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 seeks a characteristic function for a Heston stochastic volatility model that includes jumps in both price and variance, describing this as an extension of the Bates model. It provides a reference form for the Bates characteristic function,…
The document defines two expressions used in options and trading conversations. Saying volatility is well bid describes strong buying interest in options that are particularly sensitive to implied volatility, with longer-dated options given as an example…
The question asks how to model daily credit spread changes using equity returns and swap yield changes, especially when equity sensitivity varies with the level of spreads. Replies describe several possible approaches rather than establishing a single best…
The document asks how to obtain a covariance matrix when modeling asset returns with an AR(1)-GJR-GARCH(1,1) specification. A univariate GARCH model estimates conditional volatility for an individual return series, but that alone does not model the…
The document compares a standard GARCH(1,1) conditional variance specification with a version that adds an asymmetric term. In the second model, a dummy variable activates an extra squared-residual contribution when the previous innovation is positive. The…
The document asks how to measure and simulate gradual rises followed by sharp market declines. It presents threshold GARCH as a way to model return asymmetry, with APARCH as a related model family, and points to jump diffusions, often paired with stochastic…
The document discusses when to roll a six-month call option into a longer-dated option, such as one expiring in nine or twelve months. Its main suggestion is to consider rolling when implied volatility in the existing LEAP is elevated and fewer than six…
The document explains the intuition behind representing a variance swap hedge as a weighted portfolio of vanilla options across strikes. The integral represents a continuous strip: at each strike, the portfolio holds an amount determined by a weighting…
The document discusses how to calculate a stressed performance scenario under the PRIIPs framework when the product has a recommended holding period (RHP). The response distinguishes the historical data used to estimate stressed volatility from the future…
The document addresses calibrating the SABR parameters rho and nu when beta and alpha are fixed. The target is to minimize the sum of squared differences between observed market volatilities and model-implied volatilities. The questioner’s R call supplies…
The document compares approaches for calculating American-option implied volatility repeatedly in a production setting. It discusses closed-form approximations, including Barone-Adesi–Whaley, Roll-Geske-Whaley, Ju–Zhong, and Bjerksund–Stensland, while…
The document asks how today’s implied volatility for a forward-start call relates to the implied volatility observed when the option begins. The call’s strike is set as a multiple of the stock price at a future start date, and its payoff depends on the stock…
The document explains why an autocall with a linear payoff can still have volatility exposure. The payment date is determined by whether a second index crosses a barrier: with low volatility it may never cross, while higher volatility increases the chance of…
The document explains how to obtain a partial differential equation for a discount factor used to express a futures price. It starts with a pricing PDE for a claim depending on the spot price and interest rate, then substitutes the similarity form in which…
The document discusses ways to investigate whether returns lead volatility or volatility leads returns. One suggested exploratory approach is to compare correlations between time-shifted returns and volatility with correlations between time-shifted…
The document asks how to interpret a VaR estimate for extreme positive returns after using extreme value theory to model both negative and positive tails. The response distinguishes downside risk from the upper tail: when losses correspond to negative…
The document asks how sums of squared log returns can approximate integrated variance, and why the approximation works even when returns are sampled daily. It distinguishes realized variance, formed by summing squared returns over a sampling grid, from…
The document concerns Monte Carlo valuation of a barrier option when the underlying follows a jump-diffusion process. The question reports a simulated value that differs from the cited paper and jump probabilities that sometimes fall outside the valid…
The document diagnoses a QuantLib error raised while building a Black variance surface from option implied volatilities. The reported validation requires expiry dates to be unique and arranged in chronological order. In the supplied schedule, one-year expiry…
For standard European calls and puts, the document explains why a higher ask price usually implies a higher ask implied volatility than bid implied volatility. The key link is that, holding other inputs constant, these option prices increase as volatility…
The document considers simulating a process formed by adding Brownian motion to a compound Poisson jump process. Its example generates Gaussian Brownian increments with standard deviation scaled by the square root of the time step, then adds potential…
The document asks whether European call prices at a single maturity uniquely determine a time-independent local-volatility function, given that Dupire’s formula ordinarily uses a surface across maturities. One answer cites a result establishing a unique…
The document distinguishes the risk-reversal trading strategy from the market convention used to quote a risk reversal on a volatility surface. A risk reversal combines a call and a put, often selected at specified delta points, while the quotation…
The document compares the spot sensitivities of American and European calls when the stock pays a single dividend before expiry and interest rates are zero. It represents the American call as the expected value of the better choice at the dividend date:…