Separate two option deadlines14 minute read
Options expiration date vs last trading day
Understand why an option expiration date can differ from its last trading day, including AM or PM settlement, exercise cutoffs, holidays, pending orders, and contract checks.
Read guide →Separate open estimates from closed results14 minute read
Options realized vs unrealized P&L: what counts
Understand realized versus unrealized option profit and loss, including marks, actual fills, short premium, partial closes, rolling, exercise, assignment, expiration, and fees.
Read guide →Calculate option returns with a named denominator15 minute read
Options return percentage calculation: choose the base
Calculate option return percentage using realized P&L and a stated denominator, including premium, maximum risk, collateral, stock value, fees, annualization, and open P&L.
Read guide →What a small p-value says and what it never proves15 min read
P-Value and Statistical Significance in Finance
Understand p-values, null hypotheses, test statistics, significance levels, Type I and Type II errors, power, effect size, optional stopping, data snooping, and financial interpretation
Read guide →Two ways to decide which observations count as extreme15 min read
Peaks Over Threshold vs Block Maxima
Compare GPD threshold exceedances with GEV block maxima, including data efficiency, bias–variance choices, dependence, return levels, and diagnostics for selecting an EVT method
Read guide →Understand what an option delivers14 minute read
Physical vs cash-settled options: shares or cash
Compare physically settled and cash-settled options by deliverable, settlement amount, assignment, expiration, multiplier, portfolio impact, and contract risk.
Read guide →Two views of optimal control15 min read
Pontryagin Maximum Principle vs HJB Explained
Compare costates and Hamiltonian maximization with value functions and dynamic programming in deterministic and stochastic financial control
Read guide →Compress overlapping market variables into a few axes18 min read
Principal Component Analysis (PCA) Explained
Learn centering, scaling, covariance, component scores and loadings, explained variance, component selection, and the limits of PCA in finance.
Read guide →Design a fairer comparison before estimating effects18 min read
Propensity Scores, Matching, and Overlap
Learn what propensity scores balance, why overlap and unconfoundedness matter, how matching and weighting change the estimand, and which diagnostics make a financial study credible.
Read guide →Calculate a stock downside floor14 minute read
Protective put max profit, loss, and break-even
Calculate protective put maximum loss, unlimited upside, married-put break-even, floor value, contract coverage, hedge cost, expiration, and basis choices.
Read guide →Sell a near put and buy a farther put at one strike16 min read
Put Calendar Spread Options Strategy
Understand the long put calendar spread, strike and expiration choice, near-put assignment, maximum loss, uncertain break-even, theta, skew, rolling, and residual protection.
Read guide →Pair a farther higher-strike put with a nearer short put16 min read
Put Diagonal Spread Options Strategy
Learn the long put diagonal, strike and expiration choices, short-put assignment, remaining far-put hedge, rolling, volatility exposure, margin, break-even limits, and exits.
Read guide →Combine a bear put spread with an uncovered put15 min read
Put Ratio Spread Options Strategy
Learn the 1-by-2 put ratio spread payoff, maximum profit, debit and credit break-evens, substantial crash loss, Greeks, margin, and assignment risk.
Read guide →Second-order path variation13 min read
Quadratic Variation in Finance Explained
Learn why squared path increments survive at fine scales, produce the Itô correction, and connect diffusion volatility with realized variance
Read guide →Measure density12 min read
Radon–Nikodym Derivative in Finance Explained
Learn how the Radon–Nikodym derivative reweights probabilities, converts expectations, forms a density process, and supports risk-neutral valuation
Read guide →Separate short-ratio income from long-ratio convexity14 min read
Ratio Spread vs Backspread in Options
Compare ratio spreads and backspreads by contract direction, payoff shape, volatility, time decay, tail risk, debit or credit, margin, and assignment.
Read guide →A local experiment on either side of a cutoff18 min read
Regression Discontinuity Design: Logic and Limits
Understand cutoff assignment, continuity, sharp and fuzzy RDD, local linear regression, bandwidth selection, manipulation diagnostics, and financial threshold applications.
Read guide →Dynamic replication12 min read
Replicating Portfolios and Self-Financing Strategies Explained
Learn why identical payoffs imply identical prices, what self-financing means, and how discrete and continuous replication create option values
Read guide →Offset short stock with a synthetic long position15 min read
Reverse Conversion Options Strategy Explained
Understand reversal arbitrage using short stock, a long call, and a short put, with payoff math, stock-borrow costs, dividends, assignment, margin, and execution risk.
Read guide →Finance one option wing by selling the other16 min read
Risk Reversal Options Strategy Explained
Learn bullish and bearish risk reversals, strike selection, expiration payoff, skew exposure, short-option assignment, margin, and why zero premium does not mean zero risk.
Read guide →Separate a directional option trade from a stock hedge15 min read
Risk Reversal vs Collar Options Strategy
Compare risk reversal and collar option strategies by stock ownership, call and put direction, payoff, premium, assignment, downside protection, and upside limits.
Read guide →Manage an in-the-money cash-secured put15 minute read
Rolling cash-secured put vs assignment: true cost
Compare rolling a cash-secured put with assignment by effective share cost, cumulative premium, new strike, funding period, downside, and execution risk.
Read guide →Manage an in-the-money covered call15 minute read
Rolling covered call vs assignment: compare outcomes
Compare rolling a covered call with accepting assignment by cumulative P&L, stock basis, new strike, time, dividends, downside, and execution risk.
Read guide →Turning cumulants into accurate tail probabilities15 min read
Saddlepoint Approximation in Option Pricing Explained
Understand the saddlepoint equation, density and tail approximations, exponential tilting, option-pricing uses, and the numerical checks that matter
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