คลังความรู้

The document corrects a proposed method for estimating a lower-tail portfolio return threshold using a Student-t distribution. It explains that the standard deviation of observed returns should not be divided by the square root of the sample size when…

The document explains how to simplify a maximum-and-minimum expression involving two ordered strikes and a terminal asset price. One proof divides the possible price outcomes into three regions: below the lower strike, between the strikes, and above the…

The document distinguishes conventional interest-rate policy from quantitative easing. A central bank typically sets a short-term policy or interbank rate, while QE involves buying assets such as government bonds. When short rates are already near zero,…

The document asks why a single-look CMS cap and a CMS floor with the same expiry and at-the-money strike can show different vega exposures. The observation comes from pricing a ten-year-expiry CMS30 cap and comparing it with the corresponding floor. The…

The document poses a research question about whether the choice of volatility model can predict Value at Risk backtest outcomes in advance. It asks whether a GARCH-based VaR forecast, for example, should be more likely than an ARCH or unconditional forecast…

This short discussion addresses whether monthly CAPM returns should use prices recorded at the start or end of each month. It describes the common practice of calculating simple returns from consecutive month-end closing prices, or log returns from the ratio…

This discussion explains why two present-value calculations for a semiannual coupon bond can differ: the cash-flow dates and the rate's compounding convention must use consistent time units. It contrasts discounting each half-year payment by successive…

The document explains a first-pass way to approximate a payer swaption’s profit and loss for a move in the underlying swap rate: use a Taylor expansion. Delta represents sensitivity to a parallel shift in the swap curve, while gamma captures convexity. This…

The document presents an attempt to calculate the tangency portfolio for five risky Dow stocks and a risk-free asset using weekly simple returns over ten years. It supplies estimated asset returns, a covariance matrix, and its inverse, then applies a…

The document raises a risk-management problem for a vanilla option that terminates if realized volatility over the option’s life exceeds a preset barrier. Such a condition could reduce the option’s price, but it also makes the payoff depend on the path of…

The document asks whether a two-factor Hull–White short-rate model, also called G2++, can represent swaption volatility smiles or skews, and whether fitting it to out-of-the-money swaptions would help. The answer points to local- and stochastic-volatility…

The document addresses unstable numerical integration in Heston option pricing, where an oscillatory or slowly decaying integrand can produce negative computed prices, especially for deep out-of-the-money options. A recommended first remedy is the Little…

The question concerns estimating how a multi-day event affects volatility in one-minute equity returns, where extreme observations challenge normal-error ARCH and GARCH specifications. The response recommends matching the conditional error distribution to…

The document explains how a Lévy process such as variance gamma, NIG, or CGMY can be time-changed by the integrated rate of a mean-reverting CIR process. This produces a stochastic volatility Lévy process: the clock remains nonnegative and increasing, but…

In swaption quoting conventions, a volatility surface is often arranged with option expiry increasing down the first column and the maturity of the underlying swap increasing across the top row. Under that layout, the upper-left region represents options…

The document considers an Asian-style payoff equal to the square of the time average of an asset following geometric Brownian motion under risk-neutral dynamics. It asks whether the discounted conditional expectation has a closed-form value, noting that the…

The document poses a modeling question about extending the static private-information setup in Kyle’s market-microstructure model to continuous time. It describes the information signal as a normally distributed value plus an independent normally distributed…

The document clarifies why dividing a semiannual coupon by the actual number of calendar days in a coupon period does not calculate accrued interest under a 30/360 convention. That approach uses actual dates and actual period length, resembling an…

The document explains how to price a European claim that depends on the asset price at maturity in a recombining binomial model. Starting from the terminal payoff, it works backward through the tree, taking conditional expectations under risk-neutral…

The document poses a stochastic-process question about a process that starts above zero, drifts downward at a constant rate, and has volatility proportional to its current level while positive. Once it reaches zero, it is held there. The central questions…

The document derives the hedging error that arises when a call is priced with Black–Scholes implied volatility but the underlying stock realizes a different volatility. The option price satisfies the Black–Scholes partial differential equation using the…

The document raises a fixed-income question about why discount factors for the same maturity and market date differ when one is reported using LIBOR conventions and another using continuous compounding. It cites two tables from a reference text and notes…

The document explains why a callable bond’s Z-spread may not map cleanly to a unique price. The call option makes the bond’s value depend on whether and when the issuer exercises, and that decision is affected by both risk-free rates and credit spreads.…

The document resolves a portfolio valuation question by clarifying the option position’s direction. A portfolio holding shares plus a long call includes the call’s positive value; a portfolio that has sold the call must subtract the liability represented by…