Gamma Scalping 完全指南：用 Delta 对冲从波动中获利

import numpy as np
import matplotlib.pyplot as plt

def simulate_gamma_scalp(
    S0=500,           # 初始标的价格
    K=500,            # 行权价
    IV=0.20,          # 买入期权的隐含波动率（年化）
    RV=0.25,          # 模拟的实现波动率（年化）
    T=30,             # 持仓天数
    gamma_per_dollar=0.16,  # 组合 Gamma（每$1标的变动，Delta变化多少）
    theta_per_day=-160,     # 每天的 Theta 损耗
    hedge_threshold=1.0,    # 标的移动多少触发对冲
    n_simulations=1000
):
    """
    模拟 gamma scalping 在给定实现波动率下的盈亏分布。
    简化假设：Gamma 和 Theta 在持仓期间恒定。
    """
    daily_vol = RV / np.sqrt(252)
    pnl_list = []
    
    for _ in range(n_simulations):
        price = S0
        cumulative_hedge_pnl = 0.0
        delta_position = 0.0  # 当前未对冲的 Delta（股数）
        
        for day in range(T):
            # 标的每日随机变动
            daily_return = np.random.normal(0, daily_vol)
            move = price * daily_return
            price += move
            
            # Delta 累积
            delta_position += gamma_per_dollar * move
            
            # 检查是否触发对冲
            if abs(delta_position) >= hedge_threshold * gamma_per_dollar:
                # 对冲：锁定 gamma profit
                # 近似：累积 Delta × 平均价格变动 / 2
                cumulative_hedge_pnl += 0.5 * gamma_per_dollar * move**2
                delta_position = 0.0
        
        # 总 P&L = 对冲利润 + Theta损耗
        total_pnl = cumulative_hedge_pnl + theta_per_day * T
        pnl_list.append(total_pnl)
    
    return np.array(pnl_list)

# --- 模拟不同实现波动率下的表现 ---
rv_levels = [0.12, 0.16, 0.20, 0.24, 0.28, 0.32]
iv_bought = 0.20  # 买入时的 IV

results = {}
for rv in rv_levels:
    pnls = simulate_gamma_scalp(RV=rv, IV=iv_bought)
    results[rv] = pnls

# --- 可视化 ---
fig, axes = plt.subplots(1, 2, figsize=(14, 5))

# 左图：不同 RV 下的平均 P&L
mean_pnls = [results[rv].mean() for rv in rv_levels]
colors = ["#ef4444" if m < 0 else "#22c55e" for m in mean_pnls]
axes[0].bar([f"{int(rv*100)}%" for rv in rv_levels], mean_pnls, color=colors)
axes[0].axhline(y=0, color="#6b7280", linewidth=0.8)
axes[0].set_xlabel("Realized Volatility", fontsize=11)
axes[0].set_ylabel("Average P&L ($)", fontsize=11)
axes[0].set_title("Gamma Scalping P&L vs Realized Volatility\n(IV at entry = 20%)",
                  fontsize=12)
axes[0].grid(True, alpha=0.3, axis="y")

# 右图：RV=24% 时的 P&L 分布
pnl_24 = results[0.24]
axes[1].hist(pnl_24, bins=40, color="#2563eb", alpha=0.7, edgecolor="white")
axes[1].axvline(x=0, color="#ef4444", linewidth=1.2, linestyle="--")
axes[1].axvline(x=pnl_24.mean(), color="#22c55e", linewidth=1.5,
               label=f"Mean: ${pnl_24.mean():.0f}")
axes[1].set_xlabel("P&L ($)", fontsize=11)
axes[1].set_ylabel("Frequency", fontsize=11)
axes[1].set_title("P&L Distribution (RV = 24%, IV = 20%)", fontsize=12)
axes[1].legend(fontsize=10)
axes[1].grid(True, alpha=0.3, axis="y")

plt.tight_layout()
plt.savefig("gamma-scalping-pnl-simulation.webp", dpi=150)
plt.close()

# --- 输出统计 ---
print("Gamma Scalping Simulation Results (IV = 20%, 30 days)")
print("=" * 55)
print(f"{'RV':<8} {'Mean P&L':<12} {'Win Rate':<10} {'Sharpe':<8}")
print("-" * 55)
for rv in rv_levels:
    pnl = results[rv]
    mean = pnl.mean()
    win_rate = (pnl > 0).mean()
    sharpe = pnl.mean() / pnl.std() if pnl.std() > 0 else 0
    print(f"{int(rv*100)}%{'':<5} ${mean:<10.0f} {win_rate:<10.1%} {sharpe:<8.2f}")