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.
10,263 documents
The document examines a deep out-of-the-money call whose quoted market price implies far more volatility than the data provider reports. Recalculating implied volatility with an American-option model gives a value in the vicinity of 150%, while the provider…
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 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 differentiate Value-at-Risk and Conditional Value-at-Risk for a capped random variable, formed by taking the minimum of a random variable and a threshold. It does not derive the sensitivity or specify assumptions about the…
The document explains how to infer expected policy-rate changes from an overnight indexed swap curve when a market lacks meeting-date futures. The proposed approach builds a curve whose nodes fall on policy decision effective dates, with overnight forward…
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 explains how IMM dates are applied to interest-rate swap periods and related fixing dates. For swaps, periods begin and end on the third Wednesday of each quarter, adjusted to the following business day when necessary. These adjusted dates…
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 discussion explains why a fair die’s physical outcome probabilities do not, by themselves, determine the risk-neutral probabilities. Risk-neutral probabilities are inferred from traded prices and payoffs, so a price process and the available securities…
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 asks what market variable should serve as the input to a variance-covariance matrix for a portfolio of credit derivatives such as credit default swaps. The answer recommends basing risk statistics on observable market quantities. For traded…
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 explains why swaps manually priced from a QuantLib curve may fail to reproduce the market quotes used to build that curve. In the example, the discrepancies arise because the manually constructed swaps do not exactly match the swap rate helpers’…
The document addresses how to obtain bond prices for calibrating a Hull–White interest-rate model when historical yields are available but historical prices are needed. It points to public, machine-readable reporting of some EU bond quotes and trades…
The document describes a question about extending a Vasicek short-rate simulation to the Hull–White model. It first presents the exact one-step normal transition for a constant-parameter Vasicek process: the conditional mean reverts toward a fixed long-run…
The document compares fair strikes for two LIBOR contracts that reference the same rate fixed at the first maturity but pay at different dates. It derives each strike from discounted expected payoff under the bank account numeraire, then uses a change to the…
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 asks whether factor volatilities in the multi-factor Heath–Jarrow–Morton framework may be negative. It notes that the drift expression uses products of volatility functions, then reports a reference that explicitly assumes these functions are…
The document explains how to price a LIBOR cash flow fixed at time T and paid at T plus a tenor period. It addresses which numéraire is appropriate for changing from the risk-neutral measure and whether that change remains valid when the accrual period has…
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 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:…