options-payoff

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 and 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
diagonal_spread	Buy far-expiry K1, Sell near-expiry K2	Different strikes, 2 expiries
iron_condor	Sell K2/K3, Buy K1/K4 wings	4 strikes, 2 spreads
jade_lizard	Sell put + Sell call spread, credit ≥ call width	3 strikes
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
protective_put	Long 100 shares + Buy Put K	Stock + long put
naked_put	Sell Put K	Single leg
ratio_spread	Buy 1×K1, Sell N×K2	Unequal quantities
broken_wing_butterfly	Buy K1, Sell 2×K2, Buy K3 with K3−K2 ≠ K2−K1	Asymmetric wings

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 two-sided strategies
• Current theoretical P&L at spot

Chart Specs

• X-axis: 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 (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 expiryValue() and theoreticalValue() 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 (per-share, 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() { ... }

['k1','k2',...,'iv','dte','rate','spot'].forEach(id => {
  document.getElementById(id).addEventListener('input', update);
});
update();

See references/bs_code.md for the full normCDF and bsCall/bsPut implementations.

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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 50 pts below the profit zone, expiring tomorrow")

Keep it concise — the chart speaks for itself.

For Greeks of the position, recommend greeks-calculator. For vol-context interpretation, recommend iv-surface or vol-skew.

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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