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 asks why a study of a two-factor Double Heston model calibrates against option-market observations from many Wednesdays across a year, rather than conducting a separate calibration for each date. It contrasts that setup with research using…
The document describes how to estimate a foreign-exchange risk-neutral density from vanilla option data, in the context of comparing the distribution for GBP/EUR around two historical dates. The required inputs include option prices across strikes and…
The document considers an arithmetic Brownian motion with constant volatility and asks how often it is expected to move a fixed distance from its current level, resetting the reference band after each crossing. The question is framed in terms of repeated…
The document raises the hypothesis that trend-following strategies may perform better in low-volatility conditions and asks how a trader might switch between trend and range-bound approaches. It defines volatility as the standard deviation of the price rate…
The document describes how practitioners can approximate a digital option using a narrow call spread around its strike. Buying the lower-strike call and selling the upper-strike call creates a payoff concentrated between the strikes; as the gap narrows, the…
The document explains why commodity options commonly reference futures or forwards rather than spot prices. Futures can offer liquid, standardized contracts with established price discovery and settlement conventions, making them practical underlyings for…
The document raises a question about calculating rolling volatility for a PRIIPs category 2 stress scenario. The asker has calculated the initial sequence of log returns but is unsure how to apply the formula shown in presentation slides and reports getting…
The document explains why higher volatility can increase the cost of delta-hedging a short option. Its central point is that the volatility used to price an option is an estimate of what the underlying will realize over the option’s life. If actual realized…
The discussion addresses the lack of a direct implementation for a VECM-GARCH model in R and outlines a possible approximation. First estimate an error-correction term, for example with the Johansen procedure, then specify separate conditional mean and GARCH…
The question compares Nasdaq volatility across years using average daily true range (TR). Since the index level changes over time, the author asks whether TR should be converted to a percentage or expressed through logarithms. The response says the right…
A constant maturity swap rate is the par swap rate for a chosen tenor, observed on each reset date. A CMS leg therefore references a swap rate such as the ten-year rate even when payments reset more frequently. In a CMS swap, that rate may be exchanged for a…
The post asks how a trader should adjust a volatility surface when pricing a product that includes a long option. The answer describes shifting the parameters of a chosen surface model in absolute terms, with adjustments reflecting the trader’s exposure to…
The document examines how an option’s theta changes as time passes, sometimes described as theta acceleration. It distinguishes the textbook Black–Scholes theta from a finite-difference estimate obtained by repricing after a one-day time shift. Comparing…
The question asks how to model high-frequency asset returns with a Student-t distribution after estimating two-scale realized volatility, and how to annualize the result and choose a sampling frequency. The response focuses on degrees-of-freedom estimation…
The document considers calibrating an equity stochastic-volatility model alongside a stochastic short rate, with correlations among the driving processes. It explains that the stated combination may lack a tractable closed-form pricing formula, making direct…
The document frames the model-selection problem for pricing vanilla swaptions on fixed-versus-floating or floating-versus-floating legs. Requirements include multiple floating-rate tenors, OIS and LIBOR legs across currencies, mid-curve structures, and both…
The document considers whether options can reveal the market’s expected volatility from one close to the following open. It explains that an option’s implied variance over its life represents variance accumulated across the full interval to expiry. A quoted…
The document asks whether a volatility skew creates expected profit from buying an at-the-money option and delta hedging it. Its answer separates implied volatility from the path of realized prices: a move to a particular terminal level does not reveal how…
The note examines why an equity option’s annualized at-the-money implied volatility can be higher for a shorter expiry than for a longer one. It distinguishes a downward-sloping volatility term structure from negative forward variance: comparing two implied…
The document compares two ways to estimate the price of a European call at a strike and maturity absent from the market: interpolate neighboring option prices directly, or interpolate model inputs such as implied volatility and then reprice with…
The discussion explains why delta neutrality is common in options trading while emphasizing that it depends on the trader’s objective. A market maker who earns spreads may hedge directional exposure to focus on volatility and pricing, whereas a risk taker…
The document examines why the Schöbel–Zhu stochastic volatility model can be treated as affine when deriving the stock price characteristic function. It describes augmenting the state with squared volatility and applies Itô’s lemma to obtain the dynamics of…
The document explains how to interpret realized variance formed by summing squared returns over a chosen sampling window. A sum of 5-minute squared returns covering two hours is a two-hour realized variance; annualization requires scaling by the number of…
The document describes how to recover an option’s implied volatility when its price must be estimated by Monte Carlo simulation. Independent random draws at each volatility can make estimated prices jump around, obscuring the price-versus-volatility…