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 considers how to price swaptions at expiry and tenor points that were not directly calibrated, using a SABR volatility cube built from market observations. One proposed practice is to interpolate total implied variance across the cube for the…
The document separates two ways of discussing equity option skew. Black–Scholes implied volatility expresses observed prices through a model that assumes Gaussian log returns; varying implied volatility across strikes describes the market smile or skew. An…
The document addresses whether a Bloomberg swaption premium quote represents a payer or receiver option when calibrating a Hull–White model. The answer says the cited quote is for a straddle, so its premium combines payer and receiver values. It points to…
The document surveys approaches to interpolating option prices or implied volatility while preserving no-arbitrage properties. It recommends normalizing for drift and dividends and working in forward moneyness rather than absolute strike; the resulting price…
The document distinguishes the VIX index from a volatility swap by comparing the quantities each represents. VIX is described as the square root of a variance swap strike, with variance expressed in volatility units. A volatility swap instead pays against…
The question concerns fitting a GARCH model to daily log returns to estimate stock market volatility. One answer points users to Stata’s built-in GARCH command and its help documentation, but does not provide a detailed step-by-step procedure or discuss…
The document asks how to estimate an implied volatility at a chosen strike and maturity when only FX forward rates, domestic and foreign zero rates, at-the-money volatility, and 25-delta risk reversal and butterfly quotes are available. It frames the task as…
The document raises a question about option market quoting: a book states that a strangle’s bid-offer spread expressed in volatility terms is usually wider than the at-the-money spread for the same expiry. The proposed explanation is that options struck away…
The document defines vol-vol breakeven as the instantaneous covariation of log implied volatilities for two options. For a local volatility model, when both options are the same contract, it gives a formula relating this quantity to the spot sensitivity of…
The document compares the standard CAPM beta, built from physical-measure volatilities and correlations, with a risk-neutral beta that uses option-implied quantities. It describes a paper by Buss and Vilkov that reports the risk-neutral version better…
The document discusses generating synthetic foreign-exchange data for algorithm testing, including return paths, OHLC bars, tick timing, and bid-ask spreads. Its main caution is that Gaussian noise around a trend is a poor representation of high-frequency FX…
The answers distinguish implied volatility, inferred from option prices and reflecting priced expectations, from realized volatility measured from observed price movements. They describe volatility as potentially reflecting uncertainty, investor positioning,…
The document explains the apparent conflict between volatility's effect on log returns and its effect on expected prices under geometric Brownian motion (GBM). In the standard GBM specification, the log price contains a volatility adjustment of minus one…
The document asks how angular brackets are used in quantitative finance, especially in volatility writing and in a discussion of return increments. Its examples include brackets around a stochastic integral, statements that daily returns have zero mean and…
The document responds to a question about finding structural breaks in the variance or volatility of financial time series, where the Chow test used by the questioner was not suitable. It points to sequential change-detection methods, particularly a…
The document raises a model-selection question for options on short-term interest rate futures, using SONIA as its example. It contrasts a normal model, motivated by the author's view of the underlying's distribution, with a lognormal Black model whose…
The discussion examines whether a European call can gain value as time passes when the underlying price is held fixed. It challenges the claim that positive interest rates alone rule this out and uses Black–Scholes pricing to illustrate how dividends affect…
The document examines whether dynamically delta hedging a short option guarantees recovery of the option’s initial extrinsic value when it expires out of the money. It explains that this conclusion holds only in an idealized limit: with zero transaction…
The document considers whether a return variance-covariance matrix should be identical under the physical probability measure and the risk-neutral measure. Its answer emphasizes that equality is not generally supported by empirical evidence. In particular,…
The note answers a narrow options question: what happens to the Black–Scholes delta of an out-of-the-money call as implied volatility tends to infinity. It presents the call delta formula and observes that, for a remaining time to expiry, the formula’s…
The document questions whether a prominent spike in the autocorrelation of squared intraday price changes supports the usual account of volatility clustering. It compares a figure in a highly cited article with a later figure in a book by the same authors,…
The document sets up a mean-reverting jump-diffusion with deterministic, time-varying mean-reversion, level, volatility, and jump-arrival parameters. It gives an integral representation of the process and derives expressions for its conditional mean and…
The document describes numerical instability when using the Carr–Madan Fourier transform to price deep in-the-money and out-of-the-money options under the Heston model. Direct numerical integration may produce implausible results, such as a call price above…
The document examines how to obtain volatility exposure with options when trading a complete option strip is impractical. A single dynamically hedged option retains path dependence, while a dynamically hedged straddle or strangle is described as less…