নলেজ লাইব্রেরি

The discussion examines whether a displayed bid at or below a stop price can trigger a stop order. One reply says a trade at the trigger level is generally required, rather than merely submitting a low bid. It gives a hypothetical sequence in which a market…

A constant maturity swap rate is the par swap rate for a chosen tenor, observed on each reset date. A CMS leg therefore references a swap rate such as the ten-year rate even when payments reset more frequently. In a CMS swap, that rate may be exchanged for a…

The discussion explains why a long-short portfolio can have a higher market beta than a long-only portfolio. Scaling exposure to the market scales beta, while short positions can offset some of that exposure. The example compares a portfolio beta of 0.5 with…

The post asks whether the volatility of a stock portfolio can be compared with the volatility of the S&P 500 when one is calculated from constituent volatilities and correlations and the other from observed index returns. The accepted answer says the direct…

The post asks how a trader should adjust a volatility surface when pricing a product that includes a long option. The answer describes shifting the parameters of a chosen surface model in absolute terms, with adjustments reflecting the trader’s exposure to…

The post points readers seeking a C# implementation of the Barone-Adesi-Whaley option pricing model to QLNet, a C# port of QuantLib. It identifies the library’s pricing engine as a place to find a native implementation, offering a practical route for someone…

The document describes reducing the pricing of a fixed-strike Asian call to a partial differential equation in time and a transformed state variable. The state variable tracks the remaining strike after accounting for the average accumulated so far, scaled…

The document examines how an option’s theta changes as time passes, sometimes described as theta acceleration. It distinguishes the textbook Black–Scholes theta from a finite-difference estimate obtained by repricing after a one-day time shift. Comparing…

The document presents a Markowitz-style mean-CVaR portfolio optimization setup. It defines scenario losses from portfolio returns, uses a confidence level to form CVaR, and balances expected return against tail risk with a risk preference parameter. The…

The document disentangles the delta of a forward contract’s value from the sensitivity of a quoted forward or futures price. The value of an existing forward contract has spot delta of one when other inputs are held fixed. The forward delivery price, by…

The document examines negative carry claims for long positions in short-maturity Treasury note futures, including the two-year contract. It distinguishes cash bond carry from futures roll return: futures themselves do not have carry in the same sense as…

The document clarifies what is a martingale under a forward measure and whether clean or dirty bond prices qualify. A bond price alone is not generally a martingale under the T-forward measure; the relevant martingale is the asset price expressed relative to…

The document explains why a Monte Carlo estimate for an up-and-out call can be too high when simulated paths use discrete time steps. A path may cross the barrier between sampled points and return below it before the next observation, so checking only the…

This note considers how to estimate value-at-risk for a stock-and-bond portfolio when one stock has only a short post-IPO return history. It raises two possible workarounds: bootstrap the stock's observed returns to create a longer series, or substitute…

This note describes the gap between theoretical online portfolio selection (OLPS) models and live implementation. It points to assumptions often used in research, such as no transaction fees or market impact, ample liquidity, and the ability to trade…

This note examines how a buy limit order priced above a sell limit order may execute when both reach an empty book. It explains that the matching outcome depends on event sequencing at the venue and on the national best bid and offer (NBBO). In the example,…

The discussion considers back-testing a portfolio of individual stocks intended to track an equity index or ETF. It emphasizes that matching constituent trades alone is insufficient: a faithful simulation must reproduce the index’s rules, rebalance timing,…

The note explains the second pass of a linear beta-pricing model. First, estimate each asset’s market beta from a time-series regression of its excess returns on the market’s excess return. Then use the estimated betas as independent variables in a…

The question asks how to model high-frequency asset returns with a Student-t distribution after estimating two-scale realized volatility, and how to annualize the result and choose a sampling frequency. The response focuses on degrees-of-freedom estimation…

Time and sales feeds can include prices far from the displayed best bid or offer. Such prints may reflect special trade conditions, including out-of-sequence trades or crosses, rather than ordinary executions that should immediately update an algorithm’s P&L…

The document considers a price series that begins and ends at the same level and asks whether its arithmetic mean of log returns must be zero. The answer says yes, extending the claim to ordinary returns as well. The intuition is that the net change across…

The document gathers advice for a mathematician with statistics and programming experience who wants to enter quantitative finance without first joining a hedge fund. It recommends exploring quant roles at banks or in academia, building relationships with…

The document explains the net basis in a Treasury cash bond and futures trade, addressing why it may be negative even though it is associated with delivery options. A negative reading does not by itself establish an arbitrage opportunity: funding constraints…

The document asks whether performance statistics such as profit factor and Sharpe ratio should be computed for each leg of a pairs trade separately or for the combined position. Its example shows that the measured profit factor differs depending on whether…