feat: 实物期权计算器 — 后端BSM+二叉树API+前端交互页面
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Hermes CI Fix
@@ -152,3 +152,182 @@ def api_cvp_detailed(data: dict):
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}
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except Exception as e:
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raise HTTPException(400, f"CVP详细分析失败: {str(e)}")
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# ── 实物期权计算器 ─────────────────────────────────────────────
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import math
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def _norm_cdf(x: float) -> float:
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"""标准正态分布CDF — Abramowitz & Stegun 近似 (max error ≈ 1.5×10⁻⁷)"""
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a1, a2, a3, a4, a5 = 0.254829592, -0.284496736, 1.421413741, -1.453152027, 1.061405429
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p = 0.3275911
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sign = 1.0
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if x < 0:
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sign = -1.0
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x_abs = abs(x) / math.sqrt(2.0)
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t = 1.0 / (1.0 + p * x_abs)
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y = 1.0 - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t * math.exp(-x_abs * x_abs)
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return 0.5 * (1.0 + sign * y)
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def _black_scholes_call(S0: float, X: float, t: float, r: float, sigma: float) -> dict:
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"""BSM看涨期权定价（扩张期权/延迟期权）"""
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sqrt_t = math.sqrt(t)
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d1 = (math.log(S0 / X) + (r + 0.5 * sigma ** 2) * t) / (sigma * sqrt_t)
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d2 = d1 - sigma * sqrt_t
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nd1 = _norm_cdf(d1)
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nd2 = _norm_cdf(d2)
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call_value = max(S0 * nd1 - X * math.exp(-r * t) * nd2, 0.0)
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return {"value": round(call_value, 4), "d1": round(d1, 4), "d2": round(d2, 4), "Nd1": round(nd1, 4), "Nd2": round(nd2, 4)}
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def _black_scholes_put(S0: float, X: float, t: float, r: float, sigma: float) -> dict:
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"""BSM看跌期权定价（放弃期权/收缩期权）"""
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sqrt_t = math.sqrt(t)
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d1 = (math.log(S0 / X) + (r + 0.5 * sigma ** 2) * t) / (sigma * sqrt_t)
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d2 = d1 - sigma * sqrt_t
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nd1 = _norm_cdf(-d1)
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nd2 = _norm_cdf(-d2)
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put_value = max(X * math.exp(-r * t) * nd2 - S0 * nd1, 0.0)
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return {"value": round(put_value, 4), "d1": round(d1, 4), "d2": round(d2, 4), "N(-d1)": round(nd1, 4), "N(-d2)": round(nd2, 4)}
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def _binomial_tree_call(S0: float, X: float, t: float, r: float, sigma: float, n: int = 100) -> float:
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"""二叉树欧式看涨期权定价（延迟期权）"""
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dt = t / n
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u = math.exp(sigma * math.sqrt(dt))
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d = 1.0 / u
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p = (math.exp(r * dt) - d) / (u - d)
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discount = math.exp(-r * dt)
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prices = [S0 * (u ** (n - j)) * (d ** j) for j in range(n + 1)]
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values = [max(p - X, 0.0) for p in prices]
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for i in range(n - 1, -1, -1):
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for j in range(i + 1):
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values[j] = discount * (p * values[j] + (1 - p) * values[j + 1])
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return max(values[0], 0.0)
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def _binomial_tree_american_put(S0: float, X: float, t: float, r: float, sigma: float, n: int = 100) -> float:
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"""二叉树美式看跌期权定价（可随时放弃的放弃期权）"""
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dt = t / n
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u = math.exp(sigma * math.sqrt(dt))
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d = 1.0 / u
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p = (math.exp(r * dt) - d) / (u - d)
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discount = math.exp(-r * dt)
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prices = [S0 * (u ** (n - j)) * (d ** j) for j in range(n + 1)]
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values = [max(X - p, 0.0) for p in prices]
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for i in range(n - 1, -1, -1):
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for j in range(i + 1):
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hold = discount * (p * values[j] + (1 - p) * values[j + 1])
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exercise = X - (S0 * (u ** (i - j)) * (d ** j))
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values[j] = max(hold, exercise)
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return max(values[0], 0.0)
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@router.post("/real-option")
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def api_real_option(data: dict):
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"""实物期权计算器"""
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try:
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opt_type = data.get("opt_type", "expansion") # expansion|abandon|delay|shrink
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model = data.get("model", "bs") # bs|binomial
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S0 = float(data.get("S0", 100.0))
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X = float(data.get("X", 80.0))
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t = float(data.get("t", 3.0))
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r = float(data.get("r", 0.0174))
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sigma = float(data.get("sigma", 0.30))
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expansion_factor = float(data.get("expansion_factor", 1.5))
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salvage_value = float(data.get("salvage_value", S0 * 0.3))
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n_steps = int(data.get("n_steps", 100))
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# 输入校验
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if S0 <= 0 or X <= 0 or t <= 0 or sigma <= 0:
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raise HTTPException(400, "参数必须为正数")
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if sigma > 2.0:
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raise HTTPException(400, "波动率σ不能超过200%")
