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 raises a measurement question for a volatility risk premium strategy using options on a futures contract. The underlying future expires annually, while options are available at quarterly expiries. The proposed measure is to compare the implied…
The document considers whether a continuously traded energy market can be modeled with diffusion and an auction-based market with occasional jumps. The proposed approach is to build a separate jump-diffusion process for each market, allowing the auction…
The document addresses how to interpret implied volatility for commodity options whose delivery or settlement reflects prices over a period, as in power markets. Its central point is that implied volatility is tied to the underlying specified in the option…
The document compares ways to value constant-maturity swap (CMS) products, focusing on how an annuity mapping function and convexity adjustment account for the change of measure. One approach approximates the expected mapped swap rate with a second-order…
The document asks whether a short position in the three-month VXV index and a long position in a two-month VIX future can lock in a volatility spread. The proposed reasoning is that both positions might converge to VIX exposure at the future’s expiration,…
The document explains when a European call price from a Heston model can be represented by a Black–Scholes implied volatility. It states that the Heston asset-price and variance processes do not generally have explicit pathwise solutions, though Fourier…
The document clarifies why two calculations on a rising price series produce very different values: one measures dispersion of price levels around their mean, while the other uses changes in log prices. These are different data series and have different…
The document asks why investment banks need quantitative models when exchange-traded options already have market prices. It distinguishes liquid calls and puts, whose prices are set through trading, from the role of Black–Scholes in organizing those prices…
The document considers how to calculate a mid implied volatility from bid and ask implied volatilities without choosing a pricing model. It concludes that averaging the two volatilities is the only model-free approach. The explanation maps volatility to a…
The document asks whether currency forwards that satisfy SABR dynamics individually will retain that form when combined through an FX triangle. Treating the cross rate as the product of two diffusion processes, the answer derives restrictions from matching…
The document explains why geometric Brownian motion parameters can be confusing: arithmetic returns and log returns are calculated differently, and the same distinction affects how a price process is modeled. A price path that falls and then recovers can…
The document questions whether standard GARCH models adequately describe one-minute Bitcoin returns. The sample is characterized by frequent zero returns, low return magnitudes, and apparent microstructure noise; the author also reports that squared…
The document considers how to detect a sharp price move after an extended calm period. It suggests volatility bands as a way to compare price levels with recent volatility, and identifies Bollinger Bandwidth as a related measure based on the spread between…
The document explains swimming delta as an option’s total sensitivity to the underlying when implied volatility changes with the underlying price. Standard Black–Scholes delta is a partial derivative that holds volatility constant. Under a skew-aware view, a…
The document explains why the accrual factor appears when normal swap rate volatility and correlation are mapped into a lognormal volatility parameter in a one-factor CMS model. Define the transformed rate as one plus the accrual factor times the swap rate.…
The document frames a question about whether VIX is a martingale when the S&P 500 follows a Gaussian diffusion. It defines squared VIX for a fixed tenor as the risk-neutral expectation of average integrated variance over the tenor. It then applies the…
The response offers an intuition for why at-the-money implied volatility can act like an average volatility, particularly when used in quanto option pricing. It describes a result in which squared implied volatility is represented as a time average of…
The author compares a personal implementation of the Kou double-exponential jump-diffusion model with published European option prices. The code aims to price vanilla calls by combining Poisson-weighted jump contributions, normal distribution terms, and…
The document sets up a perpetual option whose payoff is the larger of two put-like payoffs, one with strike K1 and slope −1 and the other with strike K2 and slope −2. It begins with the standard perpetual-option ordinary differential equation under geometric…
The document asks whether a single constant volatility can approximate prices produced from a curve or surface of Black implied volatilities for products such as floating-rate notes with caps or floors and constant-maturity swaps. It also asks whether a…
The note addresses why a set of SABR-calibrated volatilities may appear to show only a downward skew rather than a volatility smile. It explains that the referenced paper shifts all observed strikes so they become positive before fitting the SABR model, and…
The document compares the adoption of the MOVE and TYVIX interest-rate volatility indices with the popularity of VIX. It distinguishes MOVE, which measures implied yield volatility using rates-market quotes, from TYVIX, which measured Treasury price…
The document distinguishes implied volatility from market implied volatility, concluding that the terms generally refer to the same quantity: volatility inferred from observed option prices. It then explains why traders quote options in volatility terms…
The document explains the standard time-scaling rule for continuously compounded stock returns. Under a Brownian-motion model with independent return increments, the variance accumulated over a horizon is the sum of the variances of its increments. Variance…