State-contingent claims12 min read
Arrow–Debreu State Prices Explained
Understand state-contingent securities, why state prices differ from probabilities, and how option-price curvature reveals a risk-neutral density
Read guideOptions field guide
All guides · Page 2
Plain-language guides to earnings, implied volatility, option strategies, target prices, and time decay
331 guides
Calculate a bearish call credit spread13 minute read
Bear call spread max profit, loss, and break-even
Calculate bear call spread maximum profit, maximum loss, expiration break-even, fees, buying power, dividend risk, and short-call assignment outcomes.
Read guideCalculate a bearish put debit spread13 minute read
Bear put spread max profit, loss, and break-even
Calculate bear put spread maximum profit, maximum loss, expiration break-even, contract multiplier, costs, and short-put assignment scenarios.
Read guideWhy a model can explain history and fail the next period15 min read
Bias–Variance Tradeoff and Financial Model Overfitting
Understand prediction bias, estimation variance, irreducible noise, model complexity, time-series validation, data snooping, backtest overfitting, and governance for financial models
Read guideSeparate the two probability terms inside Black–Scholes18 min read
Black–Scholes d1 vs d2 Explained
Understand the d1 and d2 formulas, why N(d1) relates to call delta, why N(d2) relates to risk-neutral expiration ITM probability, and their limits.
Read guidePricing foundations12 min read
Black–Scholes Model Assumptions and Limits Explained
Learn how Black–Scholes prices European options through replication, what its inputs and assumptions mean, and where market reality departs from the model
Read guideConvert a box price into a comparable financing yield16 min read
Box Spread Implied Interest Rate Calculation
Calculate a box spread implied simple or continuous interest rate from strike width, executable box price, days to expiration, multiplier, fees, and rate convention.
Read guideCombine two verticals into a fixed expiration payoff16 min read
Box Spread Options Strategy Explained
Learn the four-leg box spread, fixed strike-width payoff, long and short cash flows, European versus American exercise, execution, margin, and tax risks.
Read guideCalculate every body and tail outcome before trading18 min read
Broken-Wing Butterfly Max Profit and Loss Calculation
Calculate broken-wing butterfly maximum profit, tail losses, break-evens, signed entry credit, call and put formulas, contract multiplier, fees, and assignment scenarios.
Read guideBreak butterfly symmetry to create directional tail risk17 min read
Broken-Wing Butterfly Options Strategy Explained
Learn the broken-wing or skip-strike butterfly, its 1-2-1 legs, unequal wing widths, credit and debit entries, peak payoff, tail loss, assignment, and execution risks.
Read guideCalculate a bullish call debit spread13 minute read
Bull call spread max profit, loss, and break-even
Calculate bull call spread maximum profit, maximum loss, expiration break-even, contract value, fees, and outcomes before and at expiration.
Read guideCalculate a bullish put credit spread13 minute read
Bull put spread max profit, loss, and break-even
Calculate bull put spread maximum profit, maximum loss, expiration break-even, buying power, fees, and assignment outcomes from the actual credit.
Read guideSell a near call and buy a farther call at one strike16 min read
Call Calendar Spread Options Strategy
Learn the long call calendar spread, same-strike expiration selection, near-call assignment, uncertain maximum profit, theta, vega, dividends, rolling, and exit planning.
Read guidePair a farther lower-strike call with a nearer short call16 min read
Call Diagonal Spread Options Strategy
Understand the long call diagonal, strike and expiration selection, near-term assignment, far-call time value, rolling, PMCC differences, Greeks, margin, and exit planning.
Read guideCombine a bull call spread with an uncovered call15 min read
Call Ratio Spread Options Strategy
Learn the 1-by-2 call ratio spread payoff, maximum profit, debit and credit break-evens, unlimited upside loss, Greeks, margin, and assignment risk.
Read guideChoose the option type and tail that fit the forecast16 min read
Call vs Put Broken-Wing Butterfly
Compare call and put broken-wing butterflies by leg order, wide-wing direction, expiration tails, credit, liquidity, early assignment, dividends, and settlement outcomes.
Read guideWhich Gaussian path shifts are admissible15 min read
Cameron–Martin Theorem in Finance Explained
Learn which translations preserve equivalence of Wiener measure, what the Cameron–Martin space contains, and how path shifts relate to Girsanov and finance
Read guideSeparate premium from signed position numbers14 minute read
Can an option price or value be negative?
Understand why a standard single-option premium and intrinsic value are nonnegative while option P&L, short-position value, multi-leg net prices, rolls, and broker displays can show negative numbers.
Read guideUnderstand risk liquidation before expiration16 minute read
Can my broker close my option position without permission?
Learn when a broker may liquidate an option position, why margin and expiration risk matter, what execution cannot guarantee, and how to reconcile a forced close.
Read guideSeparate option leverage from broker borrowing16 minute read
Can you buy options on margin?
Learn why long-option premium is usually paid in full, why options may still require a margin account, when interest starts, and what buying-power reduction means.
Read guideTrace the funding source before reusing proceeds15 minute read
Can you buy options with unsettled funds?
Learn when a cash account may display unsettled sale proceeds for option purchases, how good faith and freeriding violations arise, and which balance fields to verify.
Read guideIdentify the position before naming the loss limit15 minute read
Can you lose more than the option premium paid?
Learn when option loss is limited to premium and when short options, exercise, assignment, stock positions, spreads, fees, and broken hedges can create larger losses or cash obligations.
Read guideMatch approval, funding, and deliverables15 minute read
Can you trade options in a cash account?
Learn which option trades may fit a cash account, why broker approval still matters, and how full payment, covered obligations, settlement, exercise, and strategy levels affect access.
Read guideMatch retirement rules to option obligations16 minute read
Can you trade options in an IRA?
Learn when an IRA may trade options, which strategies brokers commonly restrict, how exercise and assignment must be funded, and why limited margin is not borrowing.
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