options-payoff

SKILL.md

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.