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result = {"option_type": opt_type, "model": model, "S0": S0, "X": X, "t": t, "r": r, "sigma": sigma}
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# 计算期权价值
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if opt_type in ("expansion", "delay") and model == "bs":
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bs = _black_scholes_call(S0, X, t, r, sigma)
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result["option_value"] = bs["value"]
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result["intermediate"] = {k: v for k, v in bs.items() if k != "value"}
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elif opt_type == "expansion" and model == "binomial":
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adj_X = X / expansion_factor
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bt_val = _binomial_tree_call(S0, adj_X, t, r, sigma, n_steps)
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option_value = max(bt_val * expansion_factor, 0.0)
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result["option_value"] = round(option_value, 4)
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result["intermediate"] = {"expansion_factor": expansion_factor, "adjusted_X": round(adj_X, 4), "tree_value": round(bt_val, 4)}
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elif opt_type == "delay" and model == "binomial":
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option_value = _binomial_tree_call(S0, X, t, r, sigma, n_steps)
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result["option_value"] = round(option_value, 4)
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# Also compute BS for reference
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bs = _black_scholes_call(S0, X, t, r, sigma)
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result["intermediate"] = {"n_steps": n_steps, "bs_reference": round(bs["value"], 4)}
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elif opt_type in ("abandon", "shrink") and model == "bs":
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effective_X = salvage_value if opt_type == "abandon" else X
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bs = _black_scholes_put(S0, effective_X, t, r, sigma)
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result["option_value"] = bs["value"]
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result["intermediate"] = {k: v for k, v in bs.items() if k != "value"}
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if opt_type == "abandon":
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result["intermediate"]["salvage_value"] = effective_X
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elif opt_type == "abandon" and model == "binomial":
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bt_val = _binomial_tree_american_put(S0, salvage_value, t, r, sigma, n_steps)
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result["option_value"] = round(bt_val, 4)
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result["intermediate"] = {"n_steps": n_steps, "salvage_value": salvage_value}
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else:
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raise HTTPException(400, f"不支持的组合: {opt_type} + {model}")
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# 决策建议
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val = result["option_value"]
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if val > 0:
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result["suggestion"] = "期权价值 > 0，管理弹性有价值，建议保留决策弹性，在有利时机行权"
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result["suggestion_type"] = "positive"
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else:
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result["suggestion"] = "期权价值 ≈ 0，弹性无明显价值，建议按传统NPV决策，无需等待"
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result["suggestion_type"] = "neutral"
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# 扩展NPV（假设传统NPV = S0 - X）
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npv_without = S0 - X
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expanded_npv = npv_without + val
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result["npv_without_flexibility"] = round(npv_without, 4)
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result["expanded_npv"] = round(expanded_npv, 4)
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if expanded_npv > 0:
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result["decision"] = "✅ 扩展NPV > 0，含弹性后项目整体值得投资"
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else:
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result["decision"] = "❌ 扩展NPV ≤ 0，含弹性后项目仍不值得投资"
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# 敏感性分析数据（σ从10%~90%变化）
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sensitivity = []
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for s_pct in range(5, 96, 5):
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s = s_pct / 100.0
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if opt_type in ("expansion", "delay"):
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if model == "bs":
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v = _black_scholes_call(S0, X, t, r, s)["value"]
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else:
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bt = _binomial_tree_call(S0, X, t, r, s, n_steps)
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v = bt * expansion_factor if opt_type == "expansion" else bt
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else:
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eff_X = salvage_value if opt_type == "abandon" else X
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if model == "bs":
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v = _black_scholes_put(S0, eff_X, t, r, s)["value"]
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else:
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v = _binomial_tree_american_put(S0, eff_X, t, r, s, n_steps)
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sensitivity.append({"sigma": s_pct, "option_value": round(v, 4)})
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result["sensitivity"] = sensitivity
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# 警告提示
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warnings = []
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if t * sigma * sigma * 0.5 > r:
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warnings.append("高波动+长时间，延迟价值显著")
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if S0 < X:
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warnings.append("价外期权，期权价值较低")
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if S0 > X * 1.5:
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warnings.append("深度价内，几乎确定行权")
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if sigma < 0.10:
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warnings.append("波动率过低，期权价值趋近于0")
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if t > 10:
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warnings.append("长期期权，贴现因子影响大")
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result["warnings"] = warnings
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return result
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except HTTPException:
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raise
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except Exception as e:
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raise HTTPException(400, f"实物期权计算失败: {str(e)}")
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