options-payoff

The saved excerpt is a snapshot from review. The external source remains the complete and most current version.

---
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) -