.set_seed(1024) assert(af.get_seed() == 1024) af.display(af.identity(3, 3, 1, 2, af.b8)) af.display(af.identity(3, 3, dtype=af.c32)) a = af.randu(3, 4) b = af.diag(a, extract=True) c = af.diag(a, 1, extract=True) af.display(a) af.display(b) af.display(c)
import arrayfire as af af.print_array(af.constant(100, 3,3, dtype=af.f32)) af.print_array(af.constant(25, 3,3, dtype=af.c32)) af.print_array(af.constant(2**50, 3,3, dtype=af.s64)) af.print_array(af.constant(2+3j, 3,3)) af.print_array(af.constant(3+5j, 3,3, dtype=af.c32)) af.print_array(af.range(3, 3)) af.print_array(af.iota(3, 3, tile_dims=(2,2))) af.print_array(af.randu(3, 3, 1, 2)) af.print_array(af.randu(3, 3, 1, 2, af.b8)) af.print_array(af.randu(3, 3, dtype=af.c32)) af.print_array(af.randn(3, 3, 1, 2)) af.print_array(af.randn(3, 3, dtype=af.c32)) af.set_seed(1024) assert(af.get_seed() == 1024) af.print_array(af.identity(3, 3, 1, 2, af.b8)) af.print_array(af.identity(3, 3, dtype=af.c32)) a = af.randu(3, 4) b = af.diag(a, extract=True) c = af.diag(a, 1, extract=True) af.print_array(a) af.print_array(b) af.print_array(c)
def simple_data(verbose=False):
display_func = _util.display_func(verbose)
print_func = _util.print_func(verbose)
display_func(af.constant(100, 3,3, dtype=af.Dtype.f32))
display_func(af.constant(25, 3,3, dtype=af.Dtype.c32))
display_func(af.constant(2**50, 3,3, dtype=af.Dtype.s64))
display_func(af.constant(2+3j, 3,3))
display_func(af.constant(3+5j, 3,3, dtype=af.Dtype.c32))
display_func(af.range(3, 3))
display_func(af.iota(3, 3, tile_dims=(2,2)))
display_func(af.randu(3, 3, 1, 2))
display_func(af.randu(3, 3, 1, 2, af.Dtype.b8))
display_func(af.randu(3, 3, dtype=af.Dtype.c32))
display_func(af.randn(3, 3, 1, 2))
display_func(af.randn(3, 3, dtype=af.Dtype.c32))
af.set_seed(1024)
assert(af.get_seed() == 1024)
display_func(af.identity(3, 3, 1, 2, af.Dtype.b8))
display_func(af.identity(3, 3, dtype=af.Dtype.c32))
a = af.randu(3, 4)
b = af.diag(a, extract=True)
c = af.diag(a, 1, extract=True)
display_func(a)
display_func(b)
display_func(c)
display_func(af.diag(b, extract = False))
display_func(af.diag(c, 1, extract = False))
display_func(af.join(0, a, a))
display_func(af.join(1, a, a, a))
display_func(af.tile(a, 2, 2))
display_func(af.reorder(a, 1, 0))
display_func(af.shift(a, -1, 1))
display_func(af.moddims(a, 6, 2))
display_func(af.flat(a))
display_func(af.flip(a, 0))
display_func(af.flip(a, 1))
display_func(af.lower(a, False))
display_func(af.lower(a, True))
display_func(af.upper(a, False))
display_func(af.upper(a, True))
a = af.randu(5,5)
display_func(af.transpose(a))
af.transpose_inplace(a)
display_func(a)
display_func(af.select(a > 0.3, a, -0.3))
af.replace(a, a > 0.3, -0.3)
display_func(a)
