คลังความรู้

The document explains how to convert an annual effective interest rate into a rate for a shorter period, in the context of using an interbank rate as a proxy for the monthly risk-free rate. It gives compounding-based conversions for monthly and quarterly…

The document examines how changing the shift in a SABR model affects recalibrated parameters and swaption sensitivities. It describes experiments that fit shifted SABR to a constructed volatility set, first freeing correlation and volatility of volatility,…

The document asks how to calculate a stock’s annual return when shares are bought at different times during the year. A simple beginning-to-end portfolio return works when the position is unchanged, but a midyear purchase adds cash flow that should not be…

The document outlines a proposed backtest of a receiver swaption under a one-factor Hull–White or Gaussian Markov HJM framework. It describes forward rates in Musiela form, relates continuously compounded yields to average forward rates, and gives an…

The document gives a concise reason quadratic variation matters in quantitative finance: Brownian motion has nonzero quadratic variation, whereas a continuously differentiable path has zero quadratic variation. Because Brownian motion is a central model for…

The document clarifies the difference between a portfolio’s payoff at maturity and its price when established. A proposed structure combines European puts at two strikes with a European call at a higher strike. Evaluating the payoff formula at a particular…

The document explains how the semi-variance HAR model (SHAR) extends the heterogeneous autoregressive model of realized volatility to represent asymmetric effects of past returns. It splits the daily realized variance into positive and negative…

The document explains how exercise of a call option on a futures contract creates a futures position whose mark-to-market depends on its entry price. Because futures settle daily, the delivered position is treated as entered at the most recent settlement…

The document distinguishes maximum drawdown, measured from a running portfolio-value peak to a subsequent trough, from a longest run of negative returns. A drawdown can remain unrecovered at the end of the sample; recovery is tracked separately. The answer…

The document raises preprocessing choices for modeling exchange-rate data. It asks whether rates quoted against different currencies should be converted to a common base currency, illustrating how a missing cross rate can be derived from two available rates.…

The document addresses how to estimate a portfolio’s beta when some holdings, such as recently listed companies, lack enough historical returns for reliable individual beta estimates. It considers estimating beta by regressing portfolio returns on index…

The response clarifies that a forward rate agreement, a caplet or floorlet, and an option on an FRA are different instruments. A caplet and a floorlet on the same future LIBOR fixing have complementary single-period option payoffs and can approximately…

The document examines an interpretation of the Evans–Jovanovic model of entrepreneurship under borrowing constraints. In the stated setup, an entrepreneur chooses capital to maximize production income plus the return on wealth not invested in the business,…

The document outlines a QuantLibXL workflow for valuing a floating-rate bond whose cap and floor strikes vary by coupon. It recommends supplying a strike for each coupon to the floating-rate bond, then pricing the bond with a bond engine. An Ibor coupon…

The document explains that a long-short portfolio’s volatility and Sharpe ratio can be computed from its excess-return or profit-and-loss stream, as for other portfolios. First account for financing, including the difference between cash borrowing and…

The document asks for the distribution of the time integral of standard Brownian motion over an interval from t to T, and challenges an intuitive variance based only on the interval length. The answer rewrites the integral as a stochastic integral with…

The document describes how a trading algorithm might infer another participant’s behavior from changes in displayed order-book liquidity and response timing. In its example, a large bid is partly consumed; a second participant quickly removes the remaining…

The document presents a bond-based approach to creating exposure to a five-year-five-year forward rate. The proposed portfolio is short a five-year bond and long a ten-year bond, with relative weights determined using duration-based interest-rate…

The document considers when a current forward rate can be viewed as an unbiased indicator of a future spot rate. It cites the pure expectations hypothesis, under which forward rates predict future spot rates, and mentions weaker empirical support,…

The document explains how to convert a Treasury bond futures quote written in points and thirty-seconds into a percentage of par, then into a dollar contract value. In its example, the quote 91-12 means 91 plus twelve thirty-seconds, or 91.375 percent of…

The document explains why spoofing orders may avoid execution and what financial exposure remains for the trader. In the example, a large limit order is placed away from the current bid and ask to create pressure on prices, while the trader takes a position…

The document presents an attempted trinomial-tree implementation of an uncertain volatility model for pricing European calls between minimum and maximum volatility bounds. It lays out a backward-induction scheme, defines a discrete second-difference term…

The document develops a first-order approach to immunizing a bond portfolio against nonparallel interest-rate shifts. It approximates each bond’s price change by differentiating its discounted cash flows with respect to rates at each maturity, producing…

The document asks how to model changes in implied volatility when approximating an option portfolio’s profit and loss with delta, gamma, and vega terms. It distinguishes historical VaR, which can reprice a portfolio across observed market scenarios without…