期权盈亏曲线工具：交互式Black-Scholes计算器与策略分析器

options-payoff by himself65/finance-skills

278 周安装量

880 GitHub Stars

GitHub

安装命令

npx skills add https://github.com/himself65/finance-skills --skill options-payoff

数据可视化命令行工具金融科技

🇨🇳中文介绍

包含 Shell 命令

此技能包含可能执行系统命令的 shell 命令指令（!command``）。安装前请仔细审查。

期权盈亏曲线技能

生成一个完全交互式的 HTML 小部件（通过 visualize:show_widget）显示：

到期盈亏曲线（灰色虚线）—— 到期时的内在价值
理论价值曲线（彩色实线）—— 在当前 DTE/IV 下的 Black-Scholes 价格
所有关键参数的动态滑块
实时统计数据：最大盈利、最大亏损、盈亏平衡点、当前现货价格的 P&L

步骤 1：从用户输入中提取策略

当用户提供截图或文本时，提取：

字段	查找位置	缺失时的默认值
策略类型	标题栏 / 腿描述	"custom"
标的物	股票代码	SPX
行权价	标题或腿表格中的 K1, K2, K3...	最近的整数
支付/收取的权利金

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步骤 2：识别策略类型

匹配到以下支持策略之一，然后在 references/strategies.md 中阅读相应部分。

策略	腿数	关键标识符
butterfly	买入 K1，卖出 2×K2，买入 K3	3 个行权价，标题中有"Butterfly"
vertical_spread	买入 K1，卖出 K2（相同到期日）	2 个行权价，借方或贷方
calendar_spread	买入远月 K，卖出近月 K	相同行权价，2 个到期日
iron_condor	卖出 K2/K3，买入 K1/K4 翼	4 个行权价，2 个价差
straddle	买入看涨期权 K + 买入看跌期权 K	相同行权价，两种类型
strangle	买入虚值看涨期权 + 买入虚值看跌期权	2 个行权价，均为虚值
covered_call	多头 100 股 + 卖出看涨期权 K	股票 + 空头看涨期权
naked_put	卖出看跌期权 K	单腿
ratio_spread	买入 1×K1，卖出 N×K2	数量不等

对于未列出的策略，使用 custom 模式：分解为单个腿并求和其 P&L。

步骤 3：计算盈亏

Black-Scholes 看跌期权价格

d1 = (ln(S/K) + (r + σ²/2)·T) / (σ·√T)
d2 = d1 - σ·√T
put = K·e^(-rT)·N(-d2) - S·N(-d1)

Black-Scholes 看涨期权价格（通过看跌-看涨平价）

call = put + S - K·e^(-rT)

蝶式看跌期权盈亏（到期）

if S >= K3: 0
if S >= K2: K3 - S
if S >= K1: S - K1
else: 0

每股净 P&L = 盈亏 − 支付的权利金

垂直价差（看涨借方）盈亏（到期）

long_call = max(S - K1, 0)
short_call = max(S - K2, 0)
payoff = long_call - short_call - net_debit

日历价差理论价值

日历价差无法表示为简单的到期函数——始终使用 BS 定价计算两条腿：

value = BS(S, K, T_far, r, IV_far) - BS(S, K, T_near, r, IV_near)

对于日历价差的到期曲线：近月腿到期无价值，远月腿 = 剩余 T 的 BS 价值。

铁鹰式价差盈亏（到期）

put_spread = max(K2-S, 0) - max(K1-S, 0)   // 空头看跌价差
call_spread = max(S-K3, 0) - max(S-K4, 0)  // 空头看涨价差
payoff = credit_received - put_spread - call_spread

