feat: 实物期权计算器 — 后端BSM+二叉树API+前端交互页面

backend/app/api/predict.py

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

frontend/src/permission.ts

@@ -61,6 +61,7 @@ export const MENU_ITEMS: MenuItem[] = [
   // ══════════════════════════════════════════════════════════════
   { path: '/maps-review', label: '战略回顾会', icon: 'TrendCharts', roles: ['ceo', 'finance'], group: '复盘与改进' },
   { path: '/predict', label: '预测模拟', icon: 'DataLine', roles: ['ceo', 'finance', 'it'], group: '复盘与改进' },
+  { path: '/real-options', label: '实物期权计算器', icon: 'TrendCharts', roles: ['ceo', 'finance'], group: '复盘与改进' },
 
   // ══════════════════════════════════════════════════════════════
   // GROUP 5: 系统与支持（Infra）

frontend/src/router/index.ts

@@ -27,6 +27,7 @@ const routes = [
       { path: 'deviations', name: 'DeviationDashboard', component: () => import('@/views/DeviationDashboard.vue'), meta: { title: '差异分析', roles: ['ceo', 'finance', 'business', 'it'] } },
       { path: 'cost', name: 'CostDashboard', component: () => import('@/views/CostDashboard.vue'), meta: { title: '成本分析', roles: ['ceo', 'finance', 'it'] } },
       { path: 'predict', name: 'PredictDashboard', component: () => import('@/views/PredictDashboard.vue'), meta: { title: '预测模拟', roles: ['ceo', 'finance', 'it'] } },
+      { path: 'real-options', name: 'RealOptions', component: () => import('@/views/RealOptions.vue'), meta: { title: '实物期权计算器', roles: ['ceo', 'finance'] } },
       { path: 'action-plans', name: 'ActionPlans', component: () => import('@/views/ActionPlanLibrary.vue'), meta: { title: '改善行动', roles: ['ceo', 'finance', 'business', 'it'] } },
       { path: 'reports', name: 'ReportCenter', component: () => import('@/views/ReportCenter.vue'), meta: { title: '管理报表', roles: ['ceo', 'finance', 'business'] } },
       { path: 'alignment', name: 'KPIAlignment', component: () => import('@/views/KPIAlignment.vue'), meta: { title: '战略执行看板', roles: ['ceo', 'finance', 'business', 'it'] } },

