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The document addresses the reverse of the familiar covered interest arbitrage example in which a forward exchange rate is too high. Its GBP/USD illustration explains that when the quoted forward is below the rate implied by covered interest parity, an…
The document explains the distinction between extreme price changes and jumps in a stochastic price path. A lognormal distribution can assign low probability to very large price changes over a time interval, but that does not mean the model’s path jumps…
The document explains how to describe and assess a roll between Treasury futures delivery months. The quoted market roll is the front contract price minus the back contract price, expressed in thirty-seconds. A theoretical comparison starts with the fair…
The document examines why a single simulated geometric Brownian motion path with zero drift can produce a maximum likelihood drift estimate far from zero. It defines log returns and gives the likelihood setup used to estimate drift and volatility, then…
The document describes a portfolio-construction approach that substitutes a connectedness matrix for the covariance matrix and active returns for expected returns within a mean-variance optimization framework. The matrix is built from pairwise dependence…
The document explains why realized volatility used to evaluate forecasts is not directly observable. Researchers must choose a proxy, such as one derived from returns, and recognize that the resulting measure depends on assumptions about prices, sampling,…
The document asks how to represent bracket orders in a Python backtester. A bracket consists of an entry order linked to child exit orders, typically a stop loss and a take profit, with one exit canceling the other after execution. The response recommends…
The document asks how to choose portfolio objectives for investors with different risk preferences. It questions whether the Sharpe ratio suits a risk-neutral investor and whether replacing standard deviation in its denominator with value at risk or…
The document examines an Ornstein–Uhlenbeck process whose drift targets a level equal to the process’s limiting variance. It asks whether that apparent relationship is mathematically consistent, using a process with positive mean-reversion speed, constant…
The document asks for a detailed introduction to stochastic calculus for Poisson and other jump processes, including random intensities and jump sizes. It notes that standard derivative-pricing texts tend to emphasize Brownian motion, with jump-diffusion…
The document considers estimating hedge ratios for spreads between Treasury futures when historical DV01 data are unavailable. It describes empirical DV01 as an estimate from a regression of futures price changes against changes in the yield of the…
The document discusses how to organize historical equity data so backtests can handle delistings, acquisitions, ticker changes, dividends, and splits. One proposed design assigns stable internal identifiers to companies and separately tracks stock series and…
The document describes an attempt to calibrate the two-factor G2++ interest-rate model to cap volatility quotes using QuantLib's Python interface. The example builds a yield curve, creates cap helpers from maturities and volatility inputs, sets an…
The document compares traditional asset-class risk premia with factor investing and alternative risk premia (ARPs). It frames factors as return sources within established markets, such as equity value, size, momentum, and quality, which may have different…
The document addresses a discrepancy between historical stock prices shown in a finance website interface and values in its downloadable data. The example shows an apparent inconsistency between daily high and low values and the displayed close, alongside…
The document explains why swap valuation may require separate discounting and forward curves, and why the appropriate forward curve depends on the floating rate index in a swap. For a vanilla swap, the curve built from the most liquid swap quotes and futures…
The document explains the source of a one-half term in a Fourier-based option-pricing derivation. It gives the Gil-Pelaez inversion formula, which relates an integral involving the real part of a characteristic function to the probability that the terminal…
The document examines why an option’s expected payoff cannot simply be discounted at the risk-free rate under the real-world probability distribution. The underlying asset is risky too, and its expected growth rate is uncertain and potentially dependent on…
The document describes a fixed-risk position-sizing approach used in spread betting. The trader chooses a fraction of account equity to risk, measures the distance between entry and stop in points or pips, and divides the cash risk allowance by that distance…
The document asks whether actively trading bonds could produce returns comparable to some equity strategies, given that bond returns are often associated with coupon income while equity returns include price appreciation. Its answer frames the question…
The document considers whether antithetic variates must produce a positive Monte Carlo estimate for a European call when every payoff from the original simulated draws is zero. The answer is no: pairing each draw with its antithetic counterpart does not…
The document distinguishes the real-world probability measure P from the risk-neutral measure Q and explains their roles in research and pricing. P is used to describe outcome probabilities and expected returns, while Q offers a convenient way to price cash…
The document explains how to read regression coefficients in the Carhart four-factor model. A significant positive or negative coefficient indicates that a portfolio’s returns have a corresponding relationship with a factor after accounting for the other…
The document describes a market quotation for a one-year at-the-money straddle on the difference between the ten-year and two-year constant maturity swap rates. The quoted bid and offer are given as prices in percentage terms, rather than as an implied…