gnm3000 · July 20, 2021 17:12 · Jul 20, 2021 · Jul 20, 2021
diff --git a/Cox-Ross-Rubinstein-binomial-option-pricing.py b/Cox-Ross-Rubinstein-binomial-option-pricing.py
@@ -1,26 +1,28 @@
+from math import sqrt, exp
+import pydotplus as pydot
 import numpy as np
-from numpy import exp,sqrt
+
 class Call(object):
     def __init__(self, S0, K, rate, sigma, n_periods, tyears):
-        self.S0 = S0
-        self.K = K
+        self.S0 = S0 # Today's stock price
+        self.K = K # Strike Price
         self.rate = rate
         self.sigma = sigma
         self.tyears = tyears
         self.n_periods = n_periods
         self.up_factor = exp(self.sigma * sqrt(self.tyears / self.n_periods))
         self.down_factor = 1 / self.up_factor
+        self.tree = self.option_tree()
+        self.option_price = self.tree["option_tree"][0][0]
+
     def option_tree(self):
-        num = (np.exp(self.rate * self.tyears / self.n_periods) - self.down_factor)
-        den = (self.up_factor - self.down_factor)
-        p =  num / den 
-
+        p = (np.exp(self.rate * self.tyears / self.n_periods) - self.down_factor) / (self.up_factor - self.down_factor)
+
         # Option Payoff
         contingent_payoff = lambda st, k: max(st - k, 0)
         contingent_payoff = np.vectorize(contingent_payoff)
-
-        # Creating the branches at different times of the tree.
-        # Each branch is the possible martingale price
+
+        # Creating the branches at different times of the tree. Each branch is the possible martingale price
         # of the stock at time t
         stock_price_tree = []
         for i in range(1,self.n_periods+1):
@@ -29,36 +31,71 @@ def option_tree(self):
             for j in range(i+1):
                 up_factor_repeat = i-j
                 down_factor_repeat = j
-        
-                values = np.append(np.repeat(self.up_factor, up_factor_repeat),
-                                    np.repeat(self.down_factor, down_factor_repeat))
+
+                values = np.append(np.repeat(self.up_factor, up_factor_repeat), 
+                        np.repeat(self.down_factor, down_factor_repeat))
                 stock_price = values.prod() * self.S0
                 period_prices.append(stock_price)
             stock_price_tree.append(period_prices)
-        
+
         # Getting the payoff of the call at the end of the tree
         payoffs = contingent_payoff(stock_price_tree[self.n_periods-1], self.K).tolist()
-        
+
         option_prices = [payoffs]
         # Contingent option price at period n-1
         branch_n = payoffs # brach at n-1
-        
+
         for t in range(self.n_periods):
             branch_nm1 = []
-        for i in range(len(branch_n)-1):
-            #cu: Contingent price at time n if price rises
-            #cd: Contingent price at time n if price decreases
-            cu, cd = np.array(branch_n)[[i, i+1]]
-        price = np.exp(-self.rate * self.tyears / self.n_periods)*(p*cu + (1-p)*cd)
-        branch_nm1.append(price)
-        option_prices.append(branch_nm1)
-        branch_n = branch_nm1
-        
-        option_prices = option_prices[::-1]
+            for i in range(len(branch_n)-1):
+                #cu: Contingent price at time n if price rises
+                #cd: Contingent price at time n if price decreases
+                cu, cd = np.array(branch_n)[[i, i+1]]
+                price = np.exp(-self.rate * self.tyears / self.n_periods)*(p*cu + (1-p)*cd)
+                branch_nm1.append(price)
+            option_prices.append(branch_nm1)
+            branch_n = branch_nm1
+
+        option_prices = option_prices[::-1] 
         stock_price_tree.insert(0, [self.S0])
-        
+
         return {"stock_tree": stock_price_tree,
                 "option_tree": option_prices}
+
+    def graph_tree(self, file_name = ""):
+        option_prices = self.tree["option_tree"]
+        stock_price_tree = self.tree["stock_tree"]
+
+        graph = pydot.Dot(graph_type='digraph', rankdir='LR')
 
+        branch = 0
+        counter = 1
+        for i, prices in enumerate(option_prices[:-1]):
