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The document explains when European calls and puts with the same strike and maturity should have matching implied volatilities. Under put-call parity, their implied volatilities coincide at the at-the-money forward strike when the other pricing inputs are…
The document asks how large institutional stock sales affect prices over weeks, months, or years, including the lasting losses that other large holders might face. It raises questions about whether permanent impact relates to peak temporary impact, how…
The document considers whether two cointegrated price series can be combined into a stationary spread and modeled with an Ornstein-Uhlenbeck process. The proposed workflow estimates a hedge coefficient through regression, constructs the residual spread, and…
The document distinguishes securities by the assets behind them and by how investors receive repayment. Asset-backed securities represent claims on pools of non-mortgage loans, such as auto or credit-card debt, while mortgage-backed securities represent…
The document asks whether a forward price for a financial product can be expressed as its current price divided by the price of a zero-coupon bond maturing at the settlement date. The proposed argument uses a conditional expectation under the…
The document outlines several mechanisms that can produce negative autocorrelation in short-horizon returns. The classic explanation is bid-ask bounce: trades initiated by buyers and sellers alternate between ask and bid transaction prices, creating…
The document considers how to improve an Ornstein–Uhlenbeck model of EUR/USD when it understates large two-hour price ranges. The author has calibrated the process to historical mean, standard deviation, and total absolute variation, then explored adding…
The document derives a way to constrain a fund’s next weekly return so that its rolling five-year, annualized ex-post volatility is less likely to exceed a chosen threshold. It treats the historical weekly returns as fixed, assumes the next return is…
The document shows how to price a payoff of the form (S_T f(S_T))^+ by changing from the money-market numeraire to the stock numeraire. Starting with a risk-neutral geometric Brownian motion, it defines the new measure using the discounted stock as the…
The document describes how to enumerate every sequence of up, middle, and down moves in a trinomial tree. Its example uses recursive depth-first search: extend a partial path with each of the three moves until the desired number of steps is reached, then…
The document explains leptokurtosis as a return distribution with heavier tails than a normal distribution, which means extreme outcomes occur with greater probability. For investors, that can translate into a higher chance of unusually large gains or…
The document relates Merton’s structural credit model to European option payoffs. It models company asset value as a geometric Brownian motion and treats equity at maturity as a call on firm value with debt face value as the strike. Risky debt is represented…
The document explains the expiration profit and loss bounds for a collar, consisting of long stock, a long put, and a short call at a higher strike. At expiration, the call caps the position’s upside, while the put limits its downside. The stated maximum…
The document raises a portfolio optimization problem in which tracking error is constrained using a sample covariance matrix. It describes a case with 1,000 assets but only 60 monthly return observations, producing a covariance estimate that is not positive…
The document considers an option that pays the difference between two stock prices at maturity only if the first stock stays above the second throughout the option’s life. It presents a model-free replication argument: hold one share of the first stock and…
The answer demonstrates how a fixed-rate bond can be represented in QuantLib with an evaluation date, payment schedule, day-count convention, face amount, and coupon rates. The resulting cash-flow list contains coupon payments and the final principal…
The question concerns building an inflation-swap curve with QuantLib rate helpers and encountering an error because multiple instruments share a pillar date. The practical diagnostic is to inspect each helper’s pillar date, which is the date used as a curve…
The exchange addresses where to obtain financial and related company data for U.S.-listed firms, including balance sheets, income statements, cash flows, market information, and records relevant to bankruptcy, fraud, and governance. One answer points to a…
The discussion distinguishes contemporaneous factor models from forecasting models for portfolio optimization. In the Fama–French three-factor setup described, an asset’s return is related to factor returns from the same period. That relationship can help…
The document describes a proposed product paying a notional amount times the change in the spread between 30-year and 10-year Treasury yields. The response frames the hedge as exposure to two future yields, corresponding to the 10-year and 30-year points on…
The document examines how to interpret the stock and money-market components of a portfolio formed by holding a call and discounted cash equal to the strike. Under Black–Scholes assumptions, it combines the call price with the present value of the strike and…
The document asks whether initial nonstationarity in a simulated VAR series matters when estimating a copula with kernels. It describes an experiment in a cited paper using repeated series of length 1,024 and asks whether every observation, including early…
The document works through the expiry payoff of a position that buys a put, sells a call at a higher strike, and buys another call at a still higher strike. Ignoring premiums, the long put produces gains below its strike, the position is flat between the put…
The document explains a standard regression approach for estimating a portfolio’s CAPM alpha. It recommends calculating monthly excess returns for the portfolio and market, then regressing portfolio excess returns on market excess returns. The regression…