bsm class

Author: yzoz

.gitignore

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+__pycache__

bsm.py

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+import math
+
+class BSM():
+
+    def pdf(self, x):
+        return math.exp(-x**2/2) / math.sqrt(2*math.pi)
+
+    def cdf(self, x):
+        return (1 + math.erf(x / math.sqrt(2))) / 2
+
+    def d1(self, S, K, V, T):
+        return (math.log(S / float(K)) + (V**2 / 2) * T) / (V * math.sqrt(T))
+
+    def d2(self, S, K, V, T):
+        return self.d1(S, K, V, T) - (V * math.sqrt(T))
+
+    def theo(self, S, K, V, T, dT):
+        if dT == 'C':
+            return S * self.cdf(self.d1(S, K, V, T)) - K * self.cdf(self.d2(S, K, V, T))
+        else:
+            return K * self.cdf(-self.d2(S, K, V, T)) - S * self.cdf(-self.d1(S, K, V, T))
+
+    def delta(self, S, K, V, T, dT):
+        if dT == 'C':
+            delta = self.cdf(self.d1(S, K, V, T))
+        elif dT == 'P':
+            delta = self.cdf(self.d1(S, K, V, T)) - 1
+        else:
+            delta = 1
+        return delta
+
+    def vega(self, S, K, V, T):
+        vega = (S * math.sqrt(T) * self.pdf(self.d1(S, K, V, T))) / 100
+        return vega
+
+    def theta(self, S, K, V, T):
+        theta = -((S * V * self.pdf(self.d1(S, K, V, T))) / (2 * math.sqrt(T))) / 365
+        return theta
+
+    def gamma(self, S, K, V, T):
+        gamma = self.pdf(self.d1(S, K, V, T))/(S * V * math.sqrt(T))
+        return gamma

one_example.py

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+from bsm import BSM
+
+calc = BSM()
+
+#Bitcoin example
+
+S = 21000 #Underlying (price now)
+K = 30000 #Strike
+V = 0.75 #Implied Volatility (1 / 100%)
+T = 30 / 365 #Expiration date (days from now / 365)
+dT = "C" #Call / Put
+
+print('Theo: ', round(calc.theo(S, K, V, T, dT), 2))
+print('Delta: ', round(calc.delta(S, K, V, T, dT), 2))
+print('Theta: ', round(calc.theta(S, K, V, T), 2))
+print('Vega: ', round(calc.vega(S, K, V, T), 2))
+print('Gamma: ', round(calc.gamma(S, K, V, T), 2))