frontend/src/views/RealOptions.vue

@@ -0,0 +1,147 @@
+<template>
+  <div class="page-view">
+    <div class="page-header">
+      <h3 class="page-title">实物期权计算器</h3>
+    </div>
+    <el-row :gutter="16">
+      <el-col :span="10">
+        <el-card>
+          <template #header><span>📋 参数设置</span></template>
+          <el-form label-width="120px" size="small">
+            <el-form-item label="期权类型">
+              <el-select v-model="form.option_type" style="width:100%">
+                <el-option value="expansion" label="扩张期权（看涨）" />
+                <el-option value="abandon" label="放弃期权（看跌）" />
+                <el-option value="delay" label="延迟期权（看涨）" />
+              </el-select>
+            </el-form-item>
+            <el-form-item label="计算模型">
+              <el-select v-model="form.model" style="width:100%">
+                <el-option value="bs" label="Black-Scholes" />
+                <el-option value="binomial" label="二叉树" />
+              </el-select>
+            </el-form-item>
+            <el-form-item label="标的资产 S₀ (万元)">
+              <el-input-number v-model="form.S0" :min="1" :step="10" style="width:100%" />
+            </el-form-item>
+            <el-form-item label="执行价格 X (万元)">
+              <el-input-number v-model="form.X" :min="1" :step="10" style="width:100%" />
+            </el-form-item>
+            <el-form-item label="到期时间 t (年)">
+              <el-input-number v-model="form.t" :min="0.1" :step="0.5" :precision="1" style="width:100%" />
+            </el-form-item>
+            <el-form-item label="无风险利率 r (%)">
+              <el-input-number v-model="form.r" :min="0.1" :step="0.5" :precision="2" style="width:100%" />
+            </el-form-item>
+            <el-form-item label="波动率 σ (%)">
+              <el-input-number v-model="form.sigma" :min="5" :step="5" :precision="0" style="width:100%" />
+            </el-form-item>
+            <el-form-item>
+              <el-button type="primary" @click="calculate" :loading="loading" style="width:100%">计算</el-button>
+            </el-form-item>
+            <el-form-item>
+              <el-button @click="resetDefaults" size="small">重置默认值</el-button>
+            </el-form-item>
+          </el-form>
+        </el-card>
+      </el-col>
+      <el-col :span="14">
+        <el-card v-if="result">
+          <template #header><span>📊 计算结果</span></template>
+          <div style="text-align:center;padding:20px 0;">
+            <div style="font-size:12px;color:#999;">期权价值</div>
+            <div style="font-size:48px;font-weight:700;" :style="{ color: result.option_value > 0 ? '#67c23a' : '#f56c6c' }">
+              {{ result.option_value.toFixed(2) }} <span style="font-size:16px;font-weight:400;">万元</span>
+            </div>
+          </div>
+          <el-descriptions :column="2" border size="small">
+            <el-descriptions-item label="d₁">{{ result.d1?.toFixed(4) || '-' }}</el-descriptions-item>
+            <el-descriptions-item label="d₂">{{ result.d2?.toFixed(4) || '-' }}</el-descriptions-item>
+            <el-descriptions-item label="N(d₁)">{{ result.Nd1?.toFixed(4) || '-' }}</el-descriptions-item>
+            <el-descriptions-item label="N(d₂)">{{ result.Nd2?.toFixed(4) || '-' }}</el-descriptions-item>
+            <el-descriptions-item label="模型" :span="2">{{ form.model === 'bs' ? 'Black-Scholes' : '二叉树' }}</el-descriptions-item>
+          </el-descriptions>
+          <el-alert :type="result.option_value > 0 ? 'success' : 'warning'" show-icon style="margin-top:12px;">
+            <template #title>{{ result.suggestion }}</template>
+          </el-alert>
+        </el-card>
+        <el-card v-else>
+          <el-empty description="设置参数后点击「计算」查看结果" />
+        </el-card>
+        <el-card v-if="result?.sensitivity?.length" style="margin-top:12px;">
+          <template #header><span>📈 波动率敏感性</span></template>
+          <div ref="chartRef" style="height:200px;"></div>
+        </el-card>
+      </el-col>
+    </el-row>
+  </div>
+</template>
+
+<script setup lang="ts">
+import { ref, reactive, nextTick } from 'vue'
+import { ElMessage } from 'element-plus'
+import api from '../api/index'
+
+const loading = ref(false)
+const result = ref<any>(null)
+const chartRef = ref<HTMLElement | null>(null)
+
+const form = reactive({
+  option_type: 'expansion',
+  model: 'bs',
+  S0: 100, X: 80, t: 3, r: 2.8, sigma: 30
+})
+
+async function calculate() {
+  loading.value = true
+  result.value = null
+  try {
+    const payload = {
+      option_type: form.option_type,
+      model: form.model,
+      S0: form.S0,
+      X: form.X,
+      t: form.t,
+      r: form.r / 100,
+      sigma: form.sigma / 100,
+    }
+    const r: any = await api.post('/predict/real-option', payload)
+    result.value = r
+    nextTick(() => drawChart())
+  } catch (e) {
+    ElMessage.error('计算失败')
+  }
+  loading.value = false
+}
+
+function resetDefaults() {
+  form.S0 = 100; form.X = 80; form.t = 3
+  form.r = 2.8; form.sigma = 30
+  form.option_type = 'expansion'; form.model = 'bs'
+  result.value = null
+}
+
+function drawChart() {
+  if (!result.value?.sensitivity?.length || !chartRef.value) return
+  const points = result.value.sensitivity
+  const svg = `<svg width="100%" height="200" viewBox="0 0 600 200">
+    <text x="10" y="20" font-size="12" fill="#999">期权价值(万)</text>
+    <text x="580" y="195" font-size="12" fill="#999" text-anchor="end">波动率(%)</text>
+    <polyline fill="none" stroke="#409eff" stroke-width="2"
+      points="${points.map((p: any, i: number) => `${(i / (points.length - 1)) * 580},${180 - (p.value / Math.max(...points.map((x: any) => x.value))) * 160}`).join(' ')}" />
+    ${points.map((p: any, i: number) => {
+      const x = (i / (points.length - 1)) * 580
+      const y = 180 - (p.value / Math.max(...points.map((x: any) => x.value))) * 160
+      return `<circle cx="${x}" cy="${y}" r="3" fill="#409eff"/><text x="${x}" y="${y - 8}" font-size="10" text-anchor="middle">${p.sigma_pct}%</text>`
+    }).join('')}
+    <line x1="0" y1="180" x2="580" y2="180" stroke="#e0e0e0" stroke-width="1"/>
+    <line x1="0" y1="20" x2="0" y2="180" stroke="#e0e0e0" stroke-width="1"/>
+  </svg>`
+  chartRef.value.innerHTML = svg
+}
+</script>
+
+<style scoped>
+.el-card { margin-bottom:12px; }
+.el-form-item { margin-bottom:12px; }
+</style>