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20,364 dokumentov
The document examines a chart of equity index implied skew and spot–volatility beta across option maturities. It describes implied skew as related to how implied volatility changes as the forward or spot level moves, while emphasizing that the relationship…
The document offers a concise way to extend a principal component analysis hedge-ratio method from two instruments to a basket with multiple legs. It proposes building the covariance matrix for the instruments, finding its eigenvectors, and selecting an…
The document explores how financial variables can be dependent without having linear correlation. It begins with the mathematical example of a normally distributed variable and its square, then considers financial analogies where the relationship can be…
The document examines how to interpret Value at Risk for equal long and short holdings in the same stock. It calculates separate position risks using the stated share count, price, daily volatility, and confidence multiplier, then asks how to combine them…
The document examines a formula attributed to a paper on learning-based derivative pricing. The question is how to interpret a 60-day range of daily returns when estimating volatility for Black–Scholes: if the sample standard deviation is already daily…
The document asks whether markets show a weekly activity pattern analogous to the intraday pattern in which trading is concentrated near the open and close. In particular, it considers whether Monday and Friday trading is heavier than activity midweek,…
The document compares a utility-based risk premium with the price of insurance. It defines the risk premium as the certain reduction in wealth that makes an investor indifferent to facing a zero-mean risk, and gives a small-risk approximation tied to the…
The document describes a cross-exchange futures pairs strategy involving products whose prices are expected to remain close. The trader enters one leg with a limit order and the other with a market order, aiming for price neutrality. The strategy’s signal is…
The document introduces Black–Scholes as a model for calculating a theoretical option price and asks how to interpret its d1 and d2 terms. The response says the model gives an appropriate price only if its assumptions hold. It does not explain d1 or d2…
The document describes a method for estimating an ETF’s implied funding or borrowing spread from option prices. It first adjusts American option prices toward European equivalents using the American–European price difference from a fitted volatility model.…
The document asks how to obtain daily SMB and HML data for real-time use in a Fama-French model. It points to the Ken French data library as a source for daily market, size, and value factor series, while noting that the library is updated with a delay of…
The document discusses fund-level risk measures for long-short equity portfolios, including volatility, risk-adjusted returns, drawdown, and long and short exposures. The answer adds market beta or correlation to an appropriate equity index and exposure to…
The document asks how to value commodity futures options when an investor has a specific view about the future return distribution: a substantial oil price spike is considered possible over a stated horizon, with the move expected to be brief. The goal is to…
The document presents a proposed explicit finite-difference method for a nonlinear Hamilton–Jacobi–Bellman equation with a terminal condition. The value function depends on time, a variance-like state, and a Vega state. The proposed grid uses a backward time…
The document proves that the process formed by subtracting a time-dependent linear term from the cube of Brownian motion has the conditional-expectation property of a martingale. It expands the later Brownian value around the value at the conditioning time,…
The document derives the optimal portfolio for a mean-variance objective with a full-investment constraint. It sets the first-order conditions, represents them as a block linear system, and applies block-matrix inversion to eliminate the Lagrange multiplier.…
The document describes an attempt to forecast a differenced FTSE 100 series with an ARMA mean model and GARCH disturbances using the rugarch package. The author encounters missing volatility forecasts when requesting rolling forecasts and a plotting error…
The note asks how to determine the time-dependent drift parameter in the one-factor Hull–White short-rate model when pricing zero-coupon bonds. It states the short-rate process as a mean-reverting rate with a time-varying drift and constant volatility, then…
The note considers a derivative paying an exponential function of a stock’s terminal price and asks whether a static portfolio of stock and a zero-coupon bond can guarantee at least that payoff. Such a portfolio has a payoff linear in the terminal stock…
The note explains how to interpret the units of DTS, defined as spread duration multiplied by the current credit spread. It starts from the approximate price change relation using spread duration and an absolute spread move, then rewrites the change in terms…
The document asks whether a weighted mixture of two local-volatility models can provide an implied density for path-dependent options, including barrier and touch products. It presents the mixture as a weighted average of the component models’ vanilla option…
This note explains how to interpret the mean-reversion parameter in the Vasicek and Cox–Ingersoll–Ross short-rate models. The parameter is not itself the instantaneous rate of change: the expected drift also depends on the gap between the current short rate…
The document explains how to take a short position in a synthetic instrument that can have a negative price, using spreads as examples. It lists calendar spreads, butterflies, and double butterflies, then gives a January–February calendar spread: the long…
The document considers how to estimate risk and correlation when one asset has far less price history than the rest of a portfolio. It outlines two approaches: exclude assets with histories too short for reliable estimation, or estimate their covariances…