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 explains how a dealer can handle a client’s request to reduce the notional of an existing SPX variance swap before maturity. It treats variance as additive over time: the position’s value at the unwind date can be viewed as realized cash profit…
The document describes a forex market-making bot that places offers around the mid price and refreshes them at regular intervals. In the market described, thin order books can cause sharp mid-price jumps after a large order; the moves are said to last…
The document clarifies the distinction between an option’s expected value and the instantaneous volatility of its price. Under constant rates, the conditional expected future option value is described as the current value grown at the risk-free rate;…
The document examines a proposed position-sizing rule that scales exposure using portfolio capital, a target volatility, instrument volatility and price, and a portfolio-level multiplier. That multiplier is based on the ratio of target volatility to lagged…
The document explains common desk terminology for locating swaptions on a volatility grid. The grid is organized by option expiry and underlying swap tenor: short expiries are often treated as gamma exposures, while longer expiries are associated with vega.…
For a continuous-time martingale whose price changes are driven by volatility times Brownian motion, the document explains how to express the conditional expected squared one-day return. Ito’s isometry equates the expected square of the stochastic integral…
The document considers a workflow for pricing a European call: fit a SABR volatility smile to market implied volatilities across strikes, use the fitted model to obtain volatility for the target strike, and insert that volatility into the Black–Scholes…
The document asks how to obtain the initial instantaneous forward variance curve used to calibrate variance curve models. Given market variance swap quotes, it describes a common procedure: interpolate total variance, calculated as maturity times quoted…
The document considers returns modeled as volatility multiplied by random innovations, with the innovations following a hyperbolic distribution. It asks whether to estimate volatility first and then fit the innovation distribution to standardized residuals,…
The document explains how to pursue GARCH-based simulation and forecasting in Python, distinguishing conditional volatility modeling from implied volatility. GARCH models describe the changing conditional variance of asset returns; forecasts and simulated…
The document raises a core portfolio risk question: whether historical portfolio volatility can be calculated directly from the portfolio return series or whether each asset’s volatility and the covariances among assets must be calculated separately. It…
The document asks whether a risk-neutral probability density recovered from option prices using the Breeden–Litzenberger method is the same as option gamma. One answer derives a relationship for models in which the option price is homogeneous of degree one…
The post examines a motivation for the SABR model: local volatility models are said to predict implied-volatility smile movements opposite to those observed in markets, whereas the original SABR paper is described as moving the smile in the same direction as…
The document discusses the rationale for testing whether Value at Risk exceedances are independent over time, as in Christoffersen-style backtesting. The question challenges whether this test is meaningful when a risk model might not adjust quickly enough…
The question compares a model-free volatility expression based on option prices across strikes with implied volatility obtained by inverting the Black–Scholes pricing formula. The answer clarifies that the two quantities represent different concepts. The…
The note explains how a variance dispersion position can acquire short volatility exposure after a market decline. The example starts with a vega-neutral portfolio that is short an index option and long options on individual stocks, with deltas hedged at…
The question seeks free or student-accessible books on stochastic volatility modeling. The answer recommends a book by Lorenzo Bergomi and points readers to sample chapters and presentation materials available from the author's website. It also mentions…
The discussion asks whether investors can access systematic risk premia through funds, indices, or exchange-traded products. It names carry, curve or term premium, size, value, momentum and trend, liquidity, and volatility as areas of interest, and notes…
The note surveys alternatives to the Gaussian distribution for fitting empirical stock returns, emphasizing heavy tails and the distinction between describing returns and pricing derivatives. It discusses stable Paretian distributions, the Heston…
The document considers how to infer the volatility implied by a convertible note’s issue price when the instrument includes early conversion, issuer redemption, and capped calls. A simple decomposition into bond value and option value may be inadequate once…
The document considers how to simulate asset paths under SABR when volatility and vol of volatility are high. It describes a Monte Carlo comparison between a call value obtained from Hagan's implied volatility approximation and an estimate from a discretized…
The document investigates why a year-on-year inflation swap rate may need a convexity adjustment when inferred from zero-coupon inflation swap rates. It starts with an example using a current index level and market rates at two maturities, then calculates…
The document explains why changing short-rate volatility can affect an interest rate swap’s value in the Ho–Lee model, despite the intuition that swap pricing depends on current zero-coupon bond prices. It presents the short rate as a drift term plus a…
The document raises a risk-management question about a reported PIMCO trade involving large short positions in an S&P 500 put and call strangle. It asks how other market participants might hedge long option exposure against a seller of that scale, especially…