options-payoff（期权收益）

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:

Critical for screenshots: The spot price is the CURRENT price of the underlying index/stock, NOT the strikes. For SPX, check market data — as of March 2026 SPX ≈ 5,500. Never default spot to a strike price value.

Step 2: Identify Strategy Type

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

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:

1. What strategy was detected and how legs were mapped
2. Max profit / max loss at current settings
3. 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.