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The document asks whether GARCH(1,1) parameters can be updated as each new price arrives, without rerunning the full estimation. Its answer is that maximum likelihood estimates depend on the full likelihood across observations. Because the GARCH recursion…

The document asks whether options on two separate assets, each quoted against a common currency, can create an option on their exchange ratio. Its answer says that a portfolio with payoff equal to the sum of a function of each asset separately cannot…

The document explains Bloomberg's fixed-equivalent yield for a floating-rate bond. The method first treats the bond's floating coupon payments as if they were exchanged for synthetic fixed payments at a rate available in the swap market. It then calculates…

The document asks whether daily open, close, high, and low prices for thousands of US-listed stocks can be downloaded in one low-cost bulk file, without querying each symbol separately. The responses suggest using Python's Pandas DataReader to retrieve…

The document explains why the hedge quantity for an FX option can differ from its standard Black–Scholes spot delta when the option premium is received or paid in the foreign currency. The premium itself already provides exposure to that currency, so the…

The document considers how to calculate investment performance when capital is added to or withdrawn from an account during the measurement period. A simple comparison of ending balance with starting balance can misstate strategy performance because it…

The document distinguishes the value of an un-margined forward from the daily cash flows of a marked-to-market futures contract. For a forward, the change in the comparable forward price represents a payoff at maturity; the value before maturity is that…

The document considers whether a numeric library should parallelize operations by default, using large financial data workloads as its setting. Its answer recommends making thread use configurable at runtime and through environment variables, while choosing…

The document introduces the maximum diversification portfolio objective, defined as the weighted sum of asset volatilities divided by portfolio volatility. The numerator uses asset weights and individual volatilities; the denominator depends on the…

The document explains two ways to calculate an annual return from daily prices: compute the simple return over a date interval, or compound each daily return by multiplying one plus each return and subtracting one. It also mentions log price differences as a…

The document clarifies how Itô’s lemma evaluates the stochastic integral of Brownian motion against itself. Taking the function of time and state as the square of the state, and evaluating it at Brownian motion, gives the process W squared. Itô’s lemma then…

The document explains two ways to think about probability distributions for foreign-exchange prices. For a distribution implied by traded options, it describes the risk-neutral density: butterfly spreads across strikes convey information about probabilities…

The document addresses three conceptual questions about the Vasicek and extended Vasicek term-structure models: why a zero-coupon bond is worth one unit at maturity, why bond prices may be written in an exponential affine form, and what the market price of…

The document answers a question about research on synthetic options, including their valuation and time decay. It distinguishes simple synthetic positions, such as a synthetic long stock, from more elaborate synthetic structures designed to replicate complex…

The document explains how to simulate a down-and-in barrier call under a local volatility model. At each simulation step, the volatility should be evaluated at the current time and stock level, rather than at the option’s fixed strike and maturity. The…

The note uses gold forward prices at two maturities to illustrate a carry-based arbitrage. If the later contract is priced above the earlier contract adjusted for financing and storage-related carry, a trader can buy the earlier exposure and sell the later…

The note distinguishes the roles of the ARMA and GARCH components in a return model used for directional trading. The ARMA conditional mean supplies the expected return and therefore drives a rule that goes long or short according to the forecast sign. GARCH…

The note discusses financial entropy through the lens of market efficiency and predictability, rather than treating money as a direct substitute for heat or information in physical entropy equations. It points to approximate entropy, introduced by Pincus, as…

The note explains why a jump-diffusion model may not have a unique risk-neutral measure, contrasting it with a one-stock geometric Brownian motion model. Its central intuition counts the independent sources of risk against the traded assets: Brownian shocks…

The discussion addresses how to calculate Sharpe ratios for historical portfolios and compare them with figures published by fund companies or financial portals. It asks which risk-free rate to use and how to align return and volatility calculations. The…

The discussion examines a four-step binomial valuation of a European put on a stock that moves by a fixed amount each month, with a continuously compounded risk-free rate. The proposed method recursively discounts the risk-neutral expected option payoff at…

The discussion diagnoses a municipal bond yield calculation that differs substantially from a listed yield. The bond schedule and day-count setup are shown, but the key issue is the coupon input convention: QuantLib expects rates in decimal form rather than…

The discussion asks whether an asset is equally likely to trend or range and whether that likelihood can be calculated. The answer distinguishes trend from volatility and suggests that expected return, implied volatility, and the Sharpe ratio can help…

The document describes a repeated after-hours stock price pattern observed before earnings announcements: a sharp decline shortly after the regular close, a rapid reversal above the closing price, and a second drop back toward the close before the earnings…