步骤 4：渲染小部件

在构建之前，使用 visualize:read_me 并包含模块 ["chart", "interactive"]。

必需控件（滑块）

所有行权价（K1, K2, K3... 根据策略需要）
支付/收取的权利金
数量
乘数（默认 100，为清晰起见显示）

定价变量部分：

隐含波动率 %（5–80%，步长 0.5）
DTE——到期天数（0–90）
无风险利率 %（0–8%）

全宽滑块，范围 = [min_strike - 20%, max_strike + 20%]，默认设置为实际的当前现货价格

必需统计卡片（实时更新）

最大盈利（到期）
最大亏损（到期）
盈亏平衡点——对于双边策略显示两者
当前现货价格下的理论 P&L

X 轴：SPX/标的物价格
Y 轴：总美元 P&L（非每股）
蓝色实线 = 当前 DTE/IV 下的理论价值
灰色虚线 = 到期盈亏
绿色虚线垂直线 = 行权价（K2 中间行权价更亮）
琥珀色虚线垂直线 = 当前现货价格
零轴以上填充 = 绿色 10% 不透明度；零轴以下填充 = 红色 10% 不透明度
工具提示：悬停时显示两条曲线

在小部件内部使用此 JS 结构，根据策略调整 pnlExpiry() 和 bfTheory()：

// Black-Scholes 辅助函数（始终包含）
function normCDF(x) { /* Horner 近似 */ }
function bsCall(S,K,T,r,sig) { /* 标准 BS 看涨期权 */ }
function bsPut(S,K,T,r,sig) { /* 标准 BS 看跌期权 */ }

// 策略特定的到期盈亏（返回每股价值，在权利金之前）
function expiryValue(S, ...strikes) { ... }

// 策略特定的理论价值，使用 BS
function theoreticalValue(S, ...strikes, T, r, iv) { ... }

// 主 update() 函数读取所有滑块，计算数组，销毁并重新创建 Chart.js 实例
function update() { ... }

// 附加监听器
['k1','k2',...,'iv','dte','rate','spot'].forEach(id => {
  document.getElementById(id).addEventListener('input', update);
});
update();

步骤 5：响应用户

渲染小部件后，简要解释：

检测到何种策略以及腿是如何映射的
当前设置下的最大盈利 / 最大亏损
一个关键见解（例如，“现货目前比盈利区域低 950 点，明天到期”）

保持简洁——图表本身不言自明。

references/strategies.md —— 每种策略类型的详细盈亏公式和边界情况
references/bs_code.md —— 可复制粘贴的 Black-Scholes JS 实现，包含 normCDF

如果不确定特定策略的盈亏公式边界情况，请阅读相关的参考文件。

🇺🇸English

Contains Shell Commands

This skill contains shell command directives (!command``) that may execute system commands. Review carefully before installing.

Options Payoff Curve Skill

Generates a fully interactive HTML widget (via visualize:show_widget) showing:

Expiry payoff curve (dashed gray line) — intrinsic value at expiration
Theoretical value curve (solid colored line) — Black-Scholes price at current DTE/IV
Dynamic sliders for all key parameters
Real-time stats: max profit, max loss, breakevens, current P&L at spot

Step 1: Extract Strategy From User Input

When the user provides a screenshot or text, extract:

Field	Where to find it	Default if missing
Strategy type	Title bar / leg description	"custom"
Underlying	Ticker symbol	SPX
Strike(s)	K1, K2, K3... in title or leg table	nearest round number
Premium paid/received	Filled price or avg price	5.00
Quantity	Position size	1
Multiplier	100 for equity options, 100 for SPX	100
Expiry	Date in title	30 DTE
Spot price	Current underlying price (NOT strike)	middle strike
IV	Shown in greeks panel, or estimate from vega	20%
Risk-free rate	—	4.3%

Critical for screenshots : The spot price is the CURRENT price of the underlying index/stock, NOT the strikes. Never default spot to a strike price value.

Current SPX reference price:

!`python3 -c "import yfinance as yf; print(f'SPX ≈ {yf.Ticker(\"^GSPC\").fast_info[\"lastPrice\"]:.0f}')" 2>/dev/null || echo "SPX price unavailable — check market data"`

Step 2: Identify Strategy Type

Match to one of the supported strategies below, then read the corresponding section in references/strategies.md.

