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 how to model changes in implied volatility when approximating an option portfolio’s profit and loss with delta, gamma, and vega terms. It distinguishes historical VaR, which can reprice a portfolio across observed market scenarios without…
The document asks whether the volatility smile and the volatility-of-volatility smile can both arise from dependence between spot and volatility. It proposes viewing the relationship in two directions: volatility moves affecting spot may help explain the…
The document clarifies an example about a forward-start variance swap and whether a statement about implied volatility contains a typo. It explains that the relevant forward-start swap strike represents today’s expectation of the variance-swap strike for a…
The document explains how Dupire’s formula relates local volatility to the time and strike derivatives of call prices, assuming no dividends. It walks through a small strike-and-maturity table to estimate those derivatives with finite differences and obtain…
In the Basel market risk framework, the reduced set of risk factors is used to calibrate stressed expected shortfall when a sufficiently long history is unavailable for the full model. Banks select factors relevant to their portfolio and with adequate…
The note explains why an at-the-money short-dated straddle can be approximated using implied volatility. In a Black–Scholes setting, put-call parity reduces the value of an ATM-forward straddle to twice the call value. The ATM call value is approximated as a…
The discussion clarifies whether the VIX is leading or lagging. Because it is calculated from option prices and represents the market’s implied expectation of volatility over the coming period, it is forward-looking in that sense. It does not independently…
The discussion explains why out-of-the-money VIX puts expiring on a given date can lose value even when the spot VIX falls sharply. The key distinction is that VIX options are tied to the VIX futures contract for their expiration, not directly to the spot…
The document raises a question about constructing a variance-swap replication portfolio from options. It describes an apparent jump in implied volatility when the option wing switches from puts below a strike to calls above it. The quoted explanation is that…
The document investigates whether an FX option’s time to expiry in an at-the-money delta-neutral strike calculation includes hours and minutes or counts only whole days. It applies the standard forward-based strike formula to a one-day example, using the…
The document reconciles several formulations of Durrleman’s condition for preventing butterfly arbitrage in an implied volatility surface. It explains how expressions differ when volatility is represented as raw volatility, total volatility, or total…
The document asks why volatility models often treat out-of-the-money calls and puts as a group even though their implied volatilities can differ. It identifies liquidity as a reason for focusing on OTM contracts and notes that OTM puts commonly carry higher…
The document explains how to convert a perturbative approximation for a vanilla call's equivalent Black volatility into an expansion centered at the midpoint between the current forward and strike. The original approximation expands the local volatility…
The document describes a daily-rolled backtest of EURUSD options using one-month and two-month straddles, 25-delta risk reversals, and 25-delta butterflies. Each position is held for one trading day, with the next day's valuation using the full volatility…
The document sketches why a market with stochastic volatility may be incomplete when volatility risk is driven by an independent source of randomness that cannot be traded directly. In a one-stock setting, changing the risk premium associated with the…
The document investigates a Python QuantLib TypeError raised while constructing Heston model calibration helpers for options. The replies point to mismatched input types or values as the likely cause and identify code issues to check, including an…
The response distinguishes two interpretations of a share purchase plan in which the bank can terminate during the purchase period. If the customer’s price is the average only through the termination date, the answer argues that termination does not create…
The document clarifies how SVI parameterizations describe implied volatility data. Raw and natural SVI parameterizations represent total implied variance across strikes for a single expiry, while SVI-Jump-Wings represents implied variance for a single…
The document explains why binary option quotes that appear inconsistent with a simple Black–Scholes volatility range may still be reasonable. It gives the digital call price in terms of the forward price, strike, time to expiry, rates, and volatility, then…
The document considers how to adjust a fitted vanilla-option implied volatility surface to represent a lower-volatility market or an abrupt volatility shock. It cautions that blindly adding a constant to implied volatility or multiplying it by a scale factor…
The document raises a teaching question about the apparent mismatch in subtracting half the squared standard deviation from a rate when estimating geometric growth. It notes the familiar approximation that geometric mean return equals arithmetic mean return…
The document asks whether no-arbitrage conditions are known for Bachelier, or normal, implied volatility surfaces. Normal volatility is defined through the parameter that reproduces an option price under the Bachelier formula. The author contrasts this with…
The document compares practical considerations for stochastic-volatility and GARCH option models, emphasizing that model choice depends on the option type and the goal. It argues that GARCH can be attractive because its next-step conditional volatility is…
The document surveys practical considerations for options with expiries ranging from hours to minutes. It cautions that very short-horizon returns should not be assumed to follow a lognormal process simply because the horizon is short. Instead, intraday…