+            next_prices = option_prices[i+1]
+            for np, c_price in enumerate(prices):
+                c_price = str(round(c_price,2))
+
+                nprice1 = str(round(next_prices[np], 2))
+                nprice2 = str(round(next_prices[np+1], 2))
+
+                increment = len(prices)-1
+                from_branch, to_branch1, to_branch2 = branch, counter + increment, counter + increment + 1
+                #print(from_branch,"->",to_branch1, to_branch2)
+
+                up_price = round(stock_price_tree[i][np] * self.up_factor, 2)
+                down_price = round(stock_price_tree[i][np] * self.down_factor, 2)
+                edge = pydot.Edge(from_branch, to_branch1, label = str(up_price)); graph.add_edge(edge)
+                edge = pydot.Edge(from_branch, to_branch2, label = str(down_price)); graph.add_edge(edge)
+
+                node = pydot.Node(to_branch1, label = str(nprice1)); graph.add_node(node)
+                node = pydot.Node(to_branch2, label = str(nprice2)); graph.add_node(node)
+
+                counter += 1
+                branch += 1
+
+        c0 = round(self.option_price, 2)
+        node = pydot.Node("0", label = str(c0)); graph.add_node(node)
+        graph.write_png(file_name)
 a=Call(S0=100,K=90,rate=0.001,sigma=0.001,n_periods=1,tyears=0.01)
-print(a.option_tree())
+print(a.option_tree())
+a.graph_tree(file_name="filename.png")
diff --git a/Cox-Ross-Rubinstein-binomial-option-pricing.py b/Cox-Ross-Rubinstein-binomial-option-pricing.py
@@ -0,0 +1,64 @@
+import numpy as np
+from numpy import exp,sqrt
+class Call(object):
+    def __init__(self, S0, K, rate, sigma, n_periods, tyears):
+        self.S0 = S0
+        self.K = K
+        self.rate = rate
+        self.sigma = sigma
+        self.tyears = tyears
+        self.n_periods = n_periods
+        self.up_factor = exp(self.sigma * sqrt(self.tyears / self.n_periods))
+        self.down_factor = 1 / self.up_factor
+    def option_tree(self):
+        num = (np.exp(self.rate * self.tyears / self.n_periods) - self.down_factor)
+        den = (self.up_factor - self.down_factor)
+        p =  num / den 
+
+        # Option Payoff
+        contingent_payoff = lambda st, k: max(st - k, 0)
+        contingent_payoff = np.vectorize(contingent_payoff)
+
+        # Creating the branches at different times of the tree.
+        # Each branch is the possible martingale price
+        # of the stock at time t
+        stock_price_tree = []
+        for i in range(1,self.n_periods+1):
+            # Number of prices per period
+            period_prices = []
+            for j in range(i+1):
+                up_factor_repeat = i-j
+                down_factor_repeat = j
+
+                values = np.append(np.repeat(self.up_factor, up_factor_repeat),
+                                    np.repeat(self.down_factor, down_factor_repeat))
+                stock_price = values.prod() * self.S0
+                period_prices.append(stock_price)
+            stock_price_tree.append(period_prices)
+
+        # Getting the payoff of the call at the end of the tree
+        payoffs = contingent_payoff(stock_price_tree[self.n_periods-1], self.K).tolist()
+
+        option_prices = [payoffs]
+        # Contingent option price at period n-1
+        branch_n = payoffs # brach at n-1
+
+        for t in range(self.n_periods):
+            branch_nm1 = []
+        for i in range(len(branch_n)-1):
+            #cu: Contingent price at time n if price rises
+            #cd: Contingent price at time n if price decreases
+            cu, cd = np.array(branch_n)[[i, i+1]]
+        price = np.exp(-self.rate * self.tyears / self.n_periods)*(p*cu + (1-p)*cd)
+        branch_nm1.append(price)
+        option_prices.append(branch_nm1)
+        branch_n = branch_nm1
+
+        option_prices = option_prices[::-1]
+        stock_price_tree.insert(0, [self.S0])
+
+        return {"stock_tree": stock_price_tree,
+                "option_tree": option_prices}
+
+a=Call(S0=100,K=90,rate=0.001,sigma=0.001,n_periods=1,tyears=0.01)
+print(a.option_tree())