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 answer explains why multiplying a volatility estimate by a factor close to one can correct bias in a first-exit-time volatility calculation. It distinguishes the unbiased sample variance from the sample standard deviation: taking the square root of an…
The exchange discusses estimating an option’s future price after a specified move in its underlying when future implied volatility is unknown. One approach is to make explicit assumptions about both the underlying price change and the change in implied…
The document asks how to compute a Scale of Market Shocks measure that combines volatility estimates across multiple time horizons. Its integral is taken with respect to the logarithm of the horizon, so numerical integration should use log-horizon…
The document addresses a reported difference in output from FIGARCH estimation: one specification displays coefficients and inferential statistics, while another displays only coefficients. The accepted response explains that the latter estimation did not…
The document describes a question about calibrating a local volatility surface through an inverse problem. It outlines a representation that uses B-splines across one dimension and linear interpolation across time, then penalizes variation in time and…
The procedure estimates an at-the-money implied volatility for a target maturity by using two listed option expirations that bracket it. It first selects nearby call and put strikes, estimates a forward price for each expiration from put–call parity, and…
The document raises a pricing question about a down-and-out call when the underlying follows a jump process, with the Kou double-exponential and normal inverse Gaussian models suggested to represent asymmetric jumps. It considers raw Monte Carlo simulation…
The document poses a question about constructing a risk-neutral density from out-of-the-money options. Since the density is related to the second derivative of option price with respect to strike, it asks whether convexity of option prices is needed to…
The document explains why an FX option’s delta convention must match the convention used to build a volatility smile or surface. It lists spot and forward delta, each with premium-adjusted and unadjusted forms, and notes that converting between conventions…
The note addresses whether Black–Scholes prices a call and a put equally when their strikes are equally far from the current underlying price in opposite directions. It distinguishes terminal payoffs from option values before expiry. At expiry, if the…
The document explains the combined payoff of a long up-and-in put and a short up-and-in call with the same strike, maturity, and barrier. If the underlying reaches the barrier before expiry, both options activate and behave like vanilla options. Put-call…
The document asks whether financial institutions use GARCH models in risk systems that calculate expected shortfall. It cites a practical primer by an author whose listed affiliations include a bank, as an example of practitioner-oriented discussion. The…
The document explains why option traders sometimes treat theta as a proxy for gamma, focusing on a delta-neutral portfolio. It uses the Black–Scholes differential equation to relate portfolio time decay, delta, gamma, interest rates, and the underlying…
The document examines the Black–Scholes risk-neutral drift relation and asks whether its negative volatility adjustment conflicts with the observation that higher interest rates can coincide with falling stock prices. The replies explain that the relation…
The document asks whether an implied volatility surface can be used to calculate options strategy P&L and variance swap P&L when individual option prices are unavailable. The response says a surface can support these calculations if its construction…
The document describes a volatility pattern in monthly electricity futures that changes as the delivery month progresses. Because electricity is delivered throughout the month, the contract price converges toward the monthly average as delivery unfolds. The…
The document explains why a call option on a basket of stocks is commonly described as having positive exposure to correlation. A basket’s value depends on the combined returns of its constituents, so its distribution is more complicated than the…
The document asks whether investors can isolate jump risk premia in a way that variance swaps isolate variance risk premia. It describes gap-risk contracts as a practical analogue: an over-the-counter swap or exposure embedded in a structured note, based on…
The document outlines the historical VIX methodology and distinguishes two changes to the index. In 2003, the underlying shifted from S&P 100 options to S&P 500 options, and the calculation moved from implied volatility to a variance-swap approach. In 2014,…
The document asks whether selecting the least expensive option at successive expiries can reveal an asset's most likely price path. The answers explain that option prices can be used to infer risk-neutral distributions of terminal prices at fixed maturities.…
The document asks how to tell whether an estimated correlation between two assets is stable over time, and whether the relationship is meaningfully linear. It describes a rolling correlation estimate and an ad hoc stability rule based on the largest recent…
The discussion distinguishes geometric-average and arithmetic-average Asian options under the Heston stochastic volatility model. It reports that a closed-form pricing formula is available for the geometric Asian option, while an analogous closed form is not…
The document explains why a caplet whose payoff is fixed and paid on the LIBOR fixing date is more involved than one paid at the end of the underlying accrual period. For the latter, the forward rate is modeled as a martingale under the matching maturity…
The document presents a proposed closed-form value for a convertible bond under a two-factor setup involving the stock price and a Vasicek-like interest-rate factor. The cited response expresses the value in a Black-style form, using the stock price, a…