def price_snowball(S0, K_out, K_in, T, r, sigma, coupon_rate,
n_obs=12, n_sims=10000, barrier_type="continuous"):
"""
雪球产品简化定价模型
参数：
S0 - 初始价格
K_out - 敲出价格（初始价格的百分比）
K_in - 敲入价格（初始价格的百分比）
T - 期限（年）
r - 无风险利率
sigma - 波动率
coupon_rate - 年化票息率
n_obs - 观察次数
n_sims - 模拟次数
barrier_type - 敲入类型："continuous"或"discrete"
返回：
expected_return - 预期收益率
knockout_prob - 敲出概率
knockin_prob - 敲入概率
var_95 - 95%置信区间风险价值
"""
dt = T / 252
steps = int(252 * T)
obs_steps = [int(i * steps / n_obs) for i in range(1, n_obs+1)]
payoffs = np.zeros(n_sims)
knockout_times = np.zeros(n_sims)
knockin_flags = np.zeros(n_sims)
expected_return = np.mean(payoffs) - 1
knockout_prob = np.sum(knockout_times > 0) / n_sims
knockin_prob = np.sum(knockin_flags) / n_sims
var_95 = np.percentile(payoffs, 5) - 1
return {
"expected_return": expected_return,
"knockout_prob": knockout_prob,
"knockin_prob": knockin_prob,
"var_95": var_95,
"payoff_distribution": payoffs
}
for i in range(n_sims):
path = generate_price_path(S0, r, sigma, T, steps)
knocked_out = False
for j, obs_step in enumerate(obs_steps):
if path[obs_step] >= K_out * S0:
knocked_out = True
knockout_times[i] = j + 1
payoffs[i] = 1 + coupon_rate * (j+1) / n_obs
break
if not knocked_out:
if barrier_type == "continuous":
min_price = min(path)
if min_price <= K_in * S0:
knockin_flags[i] = 1
payoffs[i] = min(1, path[-1]/S0)
else:
payoffs[i] = 1 + coupon_rate
else:
knocked_in = False
for obs_step in obs_steps:
if path[obs_step] <= K_in * S0:
knocked_in = True
knockin_flags[i] = 1
break
if knocked_in:
payoffs[i] = min(1, path[-1]/S0)
else:
payoffs[i] = 1 + coupon_rate