added financial examples

Author: Chaluvadi

examples/financial/black_scholes_options.py

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+#!/usr/bin/python
+
+#######################################################
+# Copyright (c) 2024, ArrayFire
+# All rights reserved.
+#
+# This file is distributed under 3-clause BSD license.
+# The complete license agreement can be obtained at:
+# http://arrayfire.com/licenses/BSD-3-Clause
+########################################################
+
+import math
+import sys
+from time import time
+
+# TODO: Remove -1 from sync() after default value has been put in
+import arrayfire as af
+
+sqrt2 = math.sqrt(2.0)
+
+
+def cnd(x):
+    temp = x > 0
+    return temp * (0.5 + af.erf(x / sqrt2) / 2) + (1 - temp) * (0.5 - af.erf((-x) / sqrt2) / 2)
+
+
+def black_scholes(S, X, R, V, T):
+    # S = Underlying stock price
+    # X = Strike Price
+    # R = Risk free rate of interest
+    # V = Volatility
+    # T = Time to maturity
+
+    d1 = af.log(S / X)
+    d1 = d1 + (R + (V * V) * 0.5) * T
+    d1 = d1 / (V * af.sqrt(T))
+
+    d2 = d1 - (V * af.sqrt(T))
+    cnd_d1 = cnd(d1)
+    cnd_d2 = cnd(d2)
+
+    C = S * cnd_d1 - (X * af.exp((-R) * T) * cnd_d2)
+    P = X * af.exp((-R) * T) * (1 - cnd_d2) - (S * (1 - cnd_d1))
+
+    return (C, P)
+
+
+if __name__ == "__main__":
+    if len(sys.argv) > 1:
+        af.set_device(int(sys.argv[1]))
+    af.info()
+
+    M = 4000
+
+    S = af.randu((M, 1))
+    X = af.randu((M, 1))
+    R = af.randu((M, 1))
+    V = af.randu((M, 1))
+    T = af.randu((M, 1))
+
+    (C, P) = black_scholes(S, X, R, V, T)
+    af.eval(C)
+    af.eval(P)
+    af.sync(-1)
+
+    num_iter = 100
+    for N in range(50, 501, 50):
+        S = af.randu((M, N))
+        X = af.randu((M, N))
+        R = af.randu((M, N))
+        V = af.randu((M, N))
+        T = af.randu((M, N))
+        af.sync(-1)
+
+        print("Input data size: %d elements" % (M * N))
+
+        start = time()
+        for i in range(num_iter):
+            (C, P) = black_scholes(S, X, R, V, T)
+            af.eval(C)
+            af.eval(P)
+        af.sync(-1)
+        sec = (time() - start) / num_iter
+
+        print("Mean GPU Time: %0.6f ms\n\n" % (1000.0 * sec))

examples/financial/heston_model.py

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+#!/usr/bin/python
+
+##############################################################################################
+# Copyright (c) 2015, Michael Nowotny
+# All rights reserved.
+#
+# Redistribution and use in source and binary forms, with or without modification,
+# are permitted provided that the following conditions are met:
+#
+# 1. Redistributions of source code must retain the above copyright notice,
+# this list of conditions and the following disclaimer.
+#
+# 2. Redistributions in binary form must reproduce the above copyright notice,
+# this list of conditions and the following disclaimer in the documentation and/or other
+# materials provided with the distribution.
+#
+# 3. Neither the name of the copyright holder nor the names of its contributors may be used
+# to endorse or promote products derived from this software without specific
+# prior written permission.
+#
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+# A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+# OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
+# TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+# PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+# LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+###############################################################################################
+
+import math
+import time
+
+import arrayfire as af
+
+
+def simulateHestonModel(T, N, R, mu, kappa, vBar, sigmaV, rho, x0, v0):
+
+    deltaT = T / (float)(N - 1)
+
+    x = [af.constant(x0, (R,)), af.constant(0, (R,))]
+    v = [af.constant(v0, (R,)), af.constant(0, (R,))]
+
+    sqrtDeltaT = math.sqrt(deltaT)
+    sqrtOneMinusRhoSquare = math.sqrt(1 - rho**2)
+
+    m = af.constant(0, (2,))
+    m[0] = rho
+    m[1] = sqrtOneMinusRhoSquare
+    zeroArray = af.constant(0, (R, 1))
+
+    for t in range(1, N):
+        tPrevious = (t + 1) % 2
+        tCurrent = t % 2
+
+        dBt = af.randn((R, 2)) * 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 main():
+    T = 1
+    nT = 20 * T
+    R_first = 1000
+    R = 5000000
+
+    x0 = 0  # initial log stock price
+    v0 = 0.087**2  # initial volatility
+    r = math.log(1.0319)  # risk-free rate
+    rho = -0.82  # instantaneous correlation between Brownian motions
+    sigmaV = 0.14  # variance of volatility
+    kappa = 3.46  # mean reversion speed
+    vBar = 0.008  # mean variance
+    k = math.log(0.95)  # strike price
+
+    # first run
+    (x, v) = simulateHestonModel(T, nT, R_first, r, kappa, vBar, sigmaV, rho, x0, v0)
+
+    # Price plain vanilla call option
+    tic = time.time()
+    (x, v) = simulateHestonModel(T, nT, R, r, kappa, vBar, sigmaV, rho, x0, v0)
+    af.sync(-1)
+    toc = time.time() - tic
+    K = math.exp(k)
+    zeroConstant = af.constant(0, (R,))
+    C_CPU = math.exp(-r * T) * af.mean(af.maxof(af.exp(x) - K, zeroConstant))
+    print("Time elapsed = {} secs".format(toc))
+    print("Call price = {}".format(C_CPU))
+    print(af.mean(v))
+
+
+if __name__ == "__main__":
+    main()

examples/financial/monte_carlo_options.py

@@ -0,0 +1,66 @@
+#!/usr/bin/python
+
+#######################################################
+# Copyright (c) 2024, ArrayFire
+# All rights reserved.
+#
+# This file is distributed under 3-clause BSD license.
+# The complete license agreement can be obtained at:
+# http://arrayfire.com/licenses/BSD-3-Clause
+########################################################
+
+import math
+import sys
+from time import time
+
+import arrayfire as af
+
+
+def monte_carlo_options(N, K, t, vol, r, strike, steps, use_barrier=True, B=None, ty=af.float32):
+    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 monte_carlo_simulate(N, use_barrier, num_iter=10):
+    steps = 180
+    stock_price = 100.0
+    maturity = 0.5
+    volatility = 0.3
+    rate = 0.01
+    strike = 100
+    barrier = 115.0
+
+    start = time()
+    for i in range(num_iter):
+        monte_carlo_options(N, stock_price, maturity, volatility, rate, strike, steps, use_barrier, barrier)
+
+    return (time() - start) / num_iter
+
+
+if __name__ == "__main__":
+    if len(sys.argv) > 1:
+        af.set_device(int(sys.argv[1]))
+    af.info()
+
+    monte_carlo_simulate(1000, use_barrier=False)
+    monte_carlo_simulate(1000, use_barrier=True)
+    af.sync(-1)
+
+    for n in range(10000, 100001, 10000):
+        print(
+            "Time for %7d paths - vanilla method: %4.3f ms, barrier method: % 4.3f ms\n"
+            % (n, 1000 * monte_carlo_simulate(n, False, 100), 1000 * monte_carlo_simulate(n, True, 100))
+        )