নলেজ লাইব্রেরি

The document examines a potential domain issue in a paper on utility maximization in finite probability spaces. It describes a conjugate function defined for strictly positive arguments, then questions a later expression that evaluates the function at a…

The document derives an expression for the expected log return over a time interval under a local volatility stochastic differential equation. Applying Itô’s lemma gives a drift contribution and a negative half-variance contribution; the expected stochastic…

The document asks how to calculate the variance of a discounted European call or put payoff under the Black–Scholes assumptions. Its answer outlines a second-moment approach: variance equals the expected squared payoff minus the square of its expected value.…

The document frames interest rate modeling as a historical progression, listing equilibrium models such as Vasicek and CIR, no-arbitrage models such as Ho–Lee and Hull–White, multifactor models, the HJM framework, the Libor Market Model, and the Forward…

The document asks how to infer market expectations for a future central bank decision from overnight indexed swaps or short-term interest rate futures. It introduces an OIS relationship that equates the fixed leg’s accumulation with compounded daily…

The document investigates why zero rates bootstrapped from USD overnight indexed swap quotes in QuantLib differ from Bloomberg values. It presents a curve-building example and identifies several convention mismatches that can explain the discrepancy: the OIS…

The note considers which call strike to use when a trader expects realized volatility to exceed implied volatility and plans to delta hedge, aiming for gamma gains to outweigh option decay. It explains that the approximate gamma contribution to daily profit…

The document considers whether option pricing should distinguish upward from downward volatility. One response frames asymmetric volatility as a choice of a different underlying model, with risk-neutral pricing still used to value options. It suggests…

The document clarifies broad job terminology for research into fixed-income investment strategies. Index strategies aim to track a benchmark passively, while alpha strategies use an active systematic approach intended to outperform that benchmark. Momentum…

The document explains how to extend minimum-variance portfolio construction by adding a penalty on asset weights while keeping the weights summing to one. It notes that a convex penalty yields a convex optimization problem that can be solved numerically,…

The document explains why expected shortfall for the sum of two loss variables is no greater than the sum of their separate expected shortfalls. The key idea is that the worst observations for the combined portfolio generally differ from the worst…

The document asks what implied-volatility fitting error is acceptable for an equity-index surface calibrated with stochastic-volatility models such as Heston or SABR. The replies do not establish a universal tolerance. One practical suggestion is to compare…

The document answers a request for accessible textbook guidance on constructing factor-mimicking portfolios. It recommends CFA Level III study notes as a relatively plain-language source, specifically citing two volumes from an older edition. It also points…

The document considers how to allocate a fixed portfolio among four hedge funds when their returns are assumed independent and each fund has a purchase limit. It explains that zero correlations do not prevent mean-variance optimization: the covariance matrix…

The document asks whether a QuantLib term structure can use one interpolation style for the short end and another beyond a chosen maturity. The example is an overnight-indexed swap curve with flat, stepwise behavior around central-bank meeting dates,…

The document considers how to build a weighted index from several equity index series when their market calendars do not match. It identifies two basic approaches: restrict calculations to dates common to all series, or carry forward the previous available…

The document compares distributional choices for modeling interest rates, beginning with a proposed sequence of nonnegative independent observations. Responses caution that this assumption misses persistence and changing volatility: rates tend to cluster…

The document asks how a paper’s infinite-product representation of a pricing kernel relates to the familiar one-period stochastic discount factor and the change of measure from historical probabilities to risk-neutral probabilities. It outlines an affine…

The document asks whether bootstrap resampling should happen before strategy data mining or after a candidate strategy has been selected. It describes a monthly SPY and TLT rebalancing strategy tested over six years and 72 trades, reporting a backtest Sharpe…

The document addresses how to calculate earnings before tax in a financing model when a company earns interest on cash. It asks whether interest income should be added to EBIT alongside the subtraction of interest expense. The answer cautions that interest…

The document explains an event equality for a continuous Brownian motion starting below a level u. It compares paths that reach a higher threshold, 2u−d, after the first time they hit u with paths that reach that higher threshold at any time before T. Given…

The document discusses a lower-cost approach to storing and querying market tick and bar data when specialized financial databases are too expensive. The response suggests using an OLAP server with cube-based aggregation. It describes persisting ticks at…

The document explains why two derivatives for a two-asset portfolio's volatility differ when one asset's weight is constrained to equal one minus the other's. Roncalli's marginal risk contribution is a partial derivative: it varies one asset's weight while…

The document asks how to adapt a closed-form implied volatility estimator from a call option to a put. It presents an equation attributed to Hallerbach (2004) for estimating volatility from a call price, spot price, strike, and time to expiry. This makes the…