Market snapshot · September 18, 2026 close
S&P 500 (SPY) $761.69 −0.13% Nasdaq-100 (QQQ) $721.45 +0.60% Dow (DIA) $515.88 −0.48% Russell 2000 (IWM) $284.10 −0.52% 10-Year Treasury (IEF) $90.80 −0.49% Crude Oil (USO) $153.82 −0.93% Gold (GLD) $401.17 +0.74% US Dollar Index (UUP) $28.39 −0.02% Volatility (VXX) $17.76 +0.31% Semiconductors (SMH) $573.00 +2.17% Silver (SLV) $59.93 +1.65% Emerging Markets (EEM) $67.03 +0.19% Bitcoin (BTC) $81,055.00 +4.51% Ethereum (ETH) $2,630.20 +5.92% S&P 500 (SPY) $761.69 −0.13% Nasdaq-100 (QQQ) $721.45 +0.60% Dow (DIA) $515.88 −0.48% Russell 2000 (IWM) $284.10 −0.52% 10-Year Treasury (IEF) $90.80 −0.49% Crude Oil (USO) $153.82 −0.93% Gold (GLD) $401.17 +0.74% US Dollar Index (UUP) $28.39 −0.02% Volatility (VXX) $17.76 +0.31% Semiconductors (SMH) $573.00 +2.17% Silver (SLV) $59.93 +1.65% Emerging Markets (EEM) $67.03 +0.19% Bitcoin (BTC) $81,055.00 +4.51% Ethereum (ETH) $2,630.20 +5.92%
AEACapital Research

Independent student research — not an investment firm or financial advice

Tool · Derivatives · No login

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.

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.