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
The document introduces variance swaps as instruments for taking a view on an underlying asset’s volatility, described in the question as historical volatility. It asks whether a variance swap can practically hedge vega or volga exposure, and in what market…
The document explains how a near at-the-money payer and receiver swaption pair behaves as the underlying forward swap rate moves. Its initial delta is approximately zero, though the exact value depends on the pricing setup; spot-premium treatment can also…
The document describes estimating an event-related move from options by separating variance expected across ordinary time from the extra variance attributed to the event. It uses at-the-money implied volatilities for the first two expirations after the event…
The document considers the usual estimate that annualized volatility equals monthly return standard deviation multiplied by the square root of twelve, and asks whether different month lengths should change the calculation. It explains that the relevant…
The document explains why implied volatility can still be useful even though it is calculated from an option’s market price. It presents Black–Scholes as a way to transform observed prices into volatility values, which can then be used to estimate prices for…
The document explains how to price a barrier option with a finite-difference engine in QuantLib when volatility is represented by a market implied-volatility surface. It points to the finite-difference Black–Scholes barrier engine and notes that its…
The document derives a European call value when a forward price follows a two-factor diffusion with volatility components that vary over time. It applies the exponential solution for the forward process and combines the factor variances into an integrated…
The question describes problems retrieving an implied volatility smile from a SABR volatility surface through QuantLibXL. A positive time input below one year produces a negative-time error, while another error appears to contradict the function's default…
The document explains why an in-the-money option does not necessarily become more valuable simply because expiration is closer. It separates an option’s value into intrinsic value, determined by the current underlying price and strike, and time value, which…
The document outlines the Black–Scholes derivation: apply Itô’s formula to an option whose value depends on the underlying, combine it with the underlying in a portfolio, hedge away the source of randomness, and use no-arbitrage to obtain the pricing PDE. It…
This document examines how units and parameter choices affect the Avellaneda–Stoikov market-making model. It gives the reservation-price skew and optimal spread equations, then asks how price variance, order-arrival intensity, inventory, and remaining…
The document discusses portfolio optimization using an ETF and VIX futures, comparing minimum-variance and Sharpe-maximizing approaches across different rebalancing schedules. The response focuses on minimum-variance intuition: an asset’s weight is…
The document outlines a variance-covariance approach to estimating volatility for a portfolio of cryptocurrencies. It starts from daily price changes, forms a covariance matrix of daily returns, and scales that matrix by 365 to estimate annual variance,…
The document derives the instantaneous volatility of a zero-coupon bond price under a one-factor Hull–White short-rate model. It presents the bond price as a deterministic function of time multiplied by an exponential term in the current short rate. The…
The document asks whether daily log returns can be presented directly as daily variation when the goal is not to report risk over a longer horizon. It distinguishes an individual return observation from a volatility estimate: one return shows a realized…
The document asks about an approximation discussed in a paper on delta hedging with a volatility smile: treating the sensitivity of implied volatility to the underlying price as equal to its sensitivity to strike. Under a downward-sloping smile, the cited…
The document explains how aggregate dealer gamma may affect hedging flows near options expiry. When dealers are long gamma, movements in the underlying can lead them to trade against the move, buying after declines and selling after rallies. When dealers are…
The document explains that the VIX Flip indicator can be approximated with Williams VIX Fix, a synthetic volatility measure calculated from the highest close over a recent window and the current period's low. The reported formula expresses the gap between…
The document asks whether EGARCH volatility forecasts are biased and seeks a published academic source supporting that claim. It identifies a preprint on bias correction for EGARCH estimators and a published study of finite-sample properties of EGARCH…
The document examines how changing the shift in a SABR model affects recalibrated parameters and swaption sensitivities. It describes experiments that fit shifted SABR to a constructed volatility set, first freeing correlation and volatility of volatility,…
The document explains how the semi-variance HAR model (SHAR) extends the heterogeneous autoregressive model of realized volatility to represent asymmetric effects of past returns. It splits the daily realized variance into positive and negative…
The response clarifies that a forward rate agreement, a caplet or floorlet, and an option on an FRA are different instruments. A caplet and a floorlet on the same future LIBOR fixing have complementary single-period option payoffs and can approximately…
The document outlines a QuantLibXL workflow for valuing a floating-rate bond whose cap and floor strikes vary by coupon. It recommends supplying a strike for each coupon to the floating-rate bond, then pricing the bond with a bond engine. An Ibor coupon…
The document presents an attempted trinomial-tree implementation of an uncertain volatility model for pricing European calls between minimum and maximum volatility bounds. It lays out a backward-induction scheme, defines a discrete second-difference term…