Adding heston model example

Author: michaelnowotny

examples/financial/heston_model.py

@@ -0,0 +1,100 @@
+#!/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 arrayfire as af
+import math
+import time
+
+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 main():
+    T = 1
+    nT = 10 * T
+    R_first = 1000
+    R = 20000000
+
+    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()
+    toc = time.time() - tic
+    K = math.exp(k)
+    zeroConstant = af.constant(0, R, dtype=af.Dtype.f32)
+    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()