Strategy	Legs	Key Identifiers
butterfly	Buy K1, Sell 2×K2, Buy K3	3 strikes, "Butterfly" in title
vertical_spread	Buy K1, Sell K2 (same expiry)	2 strikes, debit or credit
calendar_spread	Buy far-expiry K, Sell near-expiry K	Same strike, 2 expiries
iron_condor	Sell K2/K3, Buy K1/K4 wings	4 strikes, 2 spreads
straddle	Buy Call K + Buy Put K	Same strike, both types
strangle	Buy OTM Call + Buy OTM Put	2 strikes, both OTM
covered_call	Long 100 shares + Sell Call K	Stock + short call

For strategies not listed, use custom mode: decompose into individual legs and sum their P&Ls.

Step 3: Compute Payoffs

Black-Scholes Put Price

d1 = (ln(S/K) + (r + σ²/2)·T) / (σ·√T)
d2 = d1 - σ·√T
put = K·e^(-rT)·N(-d2) - S·N(-d1)

Black-Scholes Call Price (via put-call parity)

call = put + S - K·e^(-rT)

Butterfly Put Payoff (expiry)

if S >= K3: 0
if S >= K2: K3 - S
if S >= K1: S - K1
else: 0

Net P&L per share = payoff − premium_paid

Vertical Spread (call debit) Payoff (expiry)

long_call = max(S - K1, 0)
short_call = max(S - K2, 0)
payoff = long_call - short_call - net_debit

Calendar Spread Theoretical Value

Calendar cannot be expressed as a simple expiry function — always use BS pricing for both legs:

value = BS(S, K, T_far, r, IV_far) - BS(S, K, T_near, r, IV_near)

For expiry curve of calendar: near leg expires worthless, far leg = BS with remaining T.

Iron Condor Payoff (expiry)

put_spread = max(K2-S, 0) - max(K1-S, 0)   // short put spread
call_spread = max(S-K3, 0) - max(S-K4, 0)  // short call spread
payoff = credit_received - put_spread - call_spread

Step 4: Render the Widget

Use visualize:read_me with modules ["chart", "interactive"] before building.

Required Controls (sliders)

Structure section:

All strike prices (K1, K2, K3... as needed by strategy)
Premium paid/received
Quantity
Multiplier (100 default, show for clarity)

Pricing variables section:

IV % (5–80%, step 0.5)
DTE — days to expiry (0–90)
Risk-free rate % (0–8%)

Spot price:

Full-width slider, range = [min_strike - 20%, max_strike + 20%], defaulting to ACTUAL current spot

Required Stats Cards (live-updating)

Max profit (expiry)
Max loss (expiry)
Breakeven(s) — show both for two-sided strategies
Current theoretical P&L at spot

Chart Specs

X-axis: SPX/underlying price
Y-axis: Total USD P&L (not per-share)
Blue solid line = theoretical value at current DTE/IV
Gray dashed line = expiry payoff
Green dashed vertical = strike prices (K2 center strike brighter)
Amber dashed vertical = current spot price
Fill above zero = green 10% opacity; below zero = red 10% opacity
Tooltip: show both curves on hover

Code template

Use this JS structure inside the widget, adapting pnlExpiry() and bfTheory() per strategy:

// Black-Scholes helpers (always include)
function normCDF(x) { /* Horner approximation */ }
function bsCall(S,K,T,r,sig) { /* standard BS call */ }
function bsPut(S,K,T,r,sig) { /* standard BS put */ }

// Strategy-specific expiry payoff (returns per-share value BEFORE premium)
function expiryValue(S, ...strikes) { ... }

// Strategy-specific theoretical value using BS
function theoreticalValue(S, ...strikes, T, r, iv) { ... }

// Main update() reads all sliders, computes arrays, destroys+recreates Chart.js instance
function update() { ... }

// Attach listeners
['k1','k2',...,'iv','dte','rate','spot'].forEach(id => {
  document.getElementById(id).addEventListener('input', update);
});
update();

Step 5: Respond to User

After rendering the widget, briefly explain:

What strategy was detected and how legs were mapped
Max profit / max loss at current settings
One key insight (e.g., "spot is currently 950 pts below the profit zone, expiring tomorrow")

Keep it concise — the chart speaks for itself.

Reference Files

references/strategies.md — Detailed payoff formulas and edge cases for each strategy type
references/bs_code.md — Copy-paste ready Black-Scholes JS implementation with normCDF

Read the relevant reference file if you're unsure about payoff formula edge cases for a given strategy.

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