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 calibration as choosing a model’s parameters so its prices fit observed prices for selected liquid options. A common formulation minimizes the aggregate pricing error across instruments with specified characteristics such as strike and…
The note evaluates a proposed way to choose an expiration for uncovered puts: maximize option premium divided by days to expiration. It argues that this ratio tends to mechanically favor shorter-dated contracts, because option value generally does not rise…
The note asks how to obtain the first, second, and fourth cumulants of the variance gamma with stochastic arrival model for use in Fourier-cosine option pricing. It defines the model through a characteristic function built from a variance gamma process with…
The note explains why multiplying an option’s current theta by the days remaining can imply more decay than its current time value. It uses a deep in-the-money call as an example: most of its price is intrinsic value, while the quoted time value is small and…
The exchange discusses whether an asymmetric dynamic conditional correlation GARCH model can produce covariance forecasts beyond one day using R’s rmgarch package. The questioner believes the package supports only one-day forecasts and asks how to obtain an…
The document asks why historical volatility is commonly measured as the standard deviation of log returns. The author points out that a sequence of identical daily percentage changes would have constant log returns and thus zero standard deviation, even…
The document questions an apparent U-shaped implied-volatility pattern in SPX options, especially at far out-of-the-money strikes. A response compares the displayed pattern with a snapshot of implied volatilities for weekly options, reporting generally…
The document addresses how to construct an implied volatility smile from US equity options when no traded option has a strike exactly equal to the underlying price. It asks how to estimate at-the-money volatility and connect out-of-the-money put and call…
The document considers how to turn over-the-counter FX option quotes, reported at different strikes and maturities, into a usable volatility surface. One proposed workflow starts from standard delta quotes, converts each maturity’s deltas to strikes using…
The document investigates a negative value appearing in a plotted down-and-out call price when the underlying starts below the barrier. It presents a Black–Scholes barrier pricing expression, defines its parameters, and compares that expression with an…
The document connects volatility drag to the compounding effect of a gain followed by a loss of equal magnitude. If daily returns alternate between positive and negative moves of size equal to daily volatility, their two-day compounded return is negative,…
The question seeks a way to estimate the risk-neutral variance of an underlying stock’s gross return and considers option-implied distributions alongside estimates made from data under the physical measure. One reply assumes geometric Brownian motion under…
The note explains the convexity adjustment between forward rate agreements and interest-rate futures. It rejects the common explanation that daily futures margining alone creates the difference: collateralized FRA cash flows have a comparable reinvestment…
The note addresses why implied volatilities calculated from option prices differ across strikes. It explains that Black–Scholes implied volatility is the volatility input that reproduces a given market price under the model; when the model assumes a single…
The question describes using QuantLib to price options from a dataset containing contract start dates, expirations, and strikes. The proposed workflow groups contracts by expiration, supplies implied volatilities and market inputs to Heston model helpers,…
The document asks how to compare a volatility arbitrage strategy’s Sharpe ratio with those of established funds. It describes volatility arbitrage broadly as positioning for the difference between implied and realized volatility, often by receiving implied…
The document considers ways to hedge a long SPY position against a substantial decline: a volatility-linked ETF, an inverse leveraged ETF, and put options. It sketches possible gains and costs for each, but the proposed payoff estimates are uncertain and are…
The document addresses why option implied volatility may show a smile or a directional skew, and whether turbulent markets necessarily make one pattern more likely. Its central distinction is that a smile reflects a premium across the wings associated with…
The answer considers whether option positions can combine long gamma with short volatility, or short gamma with long volatility. It argues that a short-dated long straddle against a longer-dated short straddle does not provide the proposed combination, and…
The response offers VIX thresholds as a practical way to describe market volatility levels. It cites historical and practitioner conventions in which readings around 20 indicate heightened concern and readings above 30 are associated with significant market…
The discussion explains two identities used in variance swap analysis. Applying Itô’s lemma to the log of an asset price shows that its quadratic variation can be written as twice the integral of the asset’s proportional price change minus twice the change…
The document describes a research need for reliable Heston option prices, especially for options far out of the money. The author reports that numerical instability in a current implementation produces slightly negative or oscillating prices, which then…
The document describes how a delta-hedged option position can generate gains or losses as the underlying moves. Rebalancing the hedge offsets the option’s first-order price sensitivity, while the remaining daily change is approximated by a gamma term linked…
The document contrasts local volatility models, where price diffusion is driven by a volatility function of price and time, with stochastic volatility models that add a random volatility state coupled to the price process. It asks whether a local volatility…