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20,364 documente
The document explains how to extract a ten-year zero-coupon discount value from prices of two bonds with the same maturity but different coupon rates. Because the 8% coupon stream is exactly twice the 4% stream, subtracting twice the lower-coupon bond price…
The document explains why variance swaps can serve as vega hedges and distinguishes several meanings of vega. A variance swap has sensitivity to its variance strike; option vega may instead refer to sensitivity to a parallel volatility shift or to changes in…
The document shows how a Taylor approximation connects a variance swap expression to the correction term in the VIX variance formula. It begins with the logarithmic forward-to-reference-level ratio in the continuous-strike expression and rewrites the ratio…
The document explains CAPM equilibrium as a market-clearing condition: aggregate demand for securities matches their supply. Under the model’s assumptions, investors choose combinations of the risk-free asset and the market portfolio, with their allocation…
The document shows how a pair of European calls on the same underlying, with the same maturity, can imply an upper bound on the risk-free rate. The example uses a lower-strike call priced at 12 and a higher-strike call priced at 3, with strikes of 40 and 50…
The document considers whether the change in a company’s market capitalization over a fixed period can be adjusted using its average beta. The answer cautions that beta describes the covariance of returns with market returns, so there is no direct, generally…
The document asks whether practitioners commonly test the state and measurement noise assumptions in a linear Kalman filter, including whether the noise should be Gaussian. Its answer distinguishes the filter’s estimation objective from the stronger…
The document asks how to build a USD multi-curve setup for trading Fed Funds and Eurodollar futures, with Fed Funds and three-month LIBOR forecast curves. It compares discounting from an OIS curve based on effective Fed Funds with using the Interest on…
The document considers how to assess trading-signal performance across instruments, sectors, volatility levels, and combinations of market conditions, while managing a large number of possible segments. One response warns that increasingly fine-grained…
The document outlines a rolling-window procedure for comparing portfolios by out-of-sample variance. At each step, returns within a fixed estimation window are used to construct portfolios; the window then advances by one month, dropping the oldest…
The document derives a futures rate from the expected value of a money-market rate in a one-factor Heath–Jarrow–Morton framework. Using the bond-price dynamics, it obtains a convexity term expressed as an integral involving bond volatilities. The adjustment…
The post clarifies that marginal default probability, conditional default probability, and hazard rate describe related but distinct quantities. Over a time interval, marginal default probability is the unconditional probability that default occurs within…
The post asks how to solve the Black–Scholes heat-equation formulation for an up-and-out call. It contrasts the option's absorbing barrier condition with the vanilla call problem and the down-and-out case, where a reflection construction is suggested. The…
The post attempts to fit a log-periodic power-law model to Kuala Lumpur stock index closing levels from 1991–1994, treating price deviations as possible signs of bubbles and seeking to forecast a recession or crash. It uses a nonlinear least-squares routine…
The answer explains why the at-the-money caplet formula contains the forward rate for the accrual period. It assumes that this rate follows a lognormal process under the forward measure associated with the bond maturing at delivery. Discounting the expected…
The discussion separates the computational cost of option pricing from the difficulty of modeling market values. Under Black–Scholes–Merton assumptions, a European option has a closed-form price with little computational work. American options require…
The question concerns linking records for German companies listed in both Germany and the United States across datasets that identify securities with WKN and CUSIP codes. Matching company names and other record features can help, but the author asks whether…
The discussion distinguishes introductory portfolio theory from the more advanced subject of portfolio management. It recommends several books associated with portfolio management, while noting that these may be too advanced for a student whose course begins…
The document poses a portfolio performance question involving three assets held at the start, the later sale of one asset, and updated values for the two remaining holdings. It asks how to calculate the portfolio return over the full period, but provides no…
The document explains how to interpret return on investment when an investment loses money. It applies the standard formula, dividing the gain or loss by the initial cost, to an example in which an investment’s value falls from 24 to 2. The resulting ROI is…
The document asks whether a delta hedge that calls for a fractional share position should preserve the fractional quantity or round to a whole share. The accepted answer says to round in practice and characterizes the resulting hedge error as small relative…
The document asks how to assign an overall buy or sell direction to a complex order containing several options and a stock leg, and how to recognize an identical order versus one with every leg reversed. Its central lesson is that a structure’s direction…
The document describes a practical problem in calibrating a SABR volatility model: the fitted volatility smile differs substantially from implied volatilities observed for S&P index calls. The question identifies the market inputs needed for the calibration,…
The discussion surveys simple ways to project a company’s earnings from historical monthly data. Suggested starting points include plotting the series to inspect its behavior, fitting a log-linear trend, or applying an autoregressive model to a stationary…