Learn the math of options

Short, plain-English guides with real numbers, and a calculator for every idea.

Guides

• Implied vs realized volatilityThe gap that decides whether a trade pays on average.
• Profit chance vs expected valueHow a 90% winner can still lose money.
• How Options Verdict calculatesEvery formula and assumption.
• GlossaryOptions terms in plain English.

Strategies

Sell premium

• Iron condorCollects a credit by betting the price stays inside a range.
• Put credit spreadCollects a credit by betting the price stays above a level.
• Call credit spreadCollects a credit by betting the price stays below a level.
• Iron butterflyCollects a larger credit by betting the price pins near today's level.

Buy

• Bull call spreadPays a debit for a capped profit if the price rises.
• Bear put spreadPays a debit for a capped profit if the price falls.
• Long callPays a premium for gains if the price rises past the strike.
• Long putPays a premium for gains if the price falls past the strike.
• Long straddlePays for both a call and a put to profit from a large move either way.
• Long strangleA cheaper straddle: out-of-the-money options on both sides.

Butterflies & condors

• Call butterflyPays a small debit for a big payout if the price pins near the middle strike.
• Put broken-wing butterflyA butterfly with a wider lower wing, often opened for a credit, with no risk if the price rises.

Uncapped risk

• Cash-secured putSells a put, with cash set aside to buy the shares if assigned.
• Short strangleSells a put and a call outside the range for a bigger credit, with no protection on either side.
• Short straddleSells a put and a call at the same strike for the largest credit, betting the price barely moves.
• Jade lizardA short put plus a call credit spread, with no risk on the upside if the credit is big enough.
• Risk reversalSells a put to pay for a call: a bet on direction, often for little or no money.

With shares

• Covered callOwns 100 shares and sells a call against them for income.
• CollarOwns shares, buys a put for protection, and sells a call to pay for it.
• Protective putOwns shares and buys a put as insurance.

Tools

• Options profit calculatorPayoff, max profit and loss for 20 strategies.
• Expected value calculatorWhat a trade makes on average, from realized volatility.
• Probability of profit calculatorThe market-implied chance a trade ends with a profit.
• Position size calculatorHow many contracts fit your risk rules.
• Expected move calculatorHow far the market expects a stock to move.