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 model-risk question: when a trading desk uses the Heston stochastic-volatility model to generate a volatility surface, why might risk management use other models to produce adjustments? It names interest-rate mean reversion and other…
The document frames a derivatives-pricing question about which traded instruments are hardest or infeasible to value. Its concrete example is a best-of or other rainbow option with early exercise. A rainbow payoff depends on multiple underlying assets,…
The document explains the link between gamma and realized volatility for a delta-hedged option position. An option’s value is curved with respect to the underlying price, so a hedge that offsets its current delta removes the local linear exposure but leaves…
The document explains why observed prices and implied volatilities need not match a pricing model perfectly, using SABR and interest rate swaptions as context. Its central point is that market prices arise from trading among participants; models are…
The document describes a researcher’s search for continuous-time stochastic volatility models suitable for simulation and estimation through indirect inference. The stated preferences are models that are reasonably easy to simulate and have relatively few…
The document considers how to value American calls with five-to-ten-year maturities on an accumulation fund that has no readily available exchange price or option quotes. It notes that such long-tenor options may be available over the counter, but…
The document explains two ways to measure an option’s one-day theta when implied volatility varies across expiries. Fixed-expiry theta holds the option’s implied volatility constant during the time bump, matching the Black–Scholes convention. Fixed-tenor…
The note describes an approximate way to hedge a short VIX futures position using SPY shares. It first estimates the beta of the relevant VIX futures contract relative to SPY, then scales that beta by the stated contract multiplier and SPY price to obtain a…
The document examines a lower bound for the variance swap strike, expressed as a risk-neutral average of Black-Scholes implied variance over a standard normal coordinate. It uses a Taylor expansion around the center of that coordinate. The linear, or skew,…
The document explores whether a trader can neutralize an options portfolio’s sensitivity to implied volatility, or vega, while retaining directional exposure. Combining long and short options can offset vega because options carry vega whereas linear…
The document discusses why an implied volatility smile may be absent or not observable in some markets. Where options are not actively quoted, or only at-the-money contracts trade infrequently, there may be too little market information to construct a…
The document presents a proposed model for the change in a return-like series, with the conditional mean depending on the current level and variance. The innovation is specified as normally distributed with that variance. The variance equation depends on a…
The document considers a European call option on the VIX, expressing its payoff as the positive part of the square root of a variable representing squared VIX, minus the strike. It states a Fourier transform involving the error function and asks how that…
The document presents a question about iteratively estimating volatility under the Heston–Nandi model from simulated price data. The author simulates a price process using a separate GARCH-generated volatility series, then applies a proposed recursion to…
The document outlines mathematical preparation for studying stochastic volatility models and volatility arbitrage. It identifies calculus, differential equations, linear algebra, and probability as a sufficient foundation for engaging with standard textbooks…
The discussion explains why the drift term in a Brownian motion with constant drift and volatility does not contribute to quadratic variation, while the Brownian component contributes volatility squared times elapsed time. It introduces quadratic variation…
The document discusses gathering historical listed-option chains and interest-rate inputs for model-free implied-volatility research across several equity indices. It describes using a date override to retrieve historical option tickers for more recent…
The document compares two ways to express a daily high–low range as a percentage: divide the range by the opening price, or compare the high with the low. It argues that the open is a practical reference when measuring the range during the day, since the…
This troubleshooting account describes a failed attempt to bootstrap an optionlet volatility surface from cap and floor volatility data with QuantLibXL. The failure appeared during optionlet volatility calculation, with a root search unable to bracket a…
The discussion explains how to model portfolios whose returns are bounded on one side, using long vanilla options as the example. Rather than fitting a symmetric distribution directly to option returns, it models the underlying stock price and, where…
The document explains how the variance path enters a discretized Heston simulation. In the asset-price update, the current step uses the current variance, floored at zero under the fully truncated scheme. The correlated price shock combines the variance…
The document gives a basic historical method for estimating volatility from a time series of observed prices. Calculate consecutive log returns as the natural logarithm of each price divided by the previous price, then take the standard deviation of those…
The note explains why an out-of-the-money binary call price need not rise monotonically with implied volatility. It suggests plotting the option price across increasing volatility values and gives an example with spot just below the strike, zero interest…
The document explains an equity-linked principal-protected note whose payoff adds the index’s absolute return only if the index stays within a specified barrier throughout the observation period. Crossing the barrier removes the gain, while principal is…