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The document derives the portfolio weights that maximize the Sharpe ratio for two risky assets with equal variances and a shared correlation, alongside a risk-free rate. It defines each asset’s excess return as its expected return minus the risk-free rate,…

The discussion suggests testing a Merton jump-diffusion model on broad equity benchmarks and their exchange-traded funds, naming the Nasdaq, S&P 500, Russell 2000, and examples such as QQQ, SPY, and IWM. It notes that these liquid benchmarks can help compare…

The document addresses how to simulate the terminal price of a geometric Brownian motion (GBM). It distinguishes the arithmetic mean and variance of the resulting lognormal price from the parameters required by a lognormal random-number generator, which are…

The document explains why a listed stock may have no daily price record even when the exchange is open. A stock does not necessarily trade each day: if no buyer or seller submits an order that leads to a transaction, there may be no new trade price from…

The document explains how to turn irregular stock trade ticks into a regular time series using previous-tick interpolation. One approach converts epoch milliseconds to POSIX time, creates a five-minute grid, and uses interval lookup to select the latest…

The document explains why a futures backtest needs to model the transition from an expiring contract to a later-dated contract. A price difference between those contracts is not itself a trading gain or loss: a live trader closes the expiring position and…

The document explains how to value a payoff based on the difference between a stock price at an intermediate date and its later price. It first clarifies that the stated payoff needs a positive-part operator to describe a put-like claim; under that…

The post questions a claim that puts are priced using historical volatility while calls use implied volatility, attributing the distinction to differences in liquidity. The reply challenges that framing: implied volatility is obtained by solving an…

The post considers how to compare profit factors across forex strategy runs when trades arrive in bursts. The author proposes treating nearby orders as one cluster and weighting each trade according to the number of subsequent orders within a short window. A…

The post asks how to construct a CNY interest-rate swap curve that matches Bloomberg, focusing on discount factors beyond the short end. The author reports converting maturities through nine months with an Actual/360 simple discount formula, then using…

The document asks how to apply Itô’s lemma to an option value modeled as a function of time and a stock price. The stock has a drift that pulls its level toward a parameter P at a rate set by omega, and its diffusion term is proportional to the stock price.…

The document asks whether option sellers should prefer very short expirations, where time decay is concentrated, or sell options with more time remaining. It uses an at-the-money straddle example to compare premiums at two expirations and observes that the…

The document works through pricing a claim that pays the cube root of the underlying asset at maturity. The asset is initially specified with mean-reverting drift and proportional diffusion, while a money-market account earns a constant rate. The proposed…

The document considers how to compare an at-the-money call with an out-of-the-money call when each has a different implied volatility. Its central point is that implied volatility is inferred from market prices through a pricing model, often one that assumes…

The document explains how to account for the parity ratio when using Black–Scholes to value a third-party warrant. Parity states how many warrants are needed to exercise the right to acquire one unit of the underlying. The answer converts the warrant price…

The document considers why a stock may show little price movement after an earnings announcement, including when the reported results appear favorable or unfavorable. It challenges the questioner’s suggestion that option sellers or market makers deliberately…

The document explains why Black–Scholes specifies a geometric Brownian motion (GBM) for the underlying even though option valuation is commonly expressed using risk-neutral probabilities. Its central point is that risk-neutral pricing does not remove the…

The answer explains how a very long time series can fail a stationarity test even when shorter sections pass. It uses two stationary sequences with different means as an illustration: joining them creates a series whose mean changes at the transition, so the…

The answer addresses how to assemble a symbol list covering common stocks listed on Nasdaq and other U.S. exchanges. It recommends obtaining the Nasdaq-listed and other-listed directory files, then merging and sorting them, rather than relying on the single…

The document distinguishes an ex ante return estimate based on assumed parameters from an ex post calculation using realized mean and risk. It gives a simple normal-distribution method for estimating the probability that a return falls below zero:…

The answer explains why local volatility (LV) can misprice double-no-touch options even though it produces random realized volatility along simulated paths. Each path integrates variance across the local volatility surface, so the realized volatility varies…

The document concerns the pricing of foreign-exchange options with American-style barriers. The question contrasts closed-form formulas for European barrier calls and puts with the apparent lack of comparable guidance for American barriers. The response…

The document clarifies a terminology difference between trading practice and academic writing. At trading desks, “hedging” is commonly used for constructing a portfolio that replicates a derivative’s payoff. Academic papers more often call the same idea…

The document describes why a trader or product issuer might use a forward-starting option instead of a standard option. Such an option’s strike is set at a future date, so it mainly exposes the holder to volatility after that strike-setting date. It may be a…