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The Options Lab

AEA doesn't trade options — the Investment Policy Statement is long-only equities and ETFs. This tool exists anyway, for the same reason the Leverage Decay Study exists: understanding an instrument precisely is worth doing even for instruments I don't use, and a real Black-Scholes pricer with full Greeks and a payoff diagram is the clearest way to actually see how leverage, time decay, and volatility interact in a single contract.

Pure client-side math. Nothing you enter here is sent anywhere.

Price a contract

Enter your own numbers, or prefill spot and strike from a real holding's last real close.

Spot price ($) Strike price ($) Days to expiration Implied volatility (%) Risk-free rate (%) Type

Position

What the Greeks actually mean

Delta

Directional exposure

How much the option's price moves for a $1 move in the underlying. A 0.50 delta call behaves like owning 50 shares for a small move. Calls range 0 to 1; puts range −1 to 0.

Gamma

How fast delta changes

The rate delta itself changes as the underlying moves. High gamma means your directional exposure can shift fast — it's highest for at-the-money options close to expiration.

Theta

Time decay, per day

How much value the option loses every day, holding everything else constant. This is the cost of being long optionality — and the Leverage Decay Study's whole subject on the ETF side of the fence.

Why this belongs next to the Leverage Decay Study

A 2× leveraged ETF and a call option both give you amplified, path-dependent exposure to an underlying — and both decay in ways a simple "2× the return" or "the stock has to move X%" mental model misses. The Leverage Decay Study measures that decay empirically, with real fund data. This tool shows the same mechanism from the other direction — theoretically, before any real position exists — so you can see theta and volatility drag as the same underlying idea wearing two different instrument wrappers.

Methodology & limitations

Model. Standard Black-Scholes-Merton, European-style exercise, no dividends. Real American-style equity options can be exercised early and often carry dividend adjustments this model doesn't account for — treat this as the standard theoretical baseline, not a precise quote for a real listed contract.

Normal CDF. Computed via the Abramowitz & Stegun 7.1.26 polynomial approximation, accurate to roughly 7 decimal places — more than sufficient for option pricing.

Spot prefill. When you prefill from a real holding, the spot price used is that position's real last close, from the same dataset behind the Volatility & Correlation Engine. The volatility and rate fields are still yours to set — this tool does not pull a live implied-volatility surface or the real risk-free rate.

Not investment advice. AEA does not trade options. Nothing here is a recommendation to buy, sell, or write any options contract.