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) { ... }

// 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();

Step 5: Respond to User

After rendering the widget, briefly explain:

• What strategy was detected and how legs were mapped

• Max profit / max loss at current settings

• One key insight (e.g., "spot is currently 950 pts below the profit zone, expiring tomorrow")

Keep it concise — the chart speaks for itself.

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.