/options-payoff

name: options-payoff
description: >
  Generate an interactive options payoff curve chart with dynamic parameter controls.
  Use this skill whenever the user shares an options position screenshot, describes an options strategy,
  or asks to visualize how an options trade makes or loses money. Triggers include: any mention of
  butterfly, spread (vertical/calendar/diagonal/ratio), straddle, strangle, condor, covered call,
  protective put, iron condor, or any multi-leg options structure. Also triggers when a user pastes
  strike prices, premiums, expiry dates, or says things like "show me the payoff", "draw the P&L curve",
  "what does this trade look like", or uploads a screenshot from a broker (IBKR, TastyTrade, Robinhood, etc).
  Always use this skill even if the user only provides partial info — extract what you can and use defaults for the rest.

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 | | **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.

---

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) {