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 that Black-Scholes-Merton remains common in practice for European options, including settings where markets quote volatility and the model converts that volatility into prices. It also notes that exchanges may use Black-Scholes variants…
The document explains why a one-step-ahead prediction interval from a fitted ARIMA model need not automatically narrow as the estimation sample grows. In a simple ARIMA specification with Gaussian, homoskedastic errors, the conditional forecast variance is…
The document explains how an empirically calibrated SVI volatility surface can support option pricing and Greek estimates. SVI maps maturity and strike to an implied volatility; that volatility can then be supplied to a Black–Scholes routine to obtain a…
The document is a curated list of academic papers on historical option returns and strategies. It points readers to work on buy-write portfolios, option returns, volatility and skewness, dispersion trading, expiration effects, and whether options are…
The document asks how to expand a financial stochastic differential equation when the diffusion coefficient depends on both the underlying price and a stochastic volatility factor, as in a SABR-style model. It contrasts this setup with simpler stochastic…
The document explains why implied volatility often rises away from the at-the-money strike, drawing on three complementary interpretations. One links smile curvature to higher moments of the return distribution: convexity can reflect positive excess…
The document derives a closed-form price for a European currency call when domestic and foreign interest rates follow Hull–White dynamics and spot FX has constant volatility. It changes from the domestic risk-neutral measure to the domestic maturity-forward…
The document describes why valuation of the foreign leg of a mark-to-market cross-currency swap can require a convexity adjustment. It writes the foreign-leg cash flows and explains that the relevant expectation is taken under the domestic measure, while the…
The document asks how to break an option position’s Vega P&L into contributions from at-the-money volatility, skew, curvature, and related SVI-JW parameters. It proposes approximating the change in implied volatility with a first-order expansion in those…
The document proposes valuing the principal floor embedded in an inflation-linked bond by treating the consumer price index as an underlying asset and the floor as a put option. When traded inflation floor instruments are unavailable, it suggests estimating…
The document explains why a Black–Scholes cash-or-nothing call can be priced below 50% even when the underlying is above the strike. Its central point is that the model uses a lognormal distribution for the future price, whose positive skew means the…
The document presents an EGARCH specification for changes in a series and its conditional log variance. The mean equation includes seasonal indicators and two regime indicators interacting with seasonal effects. The variance equation includes lagged…
The document asks whether historical data can estimate American put premiums in the same way that expiry payoffs are used to estimate European put premiums. It proposes replacing the expiry return with the minimum return during the option’s life, then…
The document compares two ways to study annual return distributions: calculating a rolling one-year return for every trading day, or sampling one return per year from a fixed annual date. The example uses long-run S&P data and reports broadly similar central…
The note gives an intuition for how the Heston stochastic-volatility parameters correlation and volatility of volatility affect implied-volatility shape. It frames the smile through the risk-neutral distribution: heavier tails raise out-of-the-money option…
The document presents a QuantLib setup for pricing a vanilla European call and obtaining delta, gamma, vega, and theta. The example specifies market inputs, dates, yield and volatility curves, an option payoff and exercise date, then connects them through an…
The document clarifies that volatility is defined relative to a model and, in the Black–Scholes setting, describes the standard deviation of log returns per square root of time. It derives a confidence interval for log returns using normal quantiles, then…
The document considers selling a nearer-dated straddle and buying a later-dated one to gain exposure to volatility over a future period. This is described as an options calendar spread: approximately offsetting deltas can limit immediate directional…
The document asks whether option open interest and trading-volume changes can be incorporated into pricing models or used to forecast asset prices. It connects the question to supply and demand, implied volatility, option Greeks, and trader commitment,…
The document asks how to assess the accuracy of SABR implied volatility surfaces for a chosen equity index and historical period. Its proposed approach is to calibrate SABR, obtain the model’s implied volatilities, and compare them with historical volatility…
The document asks how to interpret references to foreign-exchange grid changes in stress testing. It gives an example in which day-to-day stress moves in the U.S. dollar are linked to vanilla EUR/USD options positioning: long strike positions expire while…
The document raises a notation and interpretation question about the market price of risk in the Heston stochastic-volatility model. In the expression discussed, one component depends on the instantaneous variance through its square root, while another…
The question compares two ways of relating monthly and annual return volatility. It assigns each month one twelfth of that year’s annual return, so all twelve monthly observations within a year are identical. Under that assumption, monthly volatility is one…
The document discusses why Black-Scholes Greeks remain common in vanilla option risk management despite the availability of stochastic-volatility models. One response favors using hedge sensitivities consistent with the model used to price trades, noting…