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 question about P&L attribution for a single stock option. It defines daily P&L as the change between desk market values and proposes explaining that change through underlying-price delta and gamma effects, implied-volatility vega, and…
The document asks how to close an in-the-money American put in a limited-margin IRA when the option has poor liquidity, uncovered options and short stock positions are prohibited, and exercising would forfeit remaining time value. It considers buying a…
The response explains why a volatility surface matters when pricing a Bermudan swaption, an option exercisable on specified dates. It first clarifies that a Bermudan contract need not be exercisable from the beginning of its life, then outlines a model-based…
This note explains how to connect a Black–Scholes call’s volatility sensitivity to the strike derivative used to price a cash-or-nothing digital option. It starts from the call price and its vega, then shows that the apparent mismatch between a term…
The discussion considers whether Markov chain Monte Carlo is useful for Bayesian inference in quantitative finance. It describes potential applications to estimating hidden-process parameters, including stochastic volatility models, and to inference for…
The exchange addresses how to obtain the underlying input needed to analyze an options dataset when spot prices are unavailable. It suggests estimating a forward price from put and call quotes at a common maturity: identify the strike where their prices are…
The document compares annualized return and volatility calculations based on logarithmic returns and simple returns. For monthly log returns, it describes scaling the mean by the number of periods in a year and scaling standard deviation by the square root…
The discussion examines why the variance sensitivity of a variance swap may seem inconsistent with the sensitivities of the options used to replicate it. Under assumptions of continuous paths and a continuum of strikes, the question treats the option…
The discussion distinguishes smoothing a price series from forecasting future values. It gives a recursive exponential-smoothing forecast in which the next estimate updates the current forecast in proportion to the latest observation's forecasting error.…
The discussion asks whether Bitcoin has a quantifiable fair value and how mispricing might be recognized. The answers describe its traded price as an outcome of supply and demand once the market is sufficiently liquid, while emphasizing that speculation is…
The document raises a practical calibration problem: fitting an SVI or SABR volatility surface to mid implied volatility produced a satisfactory fit, while separate fits to bid or ask implied volatility performed poorly. It asks how to fit surfaces to…
The document considers how to describe option risk across an implied volatility surface. Standard Black–Scholes Greeks measure sensitivity to model inputs, but Vega is difficult to aggregate across options because an implied volatility move need not be…
The document explains why a smile that bends down or up around the forward does not, by itself, establish whether option prices admit arbitrage. Smile curvature is related to the shape of the implied risk-neutral distribution: a concave smile can accompany a…
The document addresses whether Black-Scholes time to expiration should be measured in trading days or calendar days when volatility is estimated using trading-day data, and asks how the risk-free rate should be treated. One response advises keeping the time…
The document asks how market makers choose bid-ask spreads for options quoted in implied volatility terms. It gives an example of a quote with a one-point gap between bid and ask volatility, and suggests that market volatility and the need to hedge inventory…
The document asks how to price a European option on an amortizing interest-rate swap when market volatility quotes are available only for standard, non-amortizing swaptions. It outlines the usual Black-style swaption valuation using an annuity, forward swap…
The document collects suggested references for learning exotic option pricing and implementing pricing methods. The original question concerns volatility and variance swaps, jump diffusion, and explicit or implicit finite-difference methods, with particular…
The document discusses the inputs needed to price an FX option with a Black-Scholes style model when the trader has LIBOR quotes and historical exchange rates. One response suggests using the LIBOR rate nearest the option’s expiry, converting it to a…
The document examines whether a volatility surface for an inverse FX quote can be obtained by reversing call and put conventions around the at-the-money level. Its central explanation is that option delta depends on the currency used to measure the hedge. A…
The document explains how portfolio theory can be adapted when holdings and weights change over time. It describes dynamic optimization as repeatedly estimating allocations at scheduled rebalancing dates, using data available up to each date, rather than…
The document asks why volatility forecasts from an ARMA(1,1)-GARCH(1,1) model decline slightly over a multi-step forecast horizon. The displayed output shows the standard deviation estimates decreasing across successive forecast steps, while the questioner…
The document considers a GARCH(1,1) model fitted to the spread between two correlated assets. Although the reported coefficient estimates appear unremarkable, the standardized residuals show a bimodal distribution, prompting the question of whether such a…
The document asks how to approximate a down-and-out call price when the underlying follows the Heston stochastic-volatility model. It states the option payoff with a barrier condition, contrasts the problem with a Black–Scholes closed-form expression, and…
The document discusses using importance sampling to estimate prices for far out-of-the-money barrier options under local volatility. It describes changing the distribution of simulated inputs from the original density to a shifted normal density, then…