Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
12,303 documents
This beginner discussion distinguishes an option’s payoff at expiration from its value before expiration. Changing volatility does not alter the European option’s terminal payoff diagram; it changes the premium beforehand by changing the range of possible…
The document addresses the misconception that volatility is bounded by the largest possible percentage decline in a stock price. In the Black–Scholes framework, volatility scales the standard deviation of the asset’s log return over the option’s life. That…
The document asks why a Black–Scholes option price differs from an expected option payoff calculated from a spreadsheet model. One response identifies a key model mismatch: Black–Scholes assumes lognormal stock prices, while the spreadsheet uses normally…
The discussion points to two practical approaches for hedging volatility swaps. For forward-starting swaps, it cites a method that uses straddles at a particular strike, with hedge notional linked to the volatility skew at that strike. For…
The document considers valuing a European call when its underlying asset cannot be traded, so the continuous-trading replication assumptions behind Black–Scholes are unavailable. Suggested inputs and approaches include estimating the underlying’s value from…
The document contrasts implied volatility from near-expiry, at-the-money S&P 500 options with the VIX. The response characterizes VIX as a discrete approximation to the square root of a theoretical fair variance swap strike, with its calculation window set…
The document discusses where to obtain constant maturity swap (CMS) swap prices for comparing theoretical valuations with market quotes. One response points to swap-rate ticker conventions for different maturities, while another suggests looking for spread…
The document raises a formula discrepancy in the Yang–Zhang drift-independent volatility estimator. It compares the expression for the weighting constant k in the original paper with a different expression shown in R documentation, and asks why the two…
The document considers a long call calendar spread when the underlying rises above the shared strike by the short option's expiration. It asks whether the spread necessarily loses its entire opening debit, using an example in which the near-dated call is…
The post asks whether a GARCH model implies zero covariance between a squared return and a lagged return. It identifies the conditional variance as a function of past squared returns and variance, then considers how that dependence affects the expectation…
The document considers how to improve an Ornstein–Uhlenbeck model of EUR/USD when it understates large two-hour price ranges. The author has calibrated the process to historical mean, standard deviation, and total absolute variation, then explored adding…
The document derives a way to constrain a fund’s next weekly return so that its rolling five-year, annualized ex-post volatility is less likely to exceed a chosen threshold. It treats the historical weekly returns as fixed, assumes the next return is…
The document explains leptokurtosis as a return distribution with heavier tails than a normal distribution, which means extreme outcomes occur with greater probability. For investors, that can translate into a higher chance of unusually large gains or…
The document describes implied volatility as a way to represent option prices on a more interpretable and comparable scale. A pricing model maps a market option price to the volatility input that would reproduce that price, allowing traders to discuss an…
The document asks whether trading strategies can remove volatility clustering—the persistence of large or small absolute returns—and what that would imply for diversification and alpha. It contrasts the CAPM view of market exposure with anecdotal claims that…
The document asks how to estimate the variance of monthly returns when a return series includes both monthly observations and one quarterly aggregate. The proposed response describes a moment-based approach under temporal independence: infer the quarterly…
The document concerns hybrid models that combine Heston stochastic volatility with Hull–White interest rates. The question is how to approximate European option prices for model calibration, particularly when the pricing approach uses Monte Carlo simulation.…
The document poses a modeling question about whether local volatility derived from an observed implied volatility surface reproduces that surface or changes its skew. It outlines a workflow: obtain market implied volatilities, fit a model such as SVI, use…
The document explains a linear approximation for implied volatility in Emanuel Derman’s sticky implied tree model. The answer starts with local volatility modeled as a linear function of the underlying price, with slope determined by a parameter describing…
The document considers how to recover the risk-neutral density of an underlying at a given expiry from call option implied volatilities across strikes. It describes converting each implied volatility into a Black–Scholes call price, then applying the…
The note explains how a conditional expectation at a specific asset level can be expressed as a ratio of expectations weighted by the Dirac delta function. For a terminal asset value and a random variance, the numerator weights variance by the event density…
The document considers a heterogeneous portfolio in which inverse-volatility risk parity can assign very large weights to instruments whose estimated volatility has fallen relative to the rest. It describes a proposed cap that compares risk-parity weights…
The question asks how to sketch second-order Greek profiles for a European vanilla payoff, such as a butterfly, without computing a full profile. It is concerned with how Greeks vary as spot or volatility changes, including vanna, vomma, and the changes in…
The document examines the difference between an approximate daily P&L formula for a delta-hedged option and P&L calculated from changes in option and stock values. One response explains that the gamma-and-volatility expression gives an average P&L, so it…