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# Portfolio Optimization
import numpy as np
from scipy.optimize import minimize

def optimize_portfolio(returns, risk_free_rate=0.02):
    mean_returns = returns.mean() * 252
    cov_matrix = returns.cov() * 252
    
    def sharpe_ratio(weights):
        portfolio_return = np.sum(mean_returns * weights)
        portfolio_std = np.sqrt(np.dot(weights.T, 
                                       np.dot(cov_matrix, weights)))
        return -(portfolio_return - risk_free_rate) / portfolio_std
    
    constraints = {'type': 'eq', 'fun': lambda x: np.sum(x) - 1}
    bounds = tuple((0, 1) for _ in range(len(returns.columns)))
    
    result = minimize(sharpe_ratio, 
                     [1/len(returns.columns)] * len(returns.columns),
                     method='SLSQP', bounds=bounds, constraints=constraints)
    return result.x

# Async Data Pipeline
import asyncio
import aiohttp
import pandas as pd

async def fetch_market_data(endpoints):
    async with aiohttp.ClientSession() as session:
        tasks = [session.get(ep) for ep in endpoints]
        responses = await asyncio.gather(*tasks)
        data = [await r.json() for r in responses]
        return pd.DataFrame(data)

# Concurrent data fetching
endpoints = ['/quotes/AAPL', '/quotes/GOOGL', '/quotes/MSFT']
market_data = await fetch_market_data(endpoints)

# Monte Carlo Option Pricing
import numpy as np

def price_option(S0, K, T, r, sigma, n_sims=100000):
    # Simulate stock price paths
    random_shocks = np.random.normal(0, 1, (n_sims, int(T * 252)))
    dt = T / 252
    
    prices = S0 * np.exp(np.cumsum(
        (r - 0.5 * sigma**2) * dt + 
        sigma * np.sqrt(dt) * random_shocks, axis=1
    ))
    
    # Calculate option value
    payoffs = np.maximum(prices[:, -1] - K, 0)
    option_price = np.exp(-r * T) * np.mean(payoffs)
    
    return option_price

# Usage
price = price_option(S0=100, K=105, T=0.25, r=0.05, sigma=0.2)