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skills/options-strategy-advisor/scripts/black_scholes.py

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+#!/usr/bin/env python3
+"""
+Black-Scholes Options Pricing Engine
+
+Calculates theoretical option prices and Greeks using Black-Scholes model.
+
+Features:
+- European call and put pricing
+- All Greeks (Delta, Gamma, Theta, Vega, Rho)
+- Historical volatility calculation from price data
+- Dividend adjustment support
+
+Usage:
+    from black_scholes import OptionPricer
+
+    pricer = OptionPricer(
+        S=180,      # Stock price
+        K=185,      # Strike price
+        T=30/365,   # Time to expiration (years)
+        r=0.053,    # Risk-free rate
+        sigma=0.25, # Volatility
+        q=0.01      # Dividend yield
+    )
+
+    call_price = pricer.call_price()
+    delta = pricer.call_delta()
+
+Author: Claude Trading Skills
+Version: 1.0
+"""
+
+import numpy as np
+from scipy.stats import norm
+import requests
+import os
+from datetime import datetime, timedelta
+
+
+class OptionPricer:
+    """Black-Scholes option pricer with Greeks calculation"""
+
+    def __init__(self, S, K, T, r, sigma, q=0):
+        """
+        Initialize pricer with option parameters
+
+        Parameters:
+        -----------
+        S : float
+            Current stock price
+        K : float
+            Strike price
+        T : float
+            Time to expiration in years (e.g., 30/365 for 30 days)
+        r : float
+            Risk-free interest rate (annual, e.g., 0.053 for 5.3%)
+        sigma : float
+            Volatility (annual, e.g., 0.25 for 25%)
+        q : float, optional
+            Continuous dividend yield (annual, default 0)
+        """
+        self.S = S
+        self.K = K
+        self.T = T
+        self.r = r
+        self.sigma = sigma
+        self.q = q
+
+        # Validate inputs
+        if S <= 0:
+            raise ValueError("Stock price must be positive")
+        if K <= 0:
+            raise ValueError("Strike price must be positive")
+        if T <= 0:
+            raise ValueError("Time to expiration must be positive")
+        if sigma <= 0:
+            raise ValueError("Volatility must be positive")
+
+    def _d1(self):
+        """Calculate d1 parameter"""
+        numerator = np.log(self.S / self.K) + (self.r - self.q + 0.5 * self.sigma**2) * self.T
+        denominator = self.sigma * np.sqrt(self.T)
+        return numerator / denominator
+
+    def _d2(self):
+        """Calculate d2 parameter"""
+        return self._d1() - self.sigma * np.sqrt(self.T)
+
+    # =========================================================================
+    # Option Pricing
+    # =========================================================================
+
+    def call_price(self):
+        """Calculate European call option price"""
+        d1 = self._d1()
+        d2 = self._d2()
+
+        price = (self.S * np.exp(-self.q * self.T) * norm.cdf(d1) -
+                 self.K * np.exp(-self.r * self.T) * norm.cdf(d2))
+
+        return max(0, price)  # Price cannot be negative
+
+    def put_price(self):
+        """Calculate European put option price"""
+        d1 = self._d1()
+        d2 = self._d2()
+
+        price = (self.K * np.exp(-self.r * self.T) * norm.cdf(-d2) -
+                 self.S * np.exp(-self.q * self.T) * norm.cdf(-d1))
+
+        return max(0, price)
+
+    # =========================================================================
+    # Greeks - First Order
+    # =========================================================================
+
+    def call_delta(self):
+        """
+        Calculate call delta
+
+        Delta: Change in option price per $1 change in stock price
+        Range: 0 to 1 for calls
+        """
+        d1 = self._d1()
+        return np.exp(-self.q * self.T) * norm.cdf(d1)
+
+    def put_delta(self):
+        """
+        Calculate put delta
+
+        Delta: Change in option price per $1 change in stock price
+        Range: -1 to 0 for puts
+        """
+        d1 = self._d1()
