คลังความรู้

The document explains how to recover the standard deviation of a normally distributed forecast from two interval quantiles. It uses an 80% interval and a point forecast as context, then presents the general quantile relationship: a normal quantile equals the…

The discussion considers how to estimate covariance when historical relationships may shift with observable conditions. Although framed around selecting a portfolio of athletes, its examples—player matchups and racing-track characteristics—illustrate why…

The document introduces Emanuel Derman’s volatility approximation for a volatility swap under an assumed linear volatility skew. It describes the approximation as assuming a linear put skew and a flat call skew, with applicability focused on strikes…

The document asks how to interpret dollar neutrality when a portfolio shorts an index ETF and uses the resulting proceeds to finance long-only holdings. The investor describes gross positions whose long exposure exceeds the short exposure, despite the short…

The document explores whether an option-implied risk-neutral distribution can be checked by integrating its density twice and comparing the reconstructed call prices with observed option prices. It grounds the idea in the Breeden-Litzenberger relationship,…

The document explains that a volume dimension specifies the unit used to report traded amounts. For equities, volume is commonly stated as a count of shares. For bonds, the relevant unit may instead be nominal value, which refers to the bond's face or par…

The document discusses how to simulate the SFGK continuous double auction limit order book model when the theoretical tick size approaches zero. The original question concerns Poisson order arrivals over an unbounded price line and how discrete price levels…

The document considers two different quantities involving the exponential of Brownian motion: a stochastic integral with respect to Brownian motion and an ordinary time integral. It applies Itō's isometry to the stochastic integral, reducing its second…

The document surveys ways to study relationships among time series, including covariance, correlation, principal component analysis, factor analysis, cointegration, information measures, graph theory, and clustering. Its central question is whether these…

The document raises a portfolio-theory question about whether including government bonds as an available asset makes the global minimum-variance portfolio an all-bond allocation. It connects this question to the efficient frontier: the global…

The document asks how Cover’s universal portfolio algorithm compares with two simple allocations: a constant-relative-proportions portfolio that rebalances to equal weights, and a buy-and-hold allocation that initially divides wealth equally across assets.…

The document explains why the relationship between the underlying price and future volatility can affect autocall valuation. Autocalls often include digital payoffs and barrier conditions, so their value depends on the chance that the underlying crosses a…

The document addresses a discrepancy between a calculated FX option delta and a market terminal’s value. The key clarification is that the instrument is a digital vanilla, or binary, option, so ordinary vanilla Black–Scholes delta inputs and intuition do not…

The document explains why the Ornstein–Uhlenbeck (OU) process is often used as an interest rate model. Its stationarity, Gaussian behavior, Markov property, and continuous-time formulation make analysis and pricing more tractable. These assumptions are…

This discussion asks how to generalize covariance and correlation when modeling dependence in heavy-tailed settings and extreme events. One response proposes mutual information, which quantifies how much observing one variable reduces uncertainty about…

This exchange explains why SVXY, a daily inverse VIX futures exposure, did not lose all its value during the sharp volatility episode of February 2018. The key distinction is between the VIX index, which is calculated from options and is not directly…

This exchange clarifies how to interpret labels in the triple barrier method. Each labeled instance corresponds to a specific trading circumstance and receives a single outcome according to which event closes it: an upper barrier win, a lower barrier loss,…

This exchange diagnoses why a Newton–Raphson routine for Black–Scholes implied volatility diverges. The original code divides the option-price error by gamma, but implied volatility is the quantity being solved for, so the derivative needed for the update is…

The document asks whether an option can have a strike that varies randomly over time and what such products are used for. The answers point to several related structures: an Asian option uses an average of the underlying over the contract period in its…

The document investigates why a return computed from a vendor’s adjusted closing prices differs from a hand-calculated dividend-inclusive return. The explanation focuses on the ex-dividend date: the investor’s daily return includes both the new share price…

The document considers how to simulate a variance process that can turn negative under a discretized stochastic volatility model with a variance-gamma jump term. Rather than forcing the jump component itself to be nonnegative, the answer presents ways to…

The document asks how risk-neutral pricing relates to the risk aversion assumed in expected utility theory. Its answer connects risk-neutral valuation to an assumption of complete markets and no arbitrage: under those conditions, a risk-neutral measure can…

The document explains how binary options differ from vanilla options. A binary contract pays a fixed amount or nothing at expiry, whereas a vanilla call’s payoff grows with the underlying above its strike. The binary’s capped payoff and risk profile can suit…

The document addresses how changes in a short-term interest rate’s yield volatility relate to price volatility, while questioning whether a proposed bond formula applies to a short-term interest rate option. The response gives the standard first-order…