options-payoff

Options Payoff Curve Skill

If your host has not already executed the shell probes below (for example, in Codex), run the commands inside the ! wrappers with its shell tool before choosing a setup path. Use the actual output; if shell access is unavailable, report that limitation.

Generates an interactive HTML chart using the host's available visualization tool, or a standalone HTML file in Codex, 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 shown in the screenshot or text	live quote (see below); middle strike only if no quote is available
IV	Shown in greeks panel, or estimate from vega	20%
Risk-free rate	—	4.3%

Spot for screenshots: spot is the underlying's current price, and broker screenshots often omit it or show it far from the strikes — don't read it off the strike labels. Use the price shown, else a live quote (the SPX probe below, or yfinance for other underlyings). Fall back to the middle strike only when no quote is available, and tell the user you did.

Current SPX reference price:

!`python3 -c "exec('try:\n import yfinance as yf\n p=yf.Ticker(\'^GSPC\').fast_info[\'lastPrice\']\n print(f\'SPX ≈ {p:.0f}\')\nexcept Exception:\n print(\'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

When visualize:read_me is available, read modules ["chart", "interactive"] before building and use visualize:show_widget to render. Otherwise use an available host visualization tool according to its documented interface. In Codex without an inline renderer, save a complete HTML document in the workspace, include the chart dependencies and CSS, verify it in a browser when available, and return a clickable file link. Preserve all controls and calculations below. Do not call tools that the host does not expose.

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) { ... }

// Main update() reads all sliders, computes arrays, destroys+recreates Chart.js instance
function update() { ... }

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

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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 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
• references/bs_code.md — 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.