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.
8,116 documents
The document explains why pricing models need dates converted into year fractions. In Black–Scholes or Monte Carlo pricing, an option’s pricing date and expiry must be expressed as a time to maturity using a day-count convention. Swaps can use different…
The document frames a choice between forecasting a stock basket’s correlation matrix with rolling-window Kendall’s tau or a generalized orthogonal APARCH(1,1) model. The motivating use is pricing options on a basket whose maturity defines the forecast…
The document explains how to calculate an option’s volatility-related P&L when a pricing model maps observed market implied volatilities into calibrated parameters and then into the volatility used for the instrument. By the chain rule, sensitivity to each…
The document asks whether one scalar can summarize an implied volatility smile for a single maturity. It considers ATM curvature, estimated from nearby implied volatilities, and proposes SABR’s volatility-of-volatility parameter alpha as a possible…
The document asks how to represent two-month and three-month maturities from a broker’s implied FX volatility delta-tenor table when using the Black–Scholes formula. It contrasts converting the tenor to a simple year fraction, such as months over twelve,…
The document asks how to reduce Monte Carlo pricing variance for a European call by using a second call with a nearby strike as a control variate. It specifies a stock model with normally distributed log returns and a call payoff, and notes that the second…
The document considers whether a covered-call seller should close a short out-of-the-money call after it has lost much of its value, then sell a call closer to the money. The proposed benefit is to collect additional premium as the short option’s delta and…
The discussion clarifies a comparison between two short call spreads that share a short lower-strike call but use different long-call strikes. Moving the protective long call farther out of the money can increase the credit received, but it also widens the…
The discussion distinguishes stochastic volatility from the leverage-like relationship that creates an asymmetric implied volatility skew. Random volatility by itself can make returns heavier-tailed than a single normal distribution and produce a roughly…
The document discusses a coding question about simulating asset prices in a Least Squares Monte Carlo (LSM) method. The question focuses on formulas used to calculate the conditional log-price mean and volatility at an earlier time step, and asks why the…
The discussion explains why a strategy that anticipates underlying price moves and seeks delta exposure may still lose money through vega. For European vanilla calls and puts with the same strike, put-call parity implies equal vega; holding equal and…
The discussion examines the claim that election probabilities should behave like binary option prices and that volatile forecasts violate no-arbitrage principles. The accepted answer challenges this analogy and the claimed volatility rules. It describes a…
The document interprets an American put valuation expression that integrates discounted exercise payoffs against the probability density of first reaching an exercise boundary. For a proposed exercise curve, the discounted payoff at each time is weighted by…
The document derives the price and hedge for a European call on a longer-maturity zero-coupon bond using two bonds as trading instruments. Under deterministic bond volatilities, the forward bond price is modeled as lognormal under the appropriate forward…
The document explains why owning shares matters when writing a call, even though the terminal mark-to-market loss on the short call is the same in isolation. A naked call seller must obtain shares at the market price to meet assignment, so rising prices…
The discussion addresses why a Monte Carlo estimate of a Bermudan option value can fall below the true value when continuation values and exercise decisions are estimated from simulated paths. The central explanation is the supremum-estimation effect:…
The explanation changes from the foreign risk-neutral measure to the domestic measure using a Radon–Nikodym density tied to the exchange rate and money market accounts. Girsanov’s theorem shifts the correlated Brownian motions, producing domestic-measure…
The document asks how to set the contingent payment for a pay-later option whose holder receives the call payoff when the underlying finishes above the strike and then pays a fixed amount. Because the holder pays nothing at inception, the answer treats the…
The document derives a positive exponent that makes the discounted negative power of a Black–Scholes stock price a martingale, as a step toward bounding the value of an American put. It rewrites the stock process using geometric Brownian motion and separates…
The document explains why the Black–Scholes delta hedge can have gains or losses when volatility changes, despite the model’s claim of a riskless hedge. The key distinction is that the theoretical result assumes geometric Brownian motion and continuous…
The document discusses consolidating options-on-futures data from Reuters and Bloomberg when the vendors may not share a usable identifier. It proposes constructing an internal key from the underlying contract, maturity or expiry date, put or call type, and…
The document addresses which implied volatility to use when converting a quoted option delta into a strike. Its guidance is to use the volatility associated with that particular delta, together with the other inputs required by the option-pricing…
The document separates two questions in multi-period value-at-risk scaling: when volatility grows with the square root of time, and whether a local Delta-Gamma approximation preserves that behavior. The scaling rule follows when portfolio profit and loss…
The document explains the intuition behind buying an option when its implied volatility appears lower than a forecast of realized volatility. A long option position has positive gamma: as the underlying rises, its delta increases and a trader can sell some…