Asian option pricing using 2D PDE (and Monte-Carlo) example

examples/PyMPDATA_examples/Arabas_and_Farhat_2020/fig_1.ipynb

@@ -67,7 +67,7 @@
    "outputs": [],
    "source": [
     "S = simulation.S\n",
-    "psi_T = simulation.terminal_value()\n",
+    "psi_T = simulation.state()\n",
     "psi_0 = simulation.run(n_iters=2)\n",
     "psi_a = settings.analytical_solution(S)"
    ]

examples/PyMPDATA_examples/Arabas_and_Farhat_2020/setup1_european_corridor.py

@@ -21,10 +21,11 @@ def __init__(self, *, n_iters: int = 2, l2_opt: int = 2, C_opt: float = 0.034):
         self.l2_opt = l2_opt
         self.C_opt = C_opt
 
+    def terminal_condition(self, S: np.ndarray):
+        return np.exp(-self.r * self.T) * self.payoff(S)
+
     def payoff(self, S: np.ndarray):
-        return np.exp(-self.r * self.T) * (
-            np.maximum(0, self.K2 - S) - np.maximum(0, self.K1 - S)
-        )
+        return np.maximum(0, self.K2 - S) - np.maximum(0, self.K1 - S)
 
     def analytical_solution(self, S: np.ndarray):
         return BS73.p_euro(

examples/PyMPDATA_examples/Arabas_and_Farhat_2020/simulation.py

@@ -108,5 +108,6 @@ def call(self, psi, step):
 
         return self.solvers[n_iters].advectee.get()
 
-    def terminal_value(self):
+    def state(self):
+        """returns the state for MPDATA solution"""
         return self.solvers[1].advectee.get()

examples/PyMPDATA_examples/Magnuszewski_et_al_2025/Mkhize_2007.py

@@ -0,0 +1,11 @@
+import numpy as np
+from scipy.stats import norm
+
+def geometric_mkhize(s_t=100, K=100, r=0.008, sigma=0.2, T=30, T_0=0):
+    d_1 = (np.log(s_t / K) + 0.5 * (r + (sigma ** 2) / 6) * (T - T_0)) / (sigma * np.sqrt((T - T_0) / 3))
+    d_2 = d_1 - sigma * np.sqrt((T - T_0) / 3)
+    C_0 = s_t * np.exp(-0.5 * (r + (sigma ** 2) / 6) * (T - T_0)) * norm.cdf(d_1) - K * np.exp(
+        -r * (T - T_0)) * norm.cdf(d_2)
+    P_0 = K * np.exp(-r * (T - T_0)) * norm.cdf(-d_2) - s_t * np.exp(
+        -0.5 * (r + (sigma ** 2) / 6) * (T - T_0)) * norm.cdf(-d_1)
+    return C_0