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 derives the risk-neutral version of the Heston stochastic-volatility model from its historical-measure dynamics. It introduces market prices of risk as shifts to the correlated Brownian motions, then applies Girsanov's theorem to express the…
The document raises a question about how changing volatility affects the distribution of option payoffs across simulated underlying-price paths. Its proposed comparison keeps other inputs and the set of paths fixed, then compares payoff histograms produced…
The document frames a forecasting problem: estimating the volatility of a measure such as earnings or cash flows observed across multiple entities over time. It contrasts this panel setting with the familiar single-series case, where a GARCH model can be…
The document outlines how to infer caplet implied volatilities from a sequence of cap prices and swap rates, as a step toward calibrating a Hull–White interest rate model for swaption pricing. It assumes caps are at the money and explains that the inputs…
The document asks whether normally distributed simple returns need the same volatility adjustment used when translating lognormal growth into a continuously compounded rate. It explains that a lognormal price model includes a variance term because…
The document describes Bloomberg's DLIB suite as a toolkit for pricing and calibrating derivative structures, with templates for some exotic products. It presents BLAN as an option for building bespoke deals from scratch and experimenting with different…
This discussion asks whether correlations change more slowly than volatilities and whether clustering affects the two quantities differently. It cites the use of longer rolling windows for ex-ante correlation estimates than for volatility estimates in…
The document explains how daily leveraged and inverse exchange-traded products can lose value through compounding when the underlying index is volatile. It compares short sequences of positive and negative index returns and shows that the inverse product’s…
The document asks whether intraday volatility estimates based on the best bid and ask midpoint can incorporate information from deeper order book levels. A conventional midpoint uses only the top quotes, even when the book contains several visible bid and…
The document explains how correlation between asset returns and volatility innovations affects the relationship between Black–Scholes volatility and a stochastic-volatility model such as Heston. Negative correlation is reported as typical for equity indices…
The document surveys R packages for option pricing and related analysis. It names RQuantLib and NMOF for model implementations, including Black–Scholes–Merton, jump-diffusion, Heston, and characteristic-function approaches. It also points to RND for…
The document asks what the unconditional covariance matrix represents in a Dynamic Conditional Correlation GARCH model. The question contrasts a data-based covariance matrix for two series, built from their individual variances and their covariance, with the…
The document describes several uses of options pricing formulas even when markets are broadly efficient. Models can help traders assess possible mispricing, value contracts that are newly issued or lack a direct market quote, and infer quantities such as…
The document explains how to interpret the variance-rate assumption in the original Black–Scholes model. For a diffusion process, the instantaneous variance rate is the square of the coefficient multiplying the Brownian motion. In geometric Brownian motion…
The document recommends books for a statistics student seeking an introduction to financial theory and models. It points to texts on financial time series, econometrics, volatility, risk management, event studies, asset pricing, and machine learning. The…
The document explains how to derive an implied volatility surface for a currency pair from surfaces quoted for two related pairs. Its example combines EURUSD and USDJPY data to price EURJPY options. It first expresses the target option payoff in terms of the…
The document asks how to calculate the variance of integrated variance in the Heston stochastic-volatility model. It connects the problem to the closely related Cox-Ingersoll-Ross square-root process, whose integrated state variable has a known…
The document asks how a market maker might hedge a short position in down-and-in Bitcoin puts. Its answer contrasts these barrier options with vanilla puts and gives two possible risk-management actions: use Bitcoin-dollar perpetual swaps or dated futures to…
The document compares a two-state hidden Markov model applied to currency-return volatility with a simple threshold that labels observations as high or low volatility. A threshold can produce a similar-looking state sequence, but it does not account for the…
The note explains why an asset’s volatility over a fixed horizon matches the volatility of a prepaid forward contract on that asset with the same expiry. Both are measured as the standard deviation of a log return over the period. At the start, the asset…
The document considers how to represent Bollinger Bands as inputs to a neural network that predicts market direction across multiple stocks. The replies explain that the bands combine a moving average with a volatility-based width, so raw price levels are…
The document explains how to interpret the units of the parameters in the Avellaneda–Stoikov market-making model by tracing where they appear. In the price process, the volatility parameter measures price variation over time. The bid and ask quote offsets…
The document addresses implementing a characteristic function for option pricing in Excel VBA, where Excel's complex-number worksheet functions represent complex values as strings. The answer shows that these functions can be composed by passing their string…
This note explains that the market price of risk does not have to be positive. Its sign reflects how investors value exposure to a risk, in particular the relationship between that risk and the investor’s marginal utility of consumption. Investors may accept…