[arrayfire] 180/408: Added new example: heston_model in financial

[Ghislain Vaillant]

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ghisvail-guest pushed a commit to branch debian/sid
in repository arrayfire.

commit 3cedee7e7077ca4f1d72f2a291af2c5c3a012574
Author: Michael Nowotny <nowotnym at gmail.com>
Date:   Fri Jul 24 12:11:29 2015 -0400

    Added new example: heston_model in financial
---
 examples/financial/heston_model.cpp | 115 ++++++++++++++++++++++++++++++++++++
 1 file changed, 115 insertions(+)

diff --git a/examples/financial/heston_model.cpp b/examples/financial/heston_model.cpp
new file mode 100644
index 0000000..617e04b
--- /dev/null
+++ b/examples/financial/heston_model.cpp
@@ -0,0 +1,115 @@
+/**********************************************************************************************
+ * 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.
+***********************************************************************************************/
+
+#include <iostream>
+#include <arrayfire.h>
+#include <vector>
+#include <tuple>
+
+using namespace std;
+using namespace af;
+
+tuple<af::array, af::array>
+simulateHestonModel(float T, unsigned int N, unsigned int R, float mu, float kappa,
+                    float vBar, float sigmaV, float rho, float x0, float v0)
+{
+    float deltaT = T / (float)(N - 1);
+
+    std::vector<af::array> x = {af::constant(x0, R), af::constant(0, R)};
+    std::vector<af::array> v = {af::constant(v0, R), af::constant(0, R)};
+
+    float sqrtDeltaT = sqrt(deltaT);
+
+    float sqrtOneMinusRhoSquare = sqrt(1 - rho*rho);
+
+    float mArray[] = {rho, sqrtOneMinusRhoSquare};
+    af::array m(2, 1, mArray);
+
+    unsigned int tPrevious = 0, tCurrent = 0;
+    af::array zeroConstant = constant(0, R);
+
+    for (unsigned int t = 1; t < N; t++) {
+        tPrevious = (t+1) % 2;
+        tCurrent = t % 2;
+
+        af::array dBt = randn(R, 2) * sqrtDeltaT;
+        af::array sqrtVLag = af::sqrt(v[tPrevious]);
+
+        x[tCurrent]= x[tPrevious] + (mu - 0.5 * v[tPrevious]) * deltaT + (sqrtVLag * dBt(span, 0));
+        af::array vTmp = v[tPrevious] + kappa * (vBar - v[tPrevious]) * deltaT + sigmaV * (sqrtVLag * matmul(dBt, m));
+        v[tCurrent] = max(vTmp, zeroConstant);
+    }
+
+    return std::make_tuple(x[tCurrent], v[tCurrent]);
+}
+
+int main()
+{
+    float T = 1;
+    unsigned int nT = 10 * T;
+    unsigned int R_first_run = 1000;
+    unsigned int R = 20000000;
+
+    float x0 = 0; // initial log stock price
+    float v0 = pow(0.087, 2); // initial volatility
+    float r = log(1.0319); // risk-free rate
+    float rho = -0.82; // instantaneous correlation between Brownian motions
+    float sigmaV = 0.14; // variance of volatility
+    float kappa = 3.46; // mean reversion speed
+    float vBar = 0.008; // mean variance
+    float k = log(0.95); // strike price
+
+
+    // Price European call option
+    try {
+        af::array x;
+        af::array v;
+
+        // first run
+        std::tie(x, v) = simulateHestonModel(T, nT, R_first_run, r, kappa, vBar, sigmaV, rho, x0, v0);
+        af::sync(); // Ensure the first run is finished
+
+        timer::start();
+        std::tie(x, v) = simulateHestonModel(T, nT, R, r, kappa, vBar, sigmaV, rho, x0, v0);
+        af::sync();
+        cout << "Time in simulation: " << timer::stop() << endl;
+
+        af::array K = exp(constant(k, x.dims()));
+        af::array zeroConstant = constant(0, x.dims());
+        af::array C_CPU = exp(-r * T) * mean(af::max(af::exp(x) - K, zeroConstant));
+
+        af_print(C_CPU);
+        return 0;
+    } catch (af::exception& e) {
+        fprintf(stderr, "%s\n", e.what());
+        return 1;
+    }
+}

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