+        return np.exp(-self.q * self.T) * (norm.cdf(d1) - 1)
+
+    def vega(self):
+        """
+        Calculate vega (same for calls and puts)
+
+        Vega: Change in option price per 1% change in volatility
+        Always positive (options gain value when volatility increases)
+        """
+        d1 = self._d1()
+        vega = self.S * np.exp(-self.q * self.T) * norm.pdf(d1) * np.sqrt(self.T)
+        return vega / 100  # Per 1% change in volatility
+
+    def call_theta(self):
+        """
+        Calculate call theta
+
+        Theta: Change in option price per day (time decay)
+        Usually negative (options lose value as time passes)
+        """
+        d1 = self._d1()
+        d2 = self._d2()
+
+        term1 = -self.S * norm.pdf(d1) * self.sigma * np.exp(-self.q * self.T) / (2 * np.sqrt(self.T))
+        term2 = -self.r * self.K * np.exp(-self.r * self.T) * norm.cdf(d2)
+        term3 = self.q * self.S * norm.cdf(d1) * np.exp(-self.q * self.T)
+
+        theta_annual = term1 + term2 + term3
+        return theta_annual / 365  # Convert to per-day
+
+    def put_theta(self):
+        """Calculate put theta"""
+        d1 = self._d1()
+        d2 = self._d2()
+
+        term1 = -self.S * norm.pdf(d1) * self.sigma * np.exp(-self.q * self.T) / (2 * np.sqrt(self.T))
+        term2 = self.r * self.K * np.exp(-self.r * self.T) * norm.cdf(-d2)
+        term3 = -self.q * self.S * norm.cdf(-d1) * np.exp(-self.q * self.T)
+
+        theta_annual = term1 + term2 + term3
+        return theta_annual / 365
+
+    def call_rho(self):
+        """
+        Calculate call rho
+
+        Rho: Change in option price per 1% change in interest rate
+        Positive for calls (calls gain value when rates increase)
+        """
+        d2 = self._d2()
+        rho = self.K * self.T * np.exp(-self.r * self.T) * norm.cdf(d2)
+        return rho / 100  # Per 1% change
+
+    def put_rho(self):
+        """
+        Calculate put rho
+
+        Rho: Change in option price per 1% change in interest rate
+        Negative for puts (puts lose value when rates increase)
+        """
+        d2 = self._d2()
+        rho = -self.K * self.T * np.exp(-self.r * self.T) * norm.cdf(-d2)
+        return rho / 100
+
+    # =========================================================================
+    # Greeks - Second Order
+    # =========================================================================
+
+    def gamma(self):
+        """
+        Calculate gamma (same for calls and puts)
+
+        Gamma: Change in delta per $1 change in stock price
+        Shows how fast delta changes
+        Highest for ATM options, lower for OTM and ITM
+        """
+        d1 = self._d1()
+        gamma = (np.exp(-self.q * self.T) * norm.pdf(d1)) / (self.S * self.sigma * np.sqrt(self.T))
+        return gamma
+
+    # =========================================================================
+    # Utility Methods
+    # =========================================================================
+
+    def intrinsic_value(self, option_type='call'):
+        """Calculate intrinsic value"""
+        if option_type.lower() == 'call':
+            return max(0, self.S - self.K)
+        else:  # put
+            return max(0, self.K - self.S)
+
+    def time_value(self, option_type='call'):
+        """Calculate time value (extrinsic value)"""
+        if option_type.lower() == 'call':
+            price = self.call_price()
+        else:
+            price = self.put_price()
+
+        intrinsic = self.intrinsic_value(option_type)
+        return price - intrinsic
+
+    def moneyness(self):
+        """
+        Determine moneyness
+
+        Returns: 'ITM', 'ATM', or 'OTM'
+        """
+        ratio = self.S / self.K
+
+        if abs(ratio - 1.0) < 0.02:  # Within 2%
+            return 'ATM'
+        elif ratio > 1.0:
+            return 'ITM (Call) / OTM (Put)'
+        else:
+            return 'OTM (Call) / ITM (Put)'
+
+    def get_all_greeks(self, option_type='call'):
+        """
+        Get all Greeks for an option
+
+        Returns: dict with all Greeks
+        """
+        if option_type.lower() == 'call':
+            return {
+                'price': self.call_price(),
+                'delta': self.call_delta(),
+                'gamma': self.gamma(),
+                'theta': self.call_theta(),
+                'vega': self.vega(),
+                'rho': self.call_rho(),
+                'intrinsic_value': self.intrinsic_value('call'),
+                'time_value': self.time_value('call')
+            }
+        else:
+            return {
+                'price': self.put_price(),
+                'delta': self.put_delta(),
+                'gamma': self.gamma(),
+                'theta': self.put_theta(),
+                'vega': self.vega(),
+                'rho': self.put_rho(),
+                'intrinsic_value': self.intrinsic_value('put'),
+                'time_value': self.time_value('put')
+            }
+
+
+# =============================================================================
+# Historical Volatility Calculator
+# =============================================================================
+
+def calculate_historical_volatility(prices, window=30):
+    """
+    Calculate historical volatility from price data
+
+    Parameters:
+    -----------
+    prices : array-like
+        Historical prices (daily)
+    window : int
+        Lookback window in days (default 30)
+
+    Returns:
+    --------
+    float
+        Annualized historical volatility
+    """
+    if len(prices) < window + 1:
+        raise ValueError(f"Need at least {window + 1} price points")
+
+    # Calculate log returns
+    prices = np.array(prices)
+    log_returns = np.log(prices[1:] / prices[:-1])
+
+    # Use most recent 'window' returns
+    recent_returns = log_returns[-window:]
+
+    # Annualized volatility (252 trading days)
+    volatility = np.std(recent_returns) * np.sqrt(252)
+
+    return volatility
+
+
+def fetch_historical_prices_for_hv(symbol, api_key, days=90):
+    """
+    Fetch historical prices from FMP API for HV calculation
+
+    Parameters:
+    -----------
+    symbol : str
+        Stock ticker
+    api_key : str
+        FMP API key
+    days : int
+        Number of days to fetch
+
+    Returns:
+    --------
+    list
+        List of adjusted close prices
+    """
+    url = f"https://financialmodelingprep.com/api/v3/historical-price-full/{symbol}"
+    params = {'apikey': api_key}
+
+    try:
+        response = requests.get(url, params=params, timeout=30)
+        response.raise_for_status()
+        data = response.json()
+
+        if 'historical' not in data:
+            return None
+
+        # Get most recent 'days' of data
+        historical = data['historical'][:days]
+        historical = historical[::-1]  # Reverse to chronological order
+
+        prices = [item['adjClose'] for item in historical]
+        return prices
+
+    except Exception as e:
+        print(f"Error fetching prices for {symbol}: {e}")
+        return None
+
+
+# =============================================================================
+# FMP API Integration
+# =============================================================================
+
+def get_current_stock_price(symbol, api_key):
+    """Fetch current stock price from FMP API"""
+    url = f"https://financialmodelingprep.com/api/v3/quote/{symbol}"
+    params = {'apikey': api_key}
+
+    try:
+        response = requests.get(url, params=params, timeout=30)
+        response.raise_for_status()
+        data = response.json()
+
+        if data and len(data) > 0:
+            return data[0]['price']
+        return None
+
+    except Exception as e:
+        print(f"Error fetching current price for {symbol}: {e}")
+        return None
+
+
+def get_dividend_yield(symbol, api_key):
+    """Fetch dividend yield from FMP API"""
+    url = f"https://financialmodelingprep.com/api/v3/profile/{symbol}"
+    params = {'apikey': api_key}
+
+    try:
+        response = requests.get(url, params=params, timeout=30)
+        response.raise_for_status()
+        data = response.json()
+
+        if data and len(data) > 0:
+            # Last annual dividend / current price
+            last_div = data[0].get('lastDiv', 0)
+            price = data[0].get('price', 1)
+            div_yield = (last_div / price) if price > 0 else 0
+            return div_yield
+
+        return 0
+
+    except Exception:
+        return 0
+
+
+# =============================================================================
+# Example Usage
+# =============================================================================
+
+if __name__ == '__main__':
+    print("\n" + "="*70)
+    print("BLACK-SCHOLES OPTIONS PRICER - EXAMPLE")
+    print("="*70)
+
+    # Example parameters
+    stock_price = 180.00
+    strike_price = 185.00
+    days_to_expiration = 30
+    time_to_expiration = days_to_expiration / 365
+    risk_free_rate = 0.053  # 5.3%
+    volatility = 0.25  # 25%
+    dividend_yield = 0.01  # 1%
+
+    print(f"\nInput Parameters:")
+    print(f"  Stock Price: ${stock_price:.2f}")
+    print(f"  Strike Price: ${strike_price:.2f}")
+    print(f"  Days to Expiration: {days_to_expiration}")
+    print(f"  Volatility: {volatility*100:.1f}%")
+    print(f"  Risk-Free Rate: {risk_free_rate*100:.2f}%")
+    print(f"  Dividend Yield: {dividend_yield*100:.1f}%")
+
+    # Create pricer
+    pricer = OptionPricer(
+        S=stock_price,
+        K=strike_price,
+        T=time_to_expiration,
+        r=risk_free_rate,
+        sigma=volatility,
+        q=dividend_yield
+    )
+
+    # Call option
+    print(f"\n{'='*70}")
+    print("CALL OPTION")
+    print("="*70)
+
+    call_greeks = pricer.get_all_greeks('call')
+    print(f"Price: ${call_greeks['price']:.2f}")
+    print(f"Intrinsic Value: ${call_greeks['intrinsic_value']:.2f}")
+    print(f"Time Value: ${call_greeks['time_value']:.2f}")
+    print(f"\nGreeks:")
+    print(f"  Delta: {call_greeks['delta']:.4f} (${call_greeks['delta']*100:.2f} per $1 move)")
+    print(f"  Gamma: {call_greeks['gamma']:.4f} (delta changes by {call_greeks['gamma']:.4f})")
+    print(f"  Theta: ${call_greeks['theta']:.2f}/day (loses ${abs(call_greeks['theta']):.2f} per day)")
+    print(f"  Vega: ${call_greeks['vega']:.2f} per 1% IV (gains ${call_greeks['vega']:.2f} if IV +1%)")
+    print(f"  Rho: ${call_greeks['rho']:.2f} per 1% rate (gains ${call_greeks['rho']:.2f} if rate +1%)")
+
+    # Put option
+    print(f"\n{'='*70}")
+    print("PUT OPTION")
+    print("="*70)
+
+    put_greeks = pricer.get_all_greeks('put')
+    print(f"Price: ${put_greeks['price']:.2f}")
+    print(f"Intrinsic Value: ${put_greeks['intrinsic_value']:.2f}")
+    print(f"Time Value: ${put_greeks['time_value']:.2f}")
+    print(f"\nGreeks:")
+    print(f"  Delta: {put_greeks['delta']:.4f} (${put_greeks['delta']*100:.2f} per $1 move)")
+    print(f"  Gamma: {put_greeks['gamma']:.4f} (delta changes by {put_greeks['gamma']:.4f})")
+    print(f"  Theta: ${put_greeks['theta']:.2f}/day (loses ${abs(put_greeks['theta']):.2f} per day)")
+    print(f"  Vega: ${put_greeks['vega']:.2f} per 1% IV (gains ${put_greeks['vega']:.2f} if IV +1%)")
+    print(f"  Rho: ${put_greeks['rho']:.2f} per 1% rate (loses ${abs(put_greeks['rho']):.2f} if rate +1%)")
+
+    # Moneyness
+    print(f"\n{'='*70}")
+    print(f"Moneyness: {pricer.moneyness()}")
+    print("="*70 + "\n")
+
+    # Historical Volatility Example
+    print("\nHistorical Volatility Example:")
+    print("-" * 70)
+
+    # Simulate price data
+    np.random.seed(42)
+    simulated_prices = [180 * np.exp(np.sum(np.random.randn(i) * 0.01)) for i in range(90)]
+
+    hv = calculate_historical_volatility(simulated_prices, window=30)
+    print(f"30-Day Historical Volatility: {hv*100:.2f}%")
+    print(f"Implied Volatility (input): {volatility*100:.1f}%")
+
+    if hv < volatility:
+        print(f"→ IV > HV: Options may be expensive (consider selling premium)")
+    elif hv > volatility:
+        print(f"→ IV < HV: Options may be cheap (consider buying)")
+    else:
+        print(f"→ IV ≈ HV: Options fairly priced")
+
+    print("\n" + "="*70 + "\n")