R to Python

QID-2273-SFEbsprices/Metainfo.txt

@@ -12,7 +12,10 @@ Author: Szymon Borak, Elisabeth Bommes
 
 Author[Matlab]: Szymon Borak, Awdesch Melzer
 
+Author[Python]: Karolina Weyna
+
 Submitted: Tue, June 17 2014 by Thijs Benschop
+Updated: Tue, July 15, 2025 
 
 Example: 
 - 1: 'The plot is generated for the following parameter values: S = 100, K = 100, r = 0.1, tau = 0.6 and sigma = 0.15.'

QID-2273-SFEbsprices/SFEbsprices.py

@@ -0,0 +1,60 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from scipy.stats import norm
+
+def bs_call(S, K, r, tau, sigma):
+    """
+    Calculates the Black-Scholes formula for a European call option price.
+    """
+    # To prevent division by zero or log of zero, S is treated as a small positive number if it's 0.
+    S = np.maximum(S, 1e-10)
+
+    d1 = (np.log(S / K) + (r + (sigma ** 2 / 2)) * tau) / (sigma * np.sqrt(tau))
+    d2 = d1 - sigma * np.sqrt(tau)
+    C = S * norm.cdf(d1) - K * np.exp(-r * tau) * norm.cdf(d2)
+    return C
+
+# Input parameters
+lb = 0         # Lower limit of x-axis
+ub = 170       # Upper limit of x-axis
+S = np.arange(lb, ub + 1)  # Stock price range
+
+K = 100       # Strike price
+r = 0.1       # Risk-free interest rate
+tau = 0.6       # Time to maturity (blue line)
+tau2 = 0.003     # Time to maturity (red dotted line)
+sigma = 0.15      # Volatility for the first plot
+sigma2 = 0.3       # Volatility for the second plot
+
+# Calculate Black-Scholes prices for the different scenarios
+call1 = bs_call(S, K, r, tau, sigma)
+call1_2 = bs_call(S, K, r, tau2, sigma)
+call2 = bs_call(S, K, r, tau, sigma2)
+call2_2 = bs_call(S, K, r, tau2, sigma2)
+
+# Set up a figure with two subplots, similar to R's par(mfrow=c(1, 2))
+fig, axs = plt.subplots(1, 2, figsize=(14, 6))
+
+# --- Plot 1: sigma = 0.15 ---
+axs[0].plot(S, call1, color="blue", linewidth=2, label=f"Time to Maturity (τ) = {tau}")
+axs[0].plot(S, call1_2, color="red", linewidth=2, linestyle="--", label=f"Time to Maturity (τ) = {tau2}")
+axs[0].set_title("Black-Scholes Price (σ = 0.15)")
+axs[0].set_xlabel("Stock Price (S)")
+axs[0].set_ylabel("Call Price C(S, τ)")
+axs[0].set_xlim(lb, ub)
+axs[0].set_ylim(0, max(call1) * 1.05) # Add 5% padding to y-axis
+axs[0].legend()
+
+# --- Plot 2: sigma = 0.30 ---
+axs[1].plot(S, call2, color="blue", linewidth=2, label=f"Time to Maturity (τ) = {tau}")
+axs[1].plot(S, call2_2, color="red", linewidth=2, linestyle="--", label=f"Time to Maturity (τ) = {tau2}")
+axs[1].set_title("Black-Scholes Price (σ = 0.30)")
+axs[1].set_xlabel("Stock Price (S)")
+axs[1].set_ylabel("Call Price C(S, τ)")
+axs[1].set_xlim(lb, ub)
+axs[1].set_ylim(0, max(call2) * 1.05) # Add 5% padding to y-axis
+axs[1].legend()
+
+# Display the plots
+plt.tight_layout()
+plt.show()

QID-3447-SFElognormal/README.md

@@ -40,5 +40,4 @@ Submitted: Sat, July 25 2015 by quantomas
 
 <div align="center">
 <img src="https://raw.githubusercontent.com/QuantLet/SFE/master/QID-3447-SFElognormal/SFElognormal.png" alt="Image" />
-</div>
-
+</div>