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

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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. For SPX, check market data — as of March 2026 SPX ≈ 5,500. Never default spot to a strike price value.

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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 |
| naked_put | Sell Put K | Single leg |
| ratio_spread | Buy 1×K1, Sell N×K2 | Unequal quantities |

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

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Step 3: Compute Payoffs

Black-Scholes Put Price

CODEBLOCK0

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

CODEBLOCK1

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)

CODEBLOCK3

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

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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 = [minstrike - 20%, maxstrike + 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:

CODEBLOCK6

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Step 5: Respond to User

After rendering the widget, briefly explain:

1. 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.

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Reference Files

• - references/strategies.md — Detailed payoff formulas and edge cases for each strategy type
• INLINECODE8 — 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.