options-payoff

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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

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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. 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"`

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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

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

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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 = [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