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20,364 dokumenter
The document examines a one-factor Hull–White short-rate simulation and explains why a one-year time step can produce poor paths. Euler–Maruyama approximates the drift over a step of length h and scales the random shock by the square root of h; the presented…
The discussion clarifies that a Sharpe ratio can be calculated for returns with any distribution, but comparisons become misleading when distributions differ in shape. Its example contrasts two two-outcome portfolios: one has consistently moderate excess…
The document presents an eGARCH(1,1) fit to weekly Bitcoin log returns over a multi-year sample, using a generalized error distribution and a date-related dummy variable. The broader research aim is to compare volatility dynamics across Bitcoin, Ethereum,…
The document considers replacing a diversified stock portfolio with long-dated calls on the same companies, keeping the same percentage allocation across names. It asks whether diversification carries over and what additional risks the options introduce. The…
The document describes a proposed EUR/USD forecasting workflow: take end-of-day closes, log-difference them to seek stationarity, fit an ARMA model using Box–Jenkins methods, inspect residuals, and use their assumed normal distribution to form cumulative…
The document asks how to choose a drift for simulating trading volume when pricing an option whose payoff depends on volume. The proposed model treats volume as geometric Brownian motion, and the author recognizes that option pricing calls for risk-neutral…
The discussion explains how to calculate each asset’s regression beta relative to a portfolio formed from weighted asset returns. In a simple regression, beta is the covariance of the dependent variable with the explanatory variable divided by the…
The question checks how to integrate the differential of a stochastic process multiplied by a time-dependent deterministic exponential over an interval. The response confirms the endpoint expression by rewriting the product with a transformed process: let…
This discussion derives the coefficient that minimizes variance when estimating an expectation with a control variate. For an adjusted estimator of the form X plus θ times the difference between the known mean of Y and Y, the constant mean contributes no…
The discussion points readers seeking variance and volatility swap strategies toward sell-side research and foundational papers. It frames relative-value trading as comparing implied variance across markets using historical relationships: buy the market that…
The document asks whether a quanto put can have a nonzero foreign-exchange delta, despite the common impression that quanto options are insensitive to FX. The question describes a case where the put’s calculated FX delta is positive and attributes this…
The document asks how to rank assets by variation in their daily trading ranges without relying on their average range. It proposes quadratic variation: take successive observations in the range series, calculate each change, square the changes, and sum…
The document compares the Yang–Zhang volatility estimator as presented in Euan Sinclair’s book with the implementation in the TTR package. It focuses on the open and close variance terms: the book’s displayed formulas use open-to-open and close-to-close…
The document addresses how to calculate the kurtosis of a straddle payoff formed by combining call and put outcomes. The response corrects an attempted combination rule: even if cross co-kurtosis terms are assumed to vanish, the weighted sum of the…
The document examines the meaning of the effective time length used to describe exponentially weighted covariance estimates. Its central explanation starts with a recursively smoothed scalar series, expands that recursion into geometrically declining weights…
The document explains why one-minute price-history downloads for different symbols can contain different numbers of observations, even when requested with identical settings and an assumed regular trading window. The key clue is the timestamps: the returned…
The document shows how to plot fitted conditional volatility together with forecasts from a GARCH(1,1) model in R. Its example uses the fGarch package to specify and simulate a normally distributed GARCH process, fit the model, and predict future conditional…
The document explains why an instantaneous forward rate is generally not the ordinary risk-neutral expectation of a future short rate when rates are stochastic. It corrects a derivation that differentiates the expected discount factor as though the result…
The document answers a request for accessible study resources on Monte Carlo simulation for pricing derivatives at roughly master’s level. It names a course text associated with a master’s degree and recommends Paul Glasserman’s book as another source on…
The document considers how a mathematically trained researcher can find publishable questions in financial mathematics, especially beyond algorithmic trading. Its answer cautions that identifying problems with academic value and broader economic or social…
The document explains how volatility inputs differ when an option expires before its underlying commodity forward settles. It distinguishes options on different forward contracts: a quote for a two-month option on a two-month contract should not…
The document considers whether EUR/USD returns can serve as the market benchmark when applying CAPM to Bitcoin returns. Its response treats Bitcoin as a currency for this purpose and suggests constructing a broader currency-market proxy by averaging returns…
The document examines whether random trading has zero expected value before transaction costs, focusing on passive limit orders. If an uninformed trader posts bids and offers without managing execution, informed counterparties may be more likely to trade…
The document discusses discretizing a Merton-style jump-diffusion process for simulation. Rather than applying a basic Euler step directly to the asset price, the accepted answer works with log price. Each interval adds the drift adjusted for diffusion, a…