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The document examines a change-of-measure density for an asset with constant dividend yield, whose price follows a geometric Brownian motion under the physical measure. It solves the price process and substitutes that expression into a proposed density,…

The document explains dual delta as the sensitivity of an option’s value to its strike, distinguishing it from ordinary delta, which measures sensitivity to the underlying price. In the Black–Scholes–Merton framework, call dual delta is negative and relates…

The document asks whether annualized Sharpe ratios for separate years are enough to calculate a Sharpe ratio across the full period. It explains that, in general, they are not: the ratios alone do not specify the return means, volatilities, or dependence…

The document derives Black–Scholes prices for two contingent claims under geometric Brownian motion. The first pays the positive part of the difference between the stock price at maturity and its price at an earlier observation date. Conditioning on the…

The document poses a portfolio insurance problem in which an investor trades a stock and holds the remainder in a zero-interest bank account at a finite set of dates. The stock is modeled as geometric Brownian motion, and the objective is to choose stock…

The document discusses how bid-ask spreads affect a minimum-variance portfolio of stock and options. It argues that transaction costs can shift the efficient frontier and change the optimal portfolio. For small trades, it offers an approximation based on the…

The document explains the cash-flow interpretation of a vanilla interest rate swap when its fixed rate is negative. In the example, the fixed-rate payer pays a negative fixed amount and receives the floating Euribor leg. A negative fixed payment means that…

The document raises a general problem in numerical optimization: an algorithm's output may not be the global maximum or minimum, especially when the objective is difficult and the search begins from an initial vector. It frames the issue using an…

This document describes an R function for simulating multivariate constant conditional correlation GARCH processes. It distinguishes the original CCC model, where ARCH and GARCH parameter matrices are diagonal, from an extended version that permits full…

The document asks whether a forward Libor rate remains a martingale at intermediate times under the forward measure associated with its payment date. The accepted response applies the tower property of conditional expectation: if the rate is a martingale…

The document outlines a proposed historical equity backtest that starts with a total-market portfolio weighted by free-float market capitalization in a chosen year. It would then track that initial set of holdings over later years, reinvesting dividends…

The document presents a Python workflow for fitting a SABR volatility smile with QuantLib. The example supplies option strikes and implied volatilities, constructs a NoArbSabrInterpolatedSmileSection, sets initial values for alpha, beta, nu, and rho, and…

The document explains the options phrase “buy back a short strike” as purchasing an option previously sold, thereby closing that short position. The example describes placing an order to buy it back for five cents per contract, with a good-till-canceled…

The document derives the stochastic dynamics of a forward rate from the risk-neutral dynamics of zero-coupon bond prices. It first defines the instantaneous forward rate as the negative maturity derivative of the log bond price, then uses the…

The document describes a local volatility pricing implementation that derives volatility from an SSVI implied volatility surface using Dupire's formula and finite differences. The author checks the implementation by repricing the vanilla options used to…

The document considers how to choose two strategy parameters from an in-sample grid using Sharpe ratio, Sortino ratio, and maximum drawdown. Its central lesson is to assess the pattern across nearby parameter settings rather than automatically selecting the…

The document concerns numerical evaluation of the integral used to price a call option under the Heston stochastic volatility model. The question asks whether Simpson’s rule or Gauss–Legendre quadrature is suitable and seeks MATLAB or Scilab implementations.…

The document distinguishes the efficient market hypothesis (EMH) from the random walk hypothesis (RWH). EMH describes prices incorporating available information continuously; RWH says price changes are not predictable and follow a random walk. A random walk…

Index futures can trade while the constituent stocks are closed because their prices reflect changing expectations about where the index would trade if the cash market were open. News and developments abroad continue to arrive overnight, and traders use…

The discussion examines whether option-adjusted spread can support comparisons among bonds with embedded options, plain bonds, and floating-rate instruments, and whether a plain bond’s OAS matches its Z-spread. It also asks whether an OAS curve can help…

The post studies option pricing under a time-dependent Heston model in which mean reversion changes across time intervals while other listed parameters are held fixed. It compares prices from an Elice method and two Monte Carlo approaches, Milstein and…

The interview question asks what can drive a bond’s daily profit and loss after excluding carry, price changes, and interest-rate changes. The responses frame it as a conceptual prompt that tests whether a candidate can identify and organize relevant…

The post asks how to maximize a portfolio return metric computed by a large R function with one bounded input parameter. The parameter is restricted to a range from 1.0 to 1.5, starts at 1.25, and only needs precision to increments of 0.05. The author…

The document distinguishes detecting a bond’s richening or cheapening from estimating its fair value. A regression of daily price changes against related securities can accumulate residuals that show relative moves, but those moves alone cannot tell whether…