SVM

QFin/__init__.py

@@ -1,6 +1,7 @@
 from qfin.options import BlackScholesCall
 from qfin.options import BlackScholesPut
 from qfin.simulations import GeometricBrownianMotion
+from qfin.simulations import StochasticVarianceModel
 from qfin.simulations import MonteCarloBinaryCall
 from qfin.simulations import MonteCarloBinaryPut
 from qfin.simulations import MonteCarloCall

QFin/simulations.py

@@ -1,4 +1,5 @@
 import numpy as np
+from scipy.stats import norm
 
 
 class GeometricBrownianMotion:
@@ -18,6 +19,35 @@ def __init__(self, S, mu, sigma, dt, T):
         self.simulated_path = self.simulate_path(S, mu, sigma, dt, T)
 
 
+class StochasticVarianceModel:
+
+    def simulate_path(self, S, mu, r, div, alpha, beta, rho, vol_var, inst_var, dt, T):
+        prices = []
+        price_now = S
+        inst_var_now = inst_var
+        prev_inst_var = inst_var_now
+        step = 0
+        while step < T:
+            e1 = norm.ppf(np.random.random())
+            e2 = e1*rho + np.sqrt(1-(rho**2))*norm.ppf(np.random.random())
+
+            price_now = price_now + (r - div) * price_now * dt + price_now * np.sqrt(prev_inst_var * dt) * e1
+            prev_inst_var = inst_var_now
+            inst_var_now = prev_inst_var + (alpha - beta*prev_inst_var)*dt + vol_var*np.sqrt(prev_inst_var*dt)*e2
+
+            # Avoid negative cases and floor variance at zero
+            if inst_var_now > .0000001:
+                pass
+            else:
+                inst_var_now = .0000001
+            prices.append(price_now)
+            step += dt
+        return prices
+
+    def __init__(self, S, mu, r, div, alpha, beta, rho, vol_var, inst_var, dt, T):
+        self.simulated_path = self.simulate_path(S, mu, r, div, alpha, beta, rho, vol_var, inst_var, dt, T)
+
+
 class MonteCarloCall:
 
     def simulate_price(self, strike, n, r, S, mu, sigma, dt, T):
@@ -92,3 +122,16 @@ class MonteCarloBarrierPut:
 
     def __init__(self):
         pass
+
+# 100 - initial underlying asset price
+# 0 - underlying asset drift (mu)
+# .01 - risk free rate of interest
+# .05 - continuous dividend
+# .5, 2 - (alpha, beta) mean reverting parameters
+# -.7 - (rho) correlation of errors generated
+# .3 - Variance's volatility
+# 1/52 - time steps (dt)
+# 1 - time to maturity (annum)
+svm = StochasticVarianceModel(100, 0, .01, .05, .5, 2, -.7, .3, .09, 1/52, 1)
+
+print(svm.simulated_path)

setup.py

@@ -6,7 +6,7 @@
     long_description = f.read()
 
 VERSION = '0.0.16'
-DESCRIPTION = 'A Python package for mathematical finance.'
+DESCRIPTION = 'A Python library for mathematical finance.'
 
 # Setting